The $AdS_5$ non-Abelian T-dual of Klebanov-Witten as a $\mathcal{N} = 1$ linear quiver from M5-branes

Abstract

In this paper we study an $AdS_5$ solution constructed using non-Abelian T-duality, acting on the Klebanov-Witten background. We show that this is dual to a linear quiver with two tails of gauge groups of increasing rank. The field theory dynamics arises from a D4-NS5-NS5' brane set-up, generalizing the constructions discussed by Bah and Bobev. These realize $\mathcal{N}=1$ quiver gauge theories built out of $\mathcal{N}=1$ and $\mathcal{N}=2$ vector multiplets flowing to interacting fixed points in the infrared. We compute the central charge using $a$-maximization, and show its precise agreement with the holographic calculation. Our result exhibits $n^3$ scaling with the number of five-branes. This suggests an eleven-dimensional interpretation in terms of M5-branes, a generic feature of various $AdS$ backgrounds obtained via non-Abelian T-duality.

Figures (9)

• Figure 1: Brane set-up consistent with the quantized charges of the non-Abelian T-dual solution, consisting on $\alpha=1,2,\ldots,n+1$ NS5-branes (vertical black lines), $\beta=1,2,\ldots,n$ NS5'-branes (tilted red dashed lines) and $m\,N_{6}$ D4-branes (horizontal lines), where $m=1,2,\ldots,n+1$ changes by one each time a NS5-brane is crossed.
• Figure 2: General linear quiver in Bah:2013aha. Shaded (unshaded) circles represent $SU(N)$, $\mathcal{N}=1$ ($\mathcal{N}=2$) vector multiplets. Lines between them represent bifundamentals of $SU(N)\times SU(N)$. The boxes at the two ends represent $SU(N)$ fundamentals.
• Figure 3: The brane set-up associated to the Bah-Bobev $\mathcal{N}=1$ linear quivers. Vertical lines represent NS5-branes extended along $\{x_4,x_5\}$, denoted in Bah:2013aha as $v$-branes, while diagonal lines represent the NS5'-branes extended along $\{x_7,x_8\}$, denoted as $w$-branes. The same number of D4-branes extended along the $x_6$ direction stretch between adjacent 5-branes.
• Figure 4: Linear quiver proposed as dual to the non-Abelian T-dual solution. There are two matter fields $Q_j, \tilde{Q}_j$ in the bifundamental and anti-bifundamental of each pair of nodes, associated to a 5-brane connecting adjacent D4-stacks, with a total number of $j=1,\ldots,n-1$ hypermultiplets $H_j=(Q_j,\tilde{Q}_j)$ at each side of the quiver. We label $r=1,\ldots,\left[n/2\right]$ the $\sigma_j=+1$ hypermultiplets corresponding to NS5-branes and $s=1,2,\ldots,\left[n/2\right]$ the $\sigma_j=-1$ hypermultiplets from NS5'-branes, assuming an alternating distribution of both types of 5-branes. This configuration comes from a re-ordering of the branes in Figure \ref{['fig:NATDbranes']} that is consistent with Seiberg self-duality and the vanishing of the beta functions and R-symmetry anomalies. The squares in the middle of the quiver denote flavor groups corresponding either to semi-infinite D4-branes ending on the NS5 and NS5' branes or to D6-branes transversal to the D4-branes. They complete the quiver at finite $n$. We choose $\sigma_{f_1}=-\sigma_{f_2}$ for the corresponding fundamental hypermultiplets.
• Figure 5: The R-symmetry anomaly.