Constraining strongly coupled quantum field theories using symmetry

22 Jan 2026, 14:00 → 23 Jan 2026, 13:00 Europe/Rome

A fundamental challenge of the current era in theoretical physics is to understand and solve strongly coupled quantum field theories (QFTs). Meeting this challenge will necessitate a significant reformulation of the edifice of quantum field theory in which the foundations are symmetries and consistency conditions. In recent years enormous progress has been made in our understanding of QFTs based on these principles and it has become clear that many new fundamental results can be obtained in the near future. To do so it is essential to uncover the underlying organising principles by joining different facets rarely considered together. Combining cutting edge methods for the study of strongly coupled conformal field theories with the development of new techniques is the main goal of the project "Constraining strongly coupled quantum field theories using symmetry".

Thursday 22 January

14:30 → 15:30 Session 1: Agnese Bissi

Multiparticle states in CFTs

14:30 Multiparticle states in CFTs

Speaker: Agnese Bissi (Mathematical Institute, University of Oxford)

15:30 → 16:00 Coffee break

16:00 → 16:45 Session 2: Rudolfs Treilis

16:00 The magic of gauge theory: what beasts live on line operators?

By now extended operators have entered the parlance of the working theoretical physicist for well over a decade, playing an important role in areas as diverse as generalised symmetries, the study of confinement, branes in AdS/CFT correspondence and many more. In this talk we begin with a standard dogma - every operator needs to be gauge invariant - and find that it leads us to an interesting conclusion - there are far more local operators that can be defined on a line compared to empty space! We study these operators more carefully in the case of the 1/2 -BPS  line in N=4 theory for which we have fat more analytic control.

Speaker: Rudolfs TREILIS

16:45 → 17:30 Session 2: Andrea Mattiello

16:45 Lightcone Bootstrap for Multipoint Defect Correlators

We initiate a systematic study of multipoint defect correlators using the lightcone bootstrap, focusing on the simplest non-trivial example: a bulk–bulk–defect three-point function. We analyze the associated crossing equation, which relates the bulk and defect channels, in the lightcone kinematical regime where one bulk insertion approaches the lightcone of the other. In this limit, we derive a closed-form expression for the bulk conformal blocks in terms of a Lauricella function, while the defect conformal blocks are known. By studying the crossing equation in appropriate kinematical regimes, we identify the defect-channel spectrum required to reproduce the leading-twist bulk exchange. In addition to the familiar tower of transverse-twist defect operators, consistency of crossing demands the presence of a new family of mixed bulk–defect double-twist operators, whose twist equals the sum of the conformal dimensions of the external bulk and defect operators. Finally, we obtain a closed asymptotic expression for a particular combination of bulk-to-defect OPE coefficients.

Speaker: Mr Andrea Mattiello (Istituto Nazionale di Fisica Nucleare)

20:00 → 22:00 Social dinner

Friday 23 January

10:00 → 11:00 Session 1: Andrea Cavaglià

10:00 Wilson Line Defect in N=4 SYM: a Tale of Bootstrability

I will review a series of works exploring the combination of the numerical conformal bootstrap with data coming from integrability to study excitations of a Wilson line in N=4 SYM. I will discuss where the method works very well and where it meets some barriers, and ideas for future work that could help to overcome them.

Speaker: Andrea Cavaglià (Istituto Nazionale di Fisica Nucleare)

11:00 → 11:30 Coffee break

11:30 → 12:15 Session 2: Lorenzo Quintavalle

11:30 Explicit OPE, Conformal Blocks, and Casimir Operators for Virasoro CFTs

The Virasoro algebra has long played a central role in string theory and two-dimensional conformal field theory. It is therefore somewhat surprising that explicit expressions for several foundational objects have remained unknown for so long. In this talk, we present recent progress in this direction. By studying the inverse Shapovalov form (also known as the inverse Gram matrix), we derive explicit expressions for four key structures associated with the Virasoro algebra: the resolution of the identity, the operator product expansion, the Casimir operator, and the conformal blocks. The first three are expressed in terms of the algebra’s null vectors, while the conformal blocks are obtained as a new series expansion with fully explicit coefficients.

Speaker: Lorenzo Quintavalle (Università di Torino)

12:15 → 13:00 Session 2: Michele Savi

12:15 Algebraic Structures of Observables on the Wilson Line

Looking at observables on the Wilson line, we notice an enriched space of operators in contrast to the usual gauge invariant bulk operators built from traces. Focusing on N=4 SYM, where we can restrict our studies to the topological sector of a half-BPS Wilson line as to have just one adjoint valued scalar field to build operators with, we find a graded non-commutative non-freely generated ring structure. Even though the explicit construction is limited in its scope by computational constraints, it allows us to gather information that hints at universal properties of these observables.

Speaker: Michele Savi