This series consists of talks in the area of Quantum Fields and Strings.
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.
We consider conformal blocks of two heavy operators and an arbitrary number of light operators in a 1+1 dimensional CFT with large central charge. Using the monodromy method, these higher-point conformal blocks are shown to factorize into products of 4-point conformal blocks in the heavy-light limit for a class of OPE channels. This result is reproduced by considering suitable worldline configurations in the bulk conical defect geometry. We apply the CFT results to calculate the entanglement entropy of an arbitrary number of disjoint intervals for heavy states.
What natural CFT quantities can “see” in the interior of the bulk AdS in a diffeomorphism invariant way? And how can we use them to learn about the emergence of local bulk physics? Inspired by the Ryu-Takayanagi relation, we construct a class of simple non-local operators on both sides of the duality and demonstrate their equivalence. Integrals of free bulk fields along geodesics/minimal surfaces are dual to what we will call “OPE blocks”: Individual conformal family contributions to the OPE of local operators.
Painlevé equations can be obtained both from time-dependent classical Hamiltonian systems and from isomonodromic deformation problems. These realizations lead to a precise matching between Painlevé equations and Hitchin systems associated to four-dimensional N=2 SQCD as well as Argyres-Douglas theories. Long-time analysis of the Painlevé Hamiltonians dynamics allows to extract the unrefined "instanton" partition function for these theories at all strong-coupling points