Geometric Construction of N=2 Gauge Theories

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.

35 pages, harvmac, 20 figures

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• Holography, Singularities on Orbifolds and 4D N=2 SQCD
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• On N=1 gauge models from geometric engineering in M-theory
• Orbifold Singularities, Lie Algebras of the Third Kind (LATKes), and Pure Yang-Mills with Matter
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• Non-perturbative N=1 strings from geometric singularities