Quantum Fields and Strings

We study the eigenstate thermalization hypothesis in chaotic conformal field theories (CFTs) of arbitrary dimensions by computing the reduced density matrices of small size in energy eigenstates. We show that in the infinite volume limit this operator is well-approximated by a “universal” density matrix which is its projection to the primary operators that have nonzero thermal one-point functions. These operators in all two-dimensional CFTs and holographic higher-dimensional CFTs are the polynomials of stress tensor.

In this talk I will discuss a new use for conformal field theory crossing equation in the context of AdS/CFT:  the computation of loop amplitudes in AdS, dual to non-planar correlators in holographic CFTs. I will revisit this problem and the dual 1/N expansion of CFTs, in two independent ways. The first is to show how to explicitly solve the crossing equations to the first subleading order in 1/N^2, given a leading order solution. This is done as a systematic expansion in inverse powers of the spin, to all orders.

The moduli space of vacua of 3d N=4 gauge theories splits essentially into two ``branches”: the Higgs branch parametrised by the vevs of hypermultiplet scalars and the Coulomb branch parametrised by the vevs of dressed monopole operators. They can be described as complex algebraic varieties. I will present a new approach to the analysis of the Higgs and Coulomb branches based on the type IIB brane realisation of the gauge theory.

The past few years have seen a surge of interest in six-dimensional superconformal field theories (6D SCFTs). Notably, 6D SCFTs have recently been classified using F-theory, which relates these theories to elliptically-fibered Calabi-Yau manifolds. Classes of 6D SCFTs have remarkable connections to structures in group theory and therefore provide a physical link between two seemingly-unrelated mathematical objects. In this talk, we describe this link and speculate on its implications for future studies of 6D SCFTs.