Field Theory Aspects of non-Abelian T-duality and N=2 Linear Quivers

TL;DR

This work constructs 4d ${\cal N}=2$ linear quivers dual to non-Abelian T-duals of ${AdS}_5\times S^5$ by embedding the backgrounds into the Gaiotto–Maldacena GM geometries. It uncovers an explicit link between Abelian and non-Abelian T-duals, interpreting NATD as a discrete superposition of ATDs and Maldacena–Núñez interpolation smoothing the singularities. The authors compute central charges, entanglement entropy, and couplings for various completions of the NATD quiver, showing precise agreement with holographic predictions and revealing a deconstruction viewpoint where higher-dimensional dynamics emerge from a lattice of 4d gauge nodes. These results provide a concrete CFT/geometry dictionary for non-Abelian T-duality and suggest broad applicability to other AdS backgrounds and less-supersymmetric cases.

Abstract

In this paper we propose a linear quiver with gauge groups of increasing rank as field theory dual to the AdS_5 background constructed by Sfetsos and Thompson through non-Abelian T-duality. The formalism to study 4d N=2 SUSY CFTs developed by Gaiotto and Maldacena is essential for our proposal. We point out an interesting relation between (Hopf) Abelian and non-Abelian T-dual backgrounds that allows to see both backgrounds as different limits of a solution constructed by Maldacena and Nunez. This suggests different completions of the long quiver describing the CFT dual to the non-Abelian T-dual background that match different observables.

Figures (14)

• Figure 1: Brane set-up for the Abelian T-dual of $AdS_5\times S^5/\mathbb{Z}_n$. At each interval there are $N_{4}$ D4-branes.
• Figure 2: Brane set-up for the non-Abelian T-dual background. Parallel vertical branes are NS5-branes and horizontal branes are D4-branes suspended between them. At each $[n\pi,(n+1)\pi]$ interval there are $nN_6$ D4-branes.
• Figure 3: $\lambda(\eta)$ for the Abelian, non-Abelian and Maldacena-Núñez solutions in (a),(b),(c).
• Figure 4: $\mathcal{N}=2$ quivers associated to $\mathcal{N}=4$ SYM and its $\mathbb{Z}_n$ orbifold.
• Figure 5: Quiver associated to the non-Abelian T-dual background.