In a groundbreaking advancement poised to redefine core principles in theoretical physics, researchers from Kyushu University and esteemed international collaborators have unveiled insights into the nature of continuous parameters within quantum gravity. This study challenges the long-standing assumption that such parameters are freely adjustable external inputs by demonstrating—under particular theoretical conditions—that they inherently originate from operators embedded within the physical theory itself. This resolution not only revitalizes Albert Einstein’s century-old assertion regarding the intrinsic completeness of physical laws but also propels forward our comprehensive understanding of the quantum structure of spacetime.
Central to this revelation is the concept of exactly marginal operators within the framework of conformal field theory (CFT), a pivotal branch of modern physics that explores systems invariant under scale transformations. CFT serves as a formidable bridge between quantum theory and gravitational physics, especially through the lens of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. This correspondence posits a deep equivalence between gravitational theories in a curved AdS spacetime and lower-dimensional CFTs residing at its boundary, rendering CFT an indispensable tool to probe quantum gravity’s elusive traits.
At the heart of the research lies the structure known as the conformal manifold—an abstract space parameterizing a continuous family of CFTs interconnected via exactly marginal deformations. These deformations represent operators that tweak a theory’s parameters without sacrificing its conformal symmetry. The pressing theoretical puzzle was whether the existence of such a manifold necessarily implies that continuous variations in the theory’s parameters emerge from operators already encoded within the theory, rather than arbitrary, external parameters appended to the formalism.
To rigorously examine this, the interdisciplinary team led by Associate Professor Yuya Kusuki embraced an innovative approach involving conformal interfaces, mathematical constructs that serve as boundary layers interpolating between two related CFTs situated on a conformal manifold. The researchers posited that as two nearby CFTs approach equivalence, the conformal interface connecting them should become trivial. Under the plausible assumption that certain correlation functions transition smoothly as this interface dissolves, they utilized the interface’s displacement operator—which quantifies the response of the interface to infinitesimal positional shifts—to reconstruct an exactly marginal operator governing motions on the manifold.
This reconstruction represents a monumental stride because it conclusively ties continuous parameters characterizing a family of theories not to arbitrary external dials but to concrete operators intrinsic to the theory’s internal dynamics. By examining the perturbative behavior of the conformal interface, the team effectively identified the fundamental origin of parameters that might otherwise have seemed freely tunable.
What does this imply for the broader quest of quantum gravity? Through the prism of AdS/CFT duality, the intimate relationship between conformal manifolds in CFT and the moduli space of vacua in quantum gravity theories becomes transparent. This newly established principle supports the profound conjecture that quantum gravity forbids arbitrary external parameters, with all continuous couplings traceable to internal degrees of freedom—a concept resonant with a widespread expectation but hitherto unproven with such clarity.
Importantly, the present findings apply specifically to two-dimensional CFTs, a fertile domain where theoretical control is well established. Nevertheless, the researchers have expressed optimism that their methods and conceptual revelations will motivate extensions to higher-dimensional CFTs and more general quantum gravity landscapes. Extending these results could illuminate the landscape of string theories and the parameters governing candidate quantum gravity models.
Moreover, these results have significant implications for the so-called “Swampland program,” a burgeoning field striving to delineate which consistent-looking effective field theories can be embedded into quantum gravity. By constraining continuous deformations to those generated by internal operators, this study offers fresh constraints on the space of viable theories and sharpens the boundaries between the “landscape” of consistent theories and the “swampland” of inconsistent ones.
The research underscores an increasingly vital notion: the parameters defining fundamental physics are not arbitrary selections but emergent phenomena anchored within the theory’s operator framework. This insight advances a vision in which the fabric of physical law is self-contained, avoiding unexplained fundamental constants, and aligning with Einstein’s aspiration for a theory without ad hoc inputs.
Led by Kusuki alongside collaborators Shota Komatsu of CERN, Marco Meineri from the University of Turin, and Hirosi Ooguri of the California Institute of Technology, the project utilized sophisticated computational simulations combined with analytic operator algebra techniques to bring these abstract mathematical objects into clearer physical focus.
Published in the prestigious journal Physical Review Letters on June 16, 2026, the paper titled “Continuous Family of Conformal Field Theories and Exactly Marginal Operators” delineates these technical breakthroughs and their broader theoretical implications, offering a compelling blueprint for future explorations in the intersection of quantum theory and gravity.
As the physics community absorbs the ramifications of this breakthrough, it heralds a renewed momentum for using conformal field theory and holographic dualities as guiding principles to unravel the enigmatic quantum nature of gravitation, spacetime, and the universe’s foundational constants.
