Symmetries have frequently aided our study of physical systems. For conformally invariant quantum field theories there has been a lot of recent progress in what can be broadly described as "bootstrapping" these theories from their symmetries. I will review this progress and how it can be used to learn about strongly coupled theories, for which we often cannot rely on traditional perturbative methods, with a special focus on supersymmetric conformal field theories.
We investigate the structure of conformal Regge trajectories for the maximally supersymmetric (2,0) theories in six dimensions. The different conformal multiplets in a single superconformal multiplet must all have similarly-shaped Regge trajectories. We show that these super-descendant trajectories interact in interesting ways, leading to new constraints on their shape. For the four-point function of the stress tensor multiplet supersymmetry also softens the Regge behavior in some channels, and consequently we observe that 'analyticity in spin' holds for all spins greater than -3. All the physical operators in this correlator therefore lie on Regge trajectories and we describe an iterative scheme where the Lorentzian inversion formula can be used to bootstrap the four-point function. Some numerical experiments yield promising results, with OPE data approaching the numerical bootstrap results for all theories with rank greater than one.
We will motivate and introduce the study of conformal defects in superconformal field theories (SCFTs). We will show how symmetries constrain the anomaly coefficients of BPS defects. In the case of N=(2,2) surface defects in four-dimensional N=2 SCFTs these anomaly coefficients can be computed by studying a protected sub-sector captured by a two-dimensional chiral algebra.
We will motivate and introduce the study of conformal defects in superconformal field theories (SCFTs). We will show how symmetries constrain the anomaly coefficients of BPS defects. In the case of N=(2,2) surface defects in four-dimensional N=2 SCFTs these anomaly coefficients can be computed by studying a protected sub-sector captured by a two-dimensional chiral algebra.
In this talk, we will explore the relationship between non critical string theories, SU(2) supersymmetric gauge theories and WKB analysis. In particular, we will examine the role of Seiberg-Witten geometry in the context SU(2) of theories, and how this is related to the concept of string duality. We will examine the role of WKB analysis in solving the equations that come out in this context. We will focus on the physical interpretation of the various quantities that can be computed in WKB analysis, and how they can be related to observables in Seiberg-Witten theory or string theory. We will conclude by presenting the author's work on WKB analysis of finite difference equations, that naturally appear in this context.
We will illustrate the importance of the above concepts in known solutions of the Painlevé equations (tronquée and tritronquée phases). Furthermore, we will expand on the above solutions by introducing some specific characteristics of these equations like resonance, relations between Stokes constants.Then, we will expand on this by explaining a conjecture on the analytic form of these constants that has been checked with our numerical method up to very high precision. Finally, we will talk about possible future directions.
In these talks we will report the findings of our unpublished work on resurgent properties of the Painlevé I and II equations. These equations play a fundamental role in Minimal String Theories as the specific heat of 2D (Super)-Quantum Gravity. We will do a short introduction to the topic of resurgence and explain the role of Stokes constants when constructing solutions to these equations. While reviewing these tools, we will present our new method for numerically calculating these constants in very general setups to reasonably high precision.