This series consists of talks in the area of Quantum Fields and Strings.
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.
1. The notion of wall-crossing structure (as defined by Maxim Kontsevich and myself in arXiv: 1303.3253)
provides the universal framework for description of different types of wall-crossing formulas (e.g. Cecotti-Vafa in 2d or KSWCF in 4d). It also gives
a language and tools for proving algebraicity and analyticity of arising generating series (e.g. for BPS invariants).
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.
3d N=4 theories on the sphere have interesting supersymmetric sectors described by 1d QFTs and defined as the cohomology of a certain supercharge. One can define such a 1d sector for the Higgs branch or for the Coulomb branch. We study the Higgs branch case, meaning that the 1d QFT captures exact correlation functions of the Higgs branch operators of the 3d theory. The OPE of the 1d theory gives a star-product on the Higgs branch which encodes the data of these correlation functions.
The Sachdev-Ye-Kitaev model exhibits conformal invariance and a maximal Lyapunov exponent in the large-N and low temperature limit, and thus belongs to the same universality class as a two-dimensional anti-de Sitter black hole. Poles corresponding to a tower of operators that are bilinear in the microscopic Majorana fermions can be found in the four-point function of the fermions.
We will study the entanglement structure of states in Chern-Simons (CS) theory defined on n-copies of a torus. We will focus on states created by performing the path-integral of CS theory on special 3-manifolds, namely link complements of n-component links in S^3. The corresponding entanglement entropies provide new framing independent link-invariants. In U(1)_k CS theory, we will give a general formula for the entanglement entropy across a bi-partition of a generic n-link into sub-links.
I will discuss the coupling of non-relativistic field theories to curved spacetime, and develop a framework for analyzing the possible structure of non-relativistic (Lifshitz) scale anomalies using a cohomological formulation of the Wess-Zumino consistency condition. I will compare between cases with or without Galilean boost symmetry, and between cases with or without an equal time foliation of spacetime.
We study the effective twisted superpotential of 3d N=2 gauge theories compactified on a circle. This is a rich object which encodes much of the protected information in these theories. We review its properties, and survey some applications, including the algebra of Wilson loops, computation of supersymmetric partition functions on S^1 bundles, and the reduction of 3d dualities to two dimensions.
Abstract: We present the foundation for a holographic dictionary with depth perception. The dictionary consists of natural operators associated with CFT bilocals whose duals are simple, diffeomorphism-invariant bulk operators. These objects admit a description as fields in kinematic space, a phase space for such probes.
The space of causal diamonds recently brought to attention by de Boer et al. and Czech et al. provides an organizing principle for the dependence of entanglement entropy in conformal field theories on the spatial subregion considered. I will show that the inclusion relation of causal diamonds does not give rise to a consistent notion of a causal structure and thus does not provide an alternate metric on this space. I will also show that the entanglement entropy of ball shaped regions is not enough to reconstruct the areas of higher dimensional bulk surfaces in a static geometry.