Research at IPhT explores several aspects of quantum and conformal field theories (CFTs) in diverse dimensions. These include formal properties of the space and structure of CFTs, and applications to statistical physics, the AdS/CFT correspondence, and spectral problems in hyperbolic geometry. Technical tools include the conformal bootstrap, combinatorics, moduli space geometry, harmonic analysis, and random matrix theory.
Towards solving critical loop models
In the critical limit, statistical loop models give rise to two-dimensional CFTs whose understanding has long been a challenge. We are addressing this problem using numerical and analytic conformal bootstrap techniques. This has led us to a combinatorial description of the space of correlation functions, and to exact formulas for structure constants. We are also studying loop models from their lattice description, which gives rise to the Temperley-Lieb algebra and other diagram algebras.

Bootstrapping geometry
We are developing the interplay between harmonic analysis and CFT in general dimensions. This includes application of conformal bootstrap techniques to harmonic analysis on hyperbolic manifolds, yielding rigorous mathematical bounds on the spectra of differential operators, which in some cases are saturated by known manifolds to several digits of precision. Moreover, using the moduli space of principal bundles, we study geometrical objects that obey the bootstrap axioms and therefore describe correlation functions in two-dimensional CFT.

Conformal field theory, holography and black holes
Our work harnesses the holographic duality between CFTs and quantum gravity in anti-de Sitter space, both to derive fundamental constraints on quantum gravity, and to infer properties of CFTs at large central charge. This includes the study of CFT spectra and correlation functions, and properties of AdS black holes. As one example, we are developing a rigorous formalism, generalizing tools from random matrix theory and quantum chaos, for probing spectra of two-dimensional CFTs using harmonic analysis on the modular group. We are also exploring new types of non-local quantum field theories, with connections to QCD and integrability, with exactly solvable spectrum and correlation functions.

Superconformal field theory
We aim to chart the space of (super)conformal field theories in general dimensions. In four dimensional maximally-supersymmetric gauge theory, we aim to understand the consequences of non-perturbative S-duality symmetry for physical observables. In more than four dimensions, where known interacting CFTs are intrinsically strongly coupled, we study the singularity structure of the geometry of the moduli space of vacua, their complexity, and the non-trivial links between such high-dimensional theories and IR fixed points of certain three-dimensional gauge theories.
Scientific staff
Riccardo GUIDA
Sylvain RIBAULT
Dalimil MAZAC
Eric PERLMUTTER
Antoine BOURGET
Hubert SALEUR
Monica GUICA (en détachement)
Gregory KORCHEMSKY
Brando BELLAZZINI
Bertrand EYNARD
Chercheurs émérites et conseillers scientifiques
Kostov Ivan