Mathematical Physics and String Theory
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(19.11.) Resurgence, BPS states, and quantum knot invariant

Marcos Marino (Geneva U.)

19.11.2020 at 16:15

Abstract: Resurgent analysis associates, to a perturbative series, a rich structure of exponentially small corrections (also known as trans-series) and a set of Stokes constants. Recent developments indicate that, in some cases, Stokes constants are integer numbers which count BPS states in an appropriate quantum theory. This gives a new mechanism for obtaining integer invariants from perturbative series. After reviewing some background material, I will focus on the resurgent structure of complex Chern-Simons theory. In this theory there is an infinite number of Stokes constants which lead to q-series with integer coefficients, and I relate them to BPS invariants of hyperbolic knots. State integrals and their holomorphic blocks, as well as the DGG index, play an important role in the story.

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