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

News Publication Date: 16-Jun-2026

Web References: Kyushu University Institute for Advanced Study, Kyushu University

References: Shota Komatsu, Yuya Kusuki, Marco Meineri, and Hirosi Ooguri, Physical Review Letters, 16 June 2026.

Image Credits: Yuya Kusuki/Kyushu University

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Keywords

Quantum Gravity, Conformal Field Theory, Exactly Marginal Operators, Conformal Manifold, Quantum Moduli Space, AdS/CFT Correspondence, Operator Reconstruction, Displacement Operator, Conformal Interface, Fundamental Constants, Theoretical Physics, Swampland Conjecture

Einstein’s equations have withstood every experimental test for more than a century. However, according to one philosopher, they have not withstood careful scrutiny of the language used to describe them.

Daryl Janzen, an astronomer and instructor at the University of Saskatchewan, recently published a philosophical challenge in The Conversation. Janzen’s critique does not question the mathematics but instead focuses on how physicists and philosophers describe the nature of space-time itself. He argues that over the past century, the language used to describe space-time has gradually merged two separate concepts into one.

Existence vs. Occurrence

The main focus of this argument is the idea of the “block universe.” In this view, also known as eternalism, space-time is a fixed, four-dimensional structure. All past, present, and future events are equally real within this block, according to this interpretation. Time does not flow, and there is no single present moment. The block contains everything that has ever occurred.

Janzen does not object to the geometry itself. His concern lies with the way the word “exists” is used in this context.

Janzen distinguishes between existence and occurrence. Objects exist because they endure through time. Events occur at a specific place and moment, and then they are over. For example, an elephant standing in a room exists. A cross-sectional snapshot of that elephant, representing a single instant removed from its timeline and frozen in place, does not exist in the same way; it only occurs.

In the block universe model, space-time holds every moment of the elephant’s existence as a four-dimensional world line. This world line shows the animal’s full path through space and time. A single cross-section, or one slice of that path, is not the elephant itself; it is only a record of what the elephant was doing at a certain moment. Janzen says the block is better understood as a representational framework rather than a physical object in the usual sense.

A Problem of When

This confusion leads to a fundamental problem. The entire block universe is said to exist, but it is unclear when it exists. A timeless structure that never unfolds cannot endure as the elephant endures from moment to moment. Meanwhile, if the whole block occurs at once, like a single flash, there is no internal experience of time that could be considered an illusion. 

To keep the sense of time passing in a block universe, the four-dimensional structure would need to endure in some sense. This would mean adding a fifth dimension, a second time axis outside the block, for the block itself to exist within; however, this extra axis is not part of Einstein’s original theory.

Janzen uses a simpler analogy. He compares the situation to describing a song that exists all at once, complete but unperformed. A song only becomes a song when it unfolds over time.

Austrian-British philosopher Ludwig Wittgenstein warned that philosophical problems arise when “language goes on holiday.” Janzen argues that physics has been in this situation for decades, reusing words such as “timeless,” “exist,” and “become” in technical senses without considering their everyday connotations.

Implications for Physics and Philosophy

One of the biggest unsolved problems in physics is how to bring together general relativity, which explains gravity and the large-scale universe, with quantum mechanics, which describes matter at the smallest scales. These two frameworks do not fit together, and every real attempt to unify them demands a clear definition of what space-time actually is.

If the language physicists use to describe space-time has been internally inconsistent for more than a century, Janzen suggests the resulting confusion may extend beyond philosophy. Clarifying what physicists mean when they talk about space-time could influence how researchers think about attempts to reconcile general relativity and quantum mechanics.

Janzen does not propose a replacement for the current framework but instead suggests that the fundamental question is not how space-time curves, but how to properly define them in the first place.

Austin Burgess is a writer and researcher with a background in sales, marketing, and data analytics. He holds an MBA, a Bachelor of Science in Business Administration, and a data analytics certification. His work focuses on breaking scientific developments, with an emphasis on emerging biology, cognitive neuroscience, and archaeological discoveries.

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