Exactly marginal deformations of quiver gauge theories as seen from brane tilings

TL;DR

This work analyzes exactly marginal deformations of ${\mathcal N}=1$ quiver gauge theories described by brane tilings, showing there are generically $d-1$ complex marginal deformations tied to the toric diagram perimeter $d$. It links these gauge-theory deformations to degrees of freedom of the underlying D5/NS5 brane system in both weak and strong coupling limits, identifying two background-field deformations (diagonal gauge coupling and a beta-like deformation) and $d-3$ brane moduli (positions and Wilson lines) that map to the remaining marginals. A concrete gauge/brane dictionary is established, with detailed examples for generalized conifolds and a careful treatment of BPS conditions and central charges. The results provide a bridge between the field-theoretic marginal structure and the geometric/brane moduli, suggesting directions for extensions to varied ranks, elliptic models, and M-theory analogs. Open questions include the role of higher NS5 charges in strong coupling and potential generalizations to non-toric or M2-brane setups.

Abstract

We study the relation between exactly marginal deformations in a large class of N=1 superconformal quiver gauge theories described by brane tilings and the degrees of freedom in the corresponding 5-brane systems. We show, with the help of NSVZ exact beta functions, that there are generically d-1 complex exactly marginal deformations of a gauge theory, where d is the perimeter of the corresponding n it, and the other two, the diagonal gauge coupling and a beta-like deformation, as background supergravity fields.toric diagram. We identify d-3 complex marginal deformations as deformations of the brane system and the Wilson lines on it, and the other two, the diagonal gauge coupling and a beta-like deformation, as background supergravity fields.

Figures (9)

• Figure 1: An example of a partition of the D5 worldvolume (a) and the corresponding toric diagram (b).
• Figure 2: Changing the charge distribution of faces to cancel the charges of the intersection.
• Figure 3: The untwisting operation of the SPP tiling. The light and dark shaded faces in (a) represent $(N,-1)$ and $(N,+1)$ faces, respectively. The result of the untwisting is shown in (b). The two vertical lines on the left and right sides are identified. Through the untwisting, $(N,-1)$ faces are turned over and become $(-N,1)$ faces. As a result, all shaded faces in (b) have NS5 charge $+1$.
• Figure 4: Three contours obtained from the boundaries of the three $(N,0)$ faces, '1', '2', and '3', in Fig. \ref{['untwistspp.eps']}(a). The symbols $\times$ indicate punctures corresponding to the cycles in the tiling, and the wavy line between the two punctures $\beta$ and $\epsilon$ represents a branch cut of $\log x$.
• Figure 5: Toric diagram of a generalized conifold.