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Subject of Research: Not applicable
Article Title: Continuous Family of Conformal Field Theories and Exactly Marginal Operators
Particle physics is the epitome of ‘big science’. To answer our most fundamental questions out about physics requires world class experiments that push the limits of whats technologically possible. Such incredible sophisticated experiments, like those at the LHC, require bigfacilities to make them possible, bigcollaborations to run them, big project planning to make dreams of new facilities a reality, and committees with big acronyms to decide what to build.
Enter the Particle Physics Project Prioritization Panel (aka P5) which is tasked with assessing the landscape of future projects and laying out a roadmap for the future of the field in the US. And because these large projects are inevitably an international endeavor, the report they released last week has a large impact on the global direction of the field. The report lays out a vision for the next decade of neutrino physics, cosmology, dark matter searches and future colliders.
P5 follows the community-wide brainstorming effort known as the Snowmass Process in which researchers from all areas of particle physics laid out a vision for the future. The Snowmass process led to a particle physics ‘wish list’, consisting of all the projects and research particle physicists would be excited to work on. The P5 process is the hard part, when this incredibly exciting and diverse research program has to be made to fit within realistic budget scenarios. Advocates for different projects and research areas had to make a case of what science their project could achieve and a detailed estimate of the costs. The panel then takes in all this input and makes a set of recommendations of how the budget should be allocated, what should projects be realized and what hopes are dashed. Though the panel only produces a set of recommendations, they are used quite extensively by the Department of Energy which actually allocates funding. If your favorite project is not endorsed by the report, its very unlikely to be funded.
The P5 report also created an awesome graphic that contains symbolism for the different aspects of the plan. The left side depicts oscillating neutrinos and the shape of the Higgs potential. The right side depicts dark matter and the large scale structure of the universe. The central ball of light is supposed to represent discoveries of the unknown. Source
Particle physics is an incredibly diverse field, covering sub-atomic to cosmic scales, so recommendations are divided up into several different areas. In this post I’ll cover the panel’s recommendations for neutrino physics and the cosmic frontier. Future colliders, perhaps the spiciest topic, will be covered in a follow up post.
The Future of Neutrino Physics
For those in the neutrino physics community all eyes were on the panels recommendations regarding the Deep Underground Neutrino Experiment (DUNE). DUNE is the US’s flagship particle physics experiment for the coming decade and aims to be the definitive worldwide neutrino experiment in the years to come. A high powered beam of neutrinos will be produced at Fermilab and sent 800 miles through the earth’s crust towards several large detectors placed in a mine in South Dakota. Its a much bigger project than previous neutrino experiments, unifying essentially the entire US community into a single collaboration.
DUNE is setup to produce world leading measurements of neutrino oscillations, the property by which neutrinos produced in one ‘flavor state’, (eg an electron-neutrino) gradually changes its state with sinusoidal probability (eg into a muon neutrino) as it propagates through space. This oscillation is made possible by a simple quantum mechanical weirdness: neutrino’s flavor state, whether it couples to electrons muons or taus, is not the same as its mass state. Neutrinos of a definite mass are therefore a mixture of the different flavors and visa versa.
Detailed measurements of this oscillation are the best way we know to determine several key neutrino properties. DUNE aims to finally pin down two crucial neutrino properties: their ‘mass ordering’, which will solidify how the different neutrino flavors and measured mass differences all fit together, and their ‘CP-violation’ which specifies whether neutrinos and their anti-matter counterparts behave the same or not. DUNE’s main competitor is the Hyper-Kamiokande experiment in Japan, another next-generation neutrino experiment with similar goals.
A depiction of the DUNE experiment. A high intensity proton beam at Fermilab is used to create a concentrated beam of neutrinos which are then sent through 800 miles of the Earth’s crust towards detectors placed deep underground South Dakota. Source
Construction of the DUNE experiment has been ongoing for several years and unfortunately has not been going quite as well as hoped. It has faced significant schedule delays and cost overruns. DUNE is now not expected to start taking data until 2031, significantly behind Hyper-Kamiokande’s projected 2027 start. These delays may lead to Hyper-K making these definitive neutrino measurements years before DUNE, which would be a significant blow to the experiment’s impact. This left many DUNE collaborators worried about its broad support from the community.
It came as a relief then when P5 report re-affirmed the strong science case for DUNE, calling it the “ultimate long baseline” neutrino experiment. The report strongly endorsed the completion of the first phase of DUNE. However, it recommended a pared-down version of its upgrade, advocating for an earlier beam upgrade in lieu of additional detectors. This re-imagined upgrade will still achieve the core physics goals of the original proposal with a significant cost savings. With this report, and news that the beleaguered underground cavern construction in South Dakota is now 90% complete, was certainly welcome holiday news to the neutrino community. This is also sets up a decade-long race between DUNE and Hyper-K to be the first to measure these key neutrino properties.
