Gauged Witten Equation and Adiabatic Limit

Abstract

The gauged linear sigma model (GLSM) is a two-dimensional supersymmetric quantum field theory introduced by Witten. It has played important roles in many studies related to string theory and mirror symmetry by both mathematicians and physicists. In previous work, the authors have completed a mathematically rigorous construction of the correlation functions of the GLSM in geometric phase. In this article, we first review the construction. Then we explain how to use the adiabatic limit technique to prove a relation between the GLSM correlation function and the Gromov–Witten invariants. Such a relation provides an enumerative interpretation of the mirror map for certain Calabi–Yau manifolds such as the quintic.