Geometric engineering of quantum field theories

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.