TL;DR
This paper introduces a geometric approach to constructing and solving non-perturbative N=2 gauge theories using string theory and mirror symmetry, providing exact solutions for various gauge theories.
Contribution
It presents a systematic geometric construction of N=2 gauge theories in different dimensions, enabling exact non-perturbative solutions including for theories without known Lagrangians.
Findings
Exact solutions for a large class of gauge theories.
Construction of theories in 4, 5, and 6 dimensions.
Application of mirror symmetry to gauge theory solutions.
Abstract
In this lecture we give an elementary introduction to the natural realization of non-perturbative N=2 quantum field theories as a low energy limit of classical string theory. We review a systematic construction of six, five, and four dimensional gauge theories using geometrical data, which provides the exact, non-perturbative solution via mirror symmetry. This construction has lead to the exact solution of a large class of gravity free gauge theories, including Super Yang Mills (SYM) theories as well as non-conventional quantum field theories without a known Lagrangian description.
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