Geometric Engineering of Quantum Field Theories

TL;DR

This paper demonstrates how non-perturbative results in N=2 quantum field theories can be derived from T-dualities in string theory through geometric and mirror symmetry techniques, providing a systematic approach to understanding their vacuum structures.

Contribution

It introduces a geometric framework that relates N=2 quantum field theories to string T-dualities without relying on duality conjectures, enabling systematic vacuum construction.

Findings

Reduces quantum field theory results to string T-dualities.

Provides a geometric realization of N=2 theories.

Suggests a systematic method for vacuum structure construction.

Abstract

Using the recent advances in our understanding of non-perturbative aspects of type II strings we show how non-trivial exact results for $N=2$ quantum field theories can be reduced to T-dualities of string theory. This is done by constructing a local geometric realization of quantum field theories together with a local application of mirror symmetry. This construction is not based on any duality conjecture and thus reduces non-trivial quantum field theory results to much better understood T-dualities of type II strings. Moreover it can be used in principle to construct in a systematic way the vacuum structure for arbitrary $N=2$ gauge theories with matter representations.