Duality and Confinement in N=1 Supersymmetric Theories from Geometric Transitions

TL;DR

This paper explores dualities and confinement phenomena in N=1 supersymmetric theories through geometric transitions in string theory, providing a comprehensive analysis of moduli spaces, brane configurations, and M-theory lifts.

Contribution

It offers a complete solution to the classical moduli space for deformed N=2 theories and connects geometric transitions with strong coupling effects in N=1 theories.

Findings

Classical moduli space fully characterized for deformed N=2 theories.

Agreement between type IIB geometries and field theory analysis.

Identification of gluino condensations with normalizable deformations.

Abstract

We study large N dualities for a general class of N=1 theories realized on type IIB D5 branes wrapping 2-cycles of local Calabi-Yau threefolds or as effective field theories on D4 branes in type IIA brane configurations. We completely solve the issue of the classical moduli space for N=2, U(N_1)x ... x U(N_n) theories deformed by a general superpotential for the adjoint and bifundamental fields. The N=1 geometries in type IIB and its T-dual brane configurations are presented and they agree with the field theory analysis. We investigate the geometric transitions in the ten dimensional theories as well as in M-theory. Strong coupling effects in field theory are analyzed in the deformed geometry with fluxes. Gluino condensations are identified the normalizable deformation parameters while the vacuum expectation values of the bifundamental fields are with the non-normalizable ones. By lifting to M theory, we get a transition from finite coverings of non-hyperelliptic curves to non-hyperelliptic curves. We also discuss orientifold theories, Seiberg dualities and mirror symmetries.