(2023-05-30) Seminar: Boris Pioline -- Counting Calabi-Yau black holes with (mock) modular forms

Abstract  

Unlike in cases with maximal or half-maximal supersymmetry, the spectrum of supersymmetric black holes in type II string theory compactified on a Calabi-Yau threefold with generic SU(3) holonomy remains partially understood. Mathematically, the BPS indices counting these states coincide by the generalized Donaldson-Thomas invariants associated to the derived category of coherent sheaves, but they are rarely known explicitly. String dualities indicate that suitable generating series of rank 0 Donaldson-Thomas invariants counting D4-D2-D0 bound states should transform as vector-valued mock modular forms, in a very precise sense. I will spell out and test these predictions in the case of one-modulus compact Calabi-Yau manifolds (such as the quintic threefold), where the BPS indices can (at least in principle) be computed from Gopakumar-Vafa invariants, using recent mathematical results by S. Feyzbakhsh and R. Thomas.

Speaker

Prof. Boris Pioline is a theoretical physicist working on high energy physics, supergravity, string theory, black holes and topological strings as well as mathematical topics relevant to this kind of physics, automorphic forms, algebraic geometry, quaternionic geometry. He is working as a Professor at LPTHE, a theoretical physics lab affiliated to CNRS and Sorbonne Université.