Cosmic Implications
While we normally think of particle physics as focused on the behavior of sub-atomic particles, its really about the study of fundamental forces and laws, no matter the method. This means that telescopes to study the oldest light in the universe, the Cosmic Microwave Background (CMB), fall into the same budget category as giant accelerators studying sub-atomic particles. Though the experiments in these two areas look very different, the questions they seek to answer are cross-cutting. Understanding how particles interact at very high energies helps us understand the earliest moments of the universe, when such particles were all interacting in a hot dense plasma. Likewise, by studying the these early moments of the universe and its large-scale evolution can tell us about what kinds of particles and forces are influencing its dynamics. When asking fundamental questions about the universe, one needs both the sharpest microscopes and the grandest panoramas possible.
The most prominent example of this blending of the smallest and largest scales in particle physics is dark matter. Some of our best evidence for dark matter comes analyzing the cosmic microwave background to determine how the primordial plasma behaved. These studies showed that some type of ‘cold’, matter that doesn’t interact with light, aka dark matter, was necessary to form the first clumps that eventually seeded the formation of galaxies. Without it, the universe would be much more soup-y and structureless than what we see to today.
The “cosmic web” galaxy clusters from the Millenium simulation. Measuring and understanding this web can tell us a lot about the fundamental constituents of the universe. Source
To determine what dark matter is then requires an attack from two fronts: design experiments here on earth attempting directly detect it, and further study its cosmic implications to look for more clues as to its properties.
The panel recommended next generation telescopes to study the CMB as a top priority. The so called ‘Stage 4’ CMB experiment would deploy telescopes in both the south pole and Chile’s Atacama desert to better characterize sources of atmospheric noise. The CMB has been studied extensively before, but the increased precision of CMS-S4 could shed light on mysteries like dark energy, dark matter, inflation, and the recent Hubble Tension. Given the past fruitfulness of these efforts, I think few doubted the science case for such a next generation experiment.
A mockup of one of the CMS-S4 telescopes which will be based in the Chilean desert. Note the person for scale on the right (source)
The P5 report recommended a suite of new dark matter experiments in the next decade, including the ‘ultimate’ liquid Xenon based dark matter search. Such an experiment would follow in the footsteps of massive noble gas experiments like LZ and XENONnT which have been hunting for a favored type of dark matter called WIMP’s for the last few decades. These experiments essentially build giant vats of liquid Xenon, carefully shield from any sources of external radiation, and look for signs of dark matter particles bumping into any of the Xenon atoms. The larger the vat of Xenon, the higher chance a dark matter particle will bump into something. Current generation experiments have ~7 tons of Xenon, and the next generation experiment would be even larger. The next generation aims to reach the so called ‘neutrino floor’, the point as which the experiments would be sensitive enough to observe astrophysical neutrinos bumping into the Xenon. Such neutrino interactions would look extremely similar to those of dark matter, and thus represent an unavoidable background which would signal the ultimate sensitivity of this type of experiment. WIMP’s could still be hiding in a basement below this neutrino floor, but finding them would be exceedingly difficult.
A photo of the current XENONnT experiment. This pristine cavity is then filled with liquid Xenon and closely monitored for signs of dark matter particles bumping into one of the Xenon atoms. Credit: XENON Collaboration
WIMP’s are not the only dark matter candidates in town, and recent years have also seen an explosion of interest in the broad range of dark matter possibilities, with axions being a prominent example. Other kinds of dark matter could have very different properties than WIMPs and have had much fewer dedicated experiments to search for them. There is ‘low hanging fruit’ to pluck in the way of relatively cheap experiments which can achieve world-leading sensitivity. Previously, these ‘table top’ sized experiments had a notoriously difficult time obtaining funding, as they were often crowded out of the budgets by the massive flagship projects. However, small experiments can be crucial to ensuring our best chance of dark matter discovery, as they fill in the blinds pots missed by the big projects.
The panel therefore recommended creating a new pool of funding set aside for these smaller scale projects. Allowing these smaller scale projects to flourish is important for the vibrancy and scientific diversity of the field, as the centralization of ‘big science’ projects can sometimes lead to unhealthy side effects. This specific recommendation also mirrors a broader trend of the report: to attempt to rebalance the budget portfolio to be spread more evenly and less dominated by the large projects.
