Geometric Transitions and Open String Instantons

TL;DR

This paper explores a novel class of geometric transitions involving open string instanton corrections, demonstrating a precise match between open and closed string topological amplitudes through advanced enumerative and Chern-Simons techniques.

Contribution

It introduces and analyzes a new type of geometric transition with open string instanton effects, linking open and closed string amplitudes in a novel way.

Findings

Open string instanton corrections significantly affect Chern-Simons theory.

A precise correspondence between open and closed string amplitudes is established.

Enumerative techniques and Chern-Simons computations are effectively combined.

Abstract

We investigate the physical and mathematical structure of a new class of geometric transitions proposed by Aganagic and Vafa. The distinctive aspect of these transitions is the presence of open string instanton corrections to Chern-Simons theory. We find a precise match between open and closed string topological amplitudes applying a beautiful idea proposed by Witten some time ago. The closed string amplitudes are reproduced from an open string perspective as a result of a fascinating interplay of enumerative techniques and Chern-Simons computations.