Field theory aspects of non-Abelian T-duality and N $$ \mathcal{N} $$ =2 linear quivers

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 Núñez. This suggests different completions of the long quiver describing the CFT dual to the nonAbelian T-dual background that match different observables.

Three-dimensional N = 4 $$ \mathcal{N}=4 $$ linear quivers and non-Abelian T-duals

“…(A.12). As stressed in [44], this calculation shows that non-Abelian T-duality in an interval of length π corrects the Abelian T-duality calculation by 1/n terms. In our present set-up this provides a non-trivial check of the validity of expression (6.4).…”

“…Our AdS 4 example thus provides a new AdS background in which the CFT dual can be used to define the geometry, in complete analogy with the AdS 5 case discussed in [44]. It also shows that the completion can significantly change the scaling of the free energy, and thus the CFT.…”

“…This limit was first discussed in [44] at the level of the central charges. It was shown that the central charge (and the free energy) of the SU(2) non-Abelian T-dual of AdS 5 × S 5 and that of its Abelian T-dual counterpart 3 exactly match if r is taken in a r ∈ [nπ, (n + 1)π] interval and n is sent to infinity.…”

“…We take the non compact r to be indicative of an infinite linear quiver, as shown for a related AdS 5 example in [44]. We calculate the charges in the interval r ∈ [nπ, (n + 1)π] and find,…”

“…This is shown pictorially in figure 7. It is interesting that this completion makes explicit the ideas in [44], where a completion of the non-Abelian T-dual of AdS 5 ×S 5 as a superposition of Maldacena-Nunez geometries was outlined.…”