Gromov-Witten Theory of $A_n$ type quiver varieties and Seiberg Duality

TL;DR

This paper proves the Seiberg duality conjecture for $A_n$ type quiver varieties, showing their Gromov-Witten theories are equivalent under quiver mutations, advancing understanding in mathematical physics and algebraic geometry.

Contribution

The paper establishes the Seiberg duality conjecture for $A_n$ quiver varieties, demonstrating the equivalence of their Gromov-Witten theories under quiver mutations.

Findings

Proof of Seiberg duality for $A_n$ quiver varieties

Equivalence of Gromov-Witten theories under quiver mutation

Validation of conjecture in a specific class of quiver varieties

Abstract

Seiberg duality conjecture asserts that the Gromov-Witten theories (Gauged Linear Sigma Models) of two quiver varieties related by quiver mutations are equal via variable change. In this work, we prove this conjecture for $A_n$ type quiver varieties.