MS Seminar (Mathematics - String Theory)

Speaker: Lotte Hollands (University of Amsterdam)
Title: Quantum Curves and D-Modules
Date: Thu, May 28, 2009, 15:30 - 17:00
Place: Seminar Room at IPMU Prefab. B
Abstract: String dualities show that topological string amplitudes as well as F-terms in supersymmetric gauge theories have a description in terms of free chiral fermions on a quantum curve. In this talk we start by reviewing the KP integrable hierarchy and its semi-classical interpretation in terms of conventional chiral fermions on holomorphic curves. We introduce a quantization of this system as a D-module and show that these are natural objects from a string theoretic point of view. Then we put forward a recipe to compute a quantum partition function starting from a D-module. In two examples in matrix models and gauge theory we check agreement with the well-known partition function.