Equivalence of Geometric Engineering and Hanany-Witten

TL;DR

This paper demonstrates the equivalence of three string theory realizations of gauge theories—Hanany-Witten branes, probe branes, and geometric engineering—using dualities, with examples in four-dimensional N=2 supersymmetric Yang-Mills theories.

Contribution

It establishes the equivalence of different string theory constructions of gauge theories through dualities, clarifying their interrelations.

Findings

Demonstrates equivalence via T- and S-dualities

Provides explicit examples in 4D N=2 SYM

Clarifies the relationship between different string realizations

Abstract

We show the equivalence of three different realisations of gauge theory in string theory. These are the Hanany-Witten brane constructions, the use of branes as probes and geometric engineering. We illustrate the equivalence via T- and S-dualities with the simplest non-trivial examples in four dimensions: N = 2 SYM with gauge groups SU(N_1) x SU(N_2) x .....