Title and Abstract
Extremization principles and the entropy of supersymmetric black holes
I will discuss statistical properties of supersymmetric black holes in AdS and related extremization principles. In particular, I will show how the entropy of supersymmetric black holes in AdS_5 is obtained as a Legendre transformation of a suitably defined on-shell gravitational action. Moreover, I will discuss a microscopic interpretation of this on-shell action in terms of a generalization of the supersymmetric Casimir energy of the holographically dual N=1 SCFTs. More generally, I will argue that in the context of the AdS/CFT correspondence, it is natural to regard the “entropy functions” that govern the statistical properties of supersymmetric AdS black holes as instances of extremization principles, characterizing both SCFTs and a class of extremal problems in odd-dimensional Riemannian geometry underlying supersymmetric AdS solutions.
B-brane Transport in Anomalous Gauged Linear Sigma Models
Mapping of B-branes in SCFTs determined by the different phases of a non-anomalous gauged linear sigma model (GLSM) is a well established subject in physics and mathematics. From the point of view of the GLSM, a fundamental tool to determine such functors is the so-called grade restriction rule (GRR). When the axial R-symmetry is anomalous, this picture changes and determining the functors is not so simple. Some such cases are understood in physics and mathematics as well. In this talk I will present a GLSM approach to understand how the GRR must be modified for the anomalous cases, by using results in supersymmetric localization as a guide. I will illustrate this in simple cases, mainly Hirzebruch-Jung resolutions of A_n singularities.
Refined topological strings on compact Calabi-Yau spaces
Refined topological string theory is motivated by Omega background in supersymmetric gauge theory. Previous works consider only non-compact Calabi-Yau spaces. In this talk we discuss a class compact elliptic Calabi-Yau spaces and compare the results with geometric calculations. The talk is based on parts of a work in progress with S. Katz and A. Klemm.
ETH at large c and a scrambling phase transition in eigenstates
Two dimensional conformal field theories at large central charge are chaotic. Despite this seeming obstruction, recent developments have allowed us to identify how bulk physics in AdS_3, with all its inconsistencies, emerges from a precise piece of CFT correlation functions in the OPE expansion. I will overview some of these recent developments and describe how to characterize the thermal properties of pure black-hole microstates. Additionally, I discuss how well these pure states scramble information.