Workshop description

The study of two-dimensional conformal field theories (CFTs) on arbitrary Riemann surfaces is a rich and evolving subject, revealing nontrivial consistency constraints on dynamical data. A classic example is the torus, where modular invariance imposes strong constraints on the spectrum, famously encapsulated in Cardy’s formula for the high-energy density of states.

In recent years, there has been growing interest in extending these ideas to higher-dimensional CFTs placed on manifolds other than the flat space. Among these, the geometry S1×Sd-1 has emerged as particularly fruitful, in part because it enables the study of CFTs at finite temperature. It has been recognised that consistency of CFTs on S1×Sd-1, formalised by the notion of the thermal effective field theory, can be used to constrain asymptotic behaviour of high-energy CFT data in any number of spacetime dimensions. On the other hand, even in two-dimensional theories, sharper rigorous bounds on the spectrum have recently been obtained using methods of complex analysis.

In parallel to these asymptotic studies, various uses of correlation functions on S1×Sd-1 and other non-flat geometries are starting to be explored. These include a formulation of new crossing equations satisfied by the torus two-point functions and the partition function on higher-genus manifolds; relations between relevant conformal blocks and wavefunctions of the Hitchin integrable system; presence of bulk-cone singularities in correlators as signatures of holographic theories; as well as explicit computations in Ising and O(N) models leading to new CFT data.

The goal of this workshop is to bring together leading experts on the above topics, discuss the recent developments and chart the most promising future directions in studying conformal field theories on curved and topologically nontrivial spaces. The main focus will be on field-theoretic methods, but holographic approaches and the interplay between the two will also be included.