A pie chart comparing the budget porfolio in 2023 (left) versus the projected budget in 2033 (right). Currently most of the budget is being taken up by the accelerator upgrades and cavern construction of DUNE, with some amount for the LHC upgrades. But by 2033 the panel recommends a much more equitable balance between different research area.
What Didn’t Make It
Any report like this comes with some tough choices. Budget realities mean not all projects can be funded. Besides the pairing down of some of DUNE’s upgrades, one of the biggest areas that was recommended against were ‘accessory experiments at the LHC’. In particular, MATHUSULA and the Forward Physics Facility were two experiments that proposed to build additional detectors near already existing LHC collision points to look for particles that may be missed by the current experiments. By building new detectors hundreds of meters away from the collision point, shielded by concrete and the earth, they can obtained unique sensitivity to ‘long lived’ particles capable of traversing such distances. These experiments would follow in the footsteps of the current FASER experiment, which is already producing impressive results.
While FASER found success as a relatively ‘cheap’ experiment, reusing detector components from and situating itself in a beam tunnel, these new proposals were asking for quite a bit more. The scale of these detectors would have required new caverns to be built, significantly increasing the cost. Given the cost and specialized purpose of these detectors, the panel recommended against their construction. These collaborations may now try to find ways to pare down their proposal so they can apply to the new small project portfolio.
Another major decision by the panel was to recommend against hosting a new Higgs factor collider in the US. But that will discussed more in a future post.
Conclusions
The P5 panel was faced with a difficult task, the total cost of all projects they were presented with was three times the budget. But they were able to craft a plan that continues the work of the previous decade, addresses current shortcomings and lays out an inspiring vision for the future. So far the community seems to be strongly rallying behind it. At time of writing, over 2700 community members from undergraduates to senior researchers have signed a petition endorsing the panels recommendations. This strong show of support will be key for turning these recommendations into actual funding, and hopefully lobbying congress to even increase funding so that more of this vision can be realized.
For those interested the full report as well as executive summaries of different areas can be found on the P5 website. Members of the US particle physics community are also encouraged to sign the petition endorsing the recommendations here.
And stayed tuned for part 2 of our coverage which will discuss the implications of the report on future colliders!
When students first learn quantum field theory, the mathematical language the underpins the behavior of elementary particles, they start with the simplest possible interaction you can write down : a particle with no spin and no charge scattering off another copy of itself. One then eventually moves on to the more complicated interactions that describe the behavior of fundamental particles of the Standard Model. They may quickly forget this simplified interaction as a unrealistic toy example, greatly simplified compared to the complexity the real world. Though most interactions that underpin particle physics are indeed quite a bit more complicated, nature does hold a special place for simplicity. This barebones interaction is predicted to occur in exactly one scenario : a Higgs boson scattering off itself. And one of the next big targets for particle physics is to try and observe it.
A Feynman diagram of the simplest possible interaction in quantum field theory, a spin-zero particle interacting with itself.
The Higgs is the only particle without spin in the Standard Model, and the only one that doesn’t carry any type of charge. So even though particles such as gluons can interact with other gluons, its never two of the same kind of gluons (the two interacting gluons will always carry different color charges). The Higgs is the only one that can have this ‘simplest’ form of self-interaction. Prominent theorist Nima Arkani-Hamed has said that the thought of observing this “simplest possible interaction in nature gives [him] goosebumps“.
But more than being interesting for its simplicity, this self-interaction of the Higgs underlies a crucial piece of the Standard Model: the story of how particles got their mass. The Standard Model tells us that the reason all fundamental particles have mass is their interaction with the Higgs field. Every particle’s mass is proportional to the strength of the Higgs field. The fact that particles have any mass at all is tied to the fact that the lowest energy state of the Higgs field is at a non-zero value. According to the Standard Model, early in the universe’s history when the temperature were much higher, the Higgs potential had a different shape, with its lowest energy state at field value of zero. At this point all the particles we know about were massless. As the universe cooled the shape of the Higgs potential morphed into a ‘wine bottle’ shape, and the Higgs field moved into the new minimum at non-zero value where it sits today. The symmetry of the initial state, in which the Higgs was at the center of its potential, was ‘spontaneously broken’ as its new minimum, at a location away from the center, breaks the rotation symmetry of the potential. Spontaneous symmetry breaking is a very deep theoretical idea that shows up not just in particle physics but in exotic phases of matter as well (eg superconductors).
