Marginal Deformations from Branes

TL;DR

The paper investigates four-dimensional N=1 gauge theories with $Q^4$-type superpotentials that flow to interacting superconformal fixed points, showing how these theories can be realized by brane configurations in Type II string theories. It demonstrates the existence of exactly marginal operators via NS5-brane motions and, in Type IIB, B-field flux through generalized conifold backgrounds, connecting field-theoretic marginal deformations to brane dynamics. By enumerating finite N=2 theories with one or two simple gauge factors, it distinguishes elliptic models (where $c-a=0$ and gravity duals are viable) from non-elliptic ones (which typically violate $c-a=0$ and lack simple supergravity descriptions). The work also extends the analysis to brane boxes and orientifold setups, highlighting how the AdS/CFT framework constrains which marginals correspond to viable gravity duals. Overall, it clarifies when marginal deformations in these gauge theories have geometric realizations on branes and when such theories admit holographic descriptions.

Abstract

We study brane configurations for four dimensional N=1 supersymmetric gauge theories with quartic superpotentials which flow in the infrared to manifolds of interacting superconformal fixed points. We enumerate finite N=2 theories, from which a large class of marginal N=1 theories descend. We give the brane descriptions of these theories in Type IIA and Type IIB string theory. The Type IIB descriptions are in terms of D3 branes in orientifold and generalized conifold backgrounds. We calculate the Weyl and Euler anomalies in these theories, and find that they are equal in elliptic models and unequal in a large class of finite N=2 and marginal N=1 non-elliptic theories.

Figures (32)

• Figure 1: SU($N$) with $2N$ hypermultiplets.
• Figure 2: The brane configuration corresponding to the SU$(k_1)\times$SU$(k_2) \times\cdots\times$SU$(k_M)$ theory with bifundamentals and $k_0$ flavors of SU$(k_1)$ and $k_{M+1}$ flavors of SU$(k_M)$. The vertical lines represent NS5 branes, the horizontal lines are D4 branes and the circles are D6 branes orthogonal to the $(x_4,x_6)$ plane drawn here..
• Figure 3: Brane configuration with O4 plane wrapping the compact direction.
• Figure 4: (a) ${\cal N}=2$ USp($2N$) theory with $(2N+2)$ hypermultiplets. (b) ${\cal N}=1$ USp($2N$) gauge theory with and two types of flavors, $Q$ and $f$.
• Figure 5: ${\cal N}=2$ SO($N$) theory with $(N-2)$ hypermultiplets.