Brane Boxes and Branes on Singularities

TL;DR

This paper establishes a duality between Brane Box Models and D3 branes at orbifold singularities, providing geometric and field theory insights into supersymmetric gauge theories and their marginal couplings.

Contribution

It introduces a T-duality map between Brane Box Models and singularity setups, linking geometric configurations with field theory data and extending to non-finite theories with fractional branes.

Findings

The T-duality map is interpreted via D=4 N=1 field theory data.

Geometric interpretation of marginal couplings in finite theories.

Confirmation of the mapping using AdS/CFT correspondence.

Abstract

Brane Box Models of intersecting NS and D5 branes are mapped to D3 branes at C^3/Gamma orbifold singularities and vise versa, in a setup which gives rise to N=1 supersymmetric gauge theories in four dimensions. The Brane Box Models are constructed on a two-torus. The map is interpreted as T-duality along the two directions of the torus. Some Brane Box Models contain NS fivebranes winding around (p,q) cycles in the torus, and our method provides the geometric T-dual to such objects. An amusing aspect of the mapping is that T-dual configurations are calculated using D=4 N=1 field theory data. The mapping to the singularity picture allows the geometrical interpretation of all the marginal couplings in finite field theories. This identification is further confirmed using the AdS/CFT correspondence for orbifold theories. The AdS massless fields coupling to the marginal operators in the boundary appear as stringy twisted sectors of S^5/Gamma. The mapping for theories which are non-finite requires the introduction of fractional D3 branes in the singularity picture.