Duality and confinement in $\mathcal{N}=1$ supersymmetric theories from geometric transitions

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, n i=1 U (N i ) 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. e-print archive: http://xxx.lanl.gov/hep-th/0112040

Nonsupersymmetric brane/antibrane configurations in type IIA and M theory

“…We now proceed to study this system from the IIA/M perspective [56,50,51] . Applying Tduality, we obtain a brane configuration with two NS5's extended along the curves w = ±mv and separated along x 6 with N D4's suspended between.…”

“…51 It was noted in [75] that, in the g s → 0 limit with fixed N , the gauge theories geometrically engineered by D-branes on CY singularities receive contributions only from disks and thus have only single-trace operators. Here we are refining and generalizing his argument by introducing parameters g s , g s N , and λ 4 .…”

“…It is also straightforward to generalize our method to A-D-E quiver gauge theories obtained by stretching D4/D4-branes between multiple NS5's, which is T -dual [50,51] to the local CY geometries obtained by A-D-E fibrations [44,45]. What is particularly interesting about such more general systems is that, nonsupersymmetric brane/antibrane configurations can be stable rather than metastable [53].…”

Massless flavor in geometry and matrix models

“…One direction was initiated in [1] and consisted in studying the large N dualities in the context of type A topological strings. This topological duality was embedded in the physical superstring theory in [2] and then further developed in [3,4,5,6,7,8,9] (see also [10,11,12] for an alternative approach, involving brane configurations). The main result of these studies was a method of calculating the effective superpotential of a four-dimensional field theory using aspects of the flux configurations and of the geometry of the compact/transverse space.…”

“…As the results of [14,15,16] were based on geometric transitions relating open and closed string theories, our new results shed a new light on the matrix/gauge theory relation in the presence of massless fields. We use the T-dual brane configurations [10,11,12,13] to understand the dynamics of the field theory, as the mass of the adjoint field as well as the mass and vevs of the fields transforming in the fundamental representation of the gauge group can be read from the positions of the different branes.…”