Brane Boxes and Branes on Singularities

TL;DR

<3-5 sentence high-level summary>

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.

Figures (13)

• Figure 1: Conventions for denoting the chiral multiplets which are in the fundamental of the group $SU(n_{i,j})$ and in the antifundamental of an adjacent group.
• Figure 2: The two superpotential couplings at each corner are represented by an oriented triangle of arrows.
• Figure 3: A permutation on the types of fields. In this particular example the $H, V, D$ fields are transformed into $H, D, V$ fields, respectively. The $4\times 2$ box model with trivial identifications is mapped to the $4\times 2$ model with a nontrivial identification with a horizontal jump by $p=2$. The numbers in the boxes indicate labels of the boxes.
• Figure 4: First step in the construction of the brane box model corresponding to a singularity $\hbox{${\rm C}$}^3/\Gamma$. The labels on each box denote the irreducible representation of $\Gamma$ associated to the gauge factor in that box. The basic period in the infinite array of boxes is bounded by dark lines.
• Figure 5: A typical region in a brane box model constructed from a singularity. The arrows denote the chiral multiplets $\Phi_{I,I\oplus A_1}$, $\Phi_{I,I\oplus A_2}$, and $\Phi_{I,I-A_1-A_2}$, for $I=iA_1\oplus jA_2$, which appear as the horizontal, vertical and diagonal fields.