Physics Seminar
Date: Tuesday, 17 September 2024
Time: 12.00 PM
Venue: Seminar Hall
Counting Black Holes as Algebraic Varieties
Sourav Maji
IIT Bhubaneswar.
17-09-24

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Abstract

We calculate the helicity trace index B_14 for N = 8 pure D-brane black holes using various techniques of computational algebraic geometry and find perfect agreement with the existing results in the literature. For these black holes, microstate counting is equivalent to finding the number of supersymmetric vacua of a multi-variable supersymmetric quantum mechanics which in turn is equivalent to solving a set of multi-variable polynomial equations modulo gauge symmetries. We explore four different techniques to solve a set of polynomial equations, namely Newton Polytopes, Homotopy continuation, Monodromy and Hilbert series. The first three methods rely on a mixture of symbolic and high precision numerics whereas the Hilbert series is symbolic and admit a gauge invariant analysis. Incorporating recent developments in algebraic geometry focusing on computational algorithms we present a new perspective for the black hole microstate counting problem.