A note on brane boxes at finite string coupling

TL;DR

This work analyzes type IIB brane-box constructions for 4D ${\cal N}=1$ SU($N_c$) gauge theories at finite string coupling. By examining brane bending, it derives consistency conditions that guarantee anomaly-free theories with stable vacua and finds a flavor bound ${N_f \ge N_c}$, with a typical range ${N_f \le 3N_c}$ for conventional setups. A notable result is the qualitative change when ${N_f > 3N_c}$, where additional $(p,q)$-brane intersections appear, complicating the brane web and potentially altering the field-theoretic spectrum via extra massless states. The paper also shows that naive Seiberg duality moves, as realized in type IIA, do not straightforwardly carry over to the IIB setting at finite coupling, highlighting the need to incorporate intersections or new states and outlining avenues (orientifolds, intersecting branes) for a more complete construction.

Abstract

We consider N=1 supersymmetric SU(N_c) gauge theories, using the type IIB brane construction recently proposed by Hanany and Zaffaroni. At non-zero string coupling, we find that the bending of branes imposes consistency conditions that allow only non-anomalous gauge theories with stable vacua, i.e., N_f >= N_c, to be constructed. We find qualitative differences between the brane configurations for N_f <= 3N_c and N_f > 3N_c, corresponding to asymptotically free and infrared free theories respectively. We also discuss some properties of the brane configurations that may be relevant to constructing Seiberg's duality in this framework.

Figures (4)

• Figure 1: The brane configuration for $SU(N_c)$ with arbitrary numbers of fundamentals and anti-fundamentals. The indicated number of D5 branes fill the the boxes.
• Figure 2: Three slices showing the $x_4-x_7$ plane: a) to the left of the NS branes, b) between, c) to the right of the NS branes. The lines labeled $(0,1)$ are the NS' branes and the vertical lines are the stacks of D5 branes.
• Figure 3: A section in the $x_5-x_6$ plane showing the $(p,q)$ charges of the branes. The $(0,1)$ branes are the two NS branes and the vertical line represents the D5 branes. The duality motion corresponds to exchanging the $x_6$ positions of the two NS branes.
• Figure 4: The brane configuration after the duality motion. The solid lines to the right of the D5 branes are the intersecting $(p,q)$ branes and the dashed lines show one possible face.