A diagram showing the ‘unbroken’ Higgs potential in the very early universe (left) and the ‘wine bottle’ shape it has today (right). When the Higgs at the center of its potential it has a rotational symmetry, there are no preferred directions. But once it finds it new minimum that symmetry is broken. The Higgs now sits at a particular field value away from the center and a preferred direction exists in the system.
This fantastical story of how particle’s gained their masses, one of the crown jewels of the Standard Model, has not yet been confirmed experimentally. So far we have studied the Higgs’s interactions with other particles, and started to confirm the story that it couples to particles in proportion to their mass. But to confirm this story of symmetry breaking we will to need to study the shape of the Higgs’s potential, which we can probe only through its self-interactions. Many theories of physics beyond the Standard Model, particularly those that attempt explain how the universe ended up with so much matter and very little anti-matter, predict modifications to the shape of this potential, further strengthening the importance of this measurement.
Unfortunately observing the Higgs interacting with itself and thus measuring the shape of its potential will be no easy feat. The key way to observe the Higgs’s self-interaction is to look for a single Higgs boson splitting into two. Unfortunately in the Standard Model additional processes that can produce two Higgs bosons quantum mechanically interfere with the Higgs self interaction process which produces two Higgs bosons, leading to a reduced production rate. It is expected that a Higgs boson scattering off itself occurs around 1000 times less often than the already rare processes which produce a single Higgs boson. A few years ago it was projected that by the end of the LHC’s run (with 20 times more data collected than is available today), we may barely be able to observe the Higgs’s self-interaction by combining data from both the major experiments at the LHC (ATLAS and CMS).
Fortunately, thanks to sophisticated new data analysis techniques, LHC experimentalists are currently significantly outpacing the projected sensitivity. In particular, powerful new machine learning methods have allowed physicists to cut away background events mimicking the di-Higgs signal much more than was previously thought possible. Because each of the two Higgs bosons can decay in a variety of ways, the best sensitivity will be obtained by combining multiple different ‘channels’ targeting different decay modes. It is therefore going to take a village of experimentalists each working hard to improve the sensitivity in various different channels to produce the final measurement. However with the current data set, the sensitivity is still a factor of a few away from the Standard Model prediction. Any signs of this process are only expected to come after the LHC gets an upgrade to its collision rate a few years from now.
Current experimental limits on the simultaneous production of two Higgs bosons, a process sensitive to the Higgs’s self-interaction, from ATLAS (left) and CMS (right). The predicted rate from the Standard Model is shown in red in each plot while the current sensitivity is shown with the black lines. This process is searched for in a variety of different decay modes of the Higgs (various rows on each plot). The combined sensitivity across all decay modes for each experiment allows them currently to rule out the production of two Higgs bosons at 3-4 times the rate predicted by the Standard Model. With more data collected both experiments will gain sensitivity to the range predicted by the Standard Model.
While experimentalists will work as hard as they can to study this process at the LHC, to perform a precision measurement of it, and really confirm the ‘wine bottle’ shape of the potential, its likely a new collider will be needed. Studying this process in detail is one of the main motivations to build a new high energy collider, with the current leading candidates being an even bigger proton-proton collider to succeed the LHC or a new type of high energy muon collider.
A depiction of our current uncertainty on the shape of the Higgs potential (center), our expected uncertainty at the end of the LHC (top right) and the projected uncertainty a new muon collider could achieve (bottom right). The Standard Model expectation is the tan line and the brown band shows the experimental uncertainty. Adapted from Nathaniel Craig’s talkhere
The quest to study nature’s simplest interaction will likely span several decades. But this long journey gives particle physicists a roadmap for the future, and a treasure worth traveling great lengths for.
The introduction of quantum theory through the tree metaphor illustrates the observer effect emphasized in the double slit experiment. Wave-particle duality, de Broglie wavelength, and the role of observation in altering outcomes are key concepts. The deterministic pilot wave theory offers an alternative view, which includes the Creator of the universe.
There are various conspiracy theories claiming the Apollo Moon landing was faked, some citing a spoof video as evidence. I reference my personal experiences and testimonies from Apollo astronauts, emphasizing the authenticity of the Moon landing. I highlight the significance of eye witness statements in discerning historical truth.
I discuss the distinction between operational science, which relies on repeatable experiments, and historical science, particularly cosmology. While acknowledging the contributions of renowned scientists, I argue that cosmology lacks the capacity for experimental verification and is thus not true science, but science falsely so-called.
The concepts of heaven and cosmology, including the multiverse and parallel universes, are explored. I discuss differences between physical dimensions and the spiritual realm, critiquing string theory and advocating for a spiritual understanding of heaven as distinct from physical dimensions and laws.
Abstract Fermat’s Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book...
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