Non-integrability on AdS3 supergravity backgrounds

Abstract

We investigate classical integrability on two recently discovered classes of backgrounds in massive IIA supergravity. These vacua are of the form AdS 3 × S 2 × R × CY 2 , they preserve small N = (0, 4) supersymmetry and are associated with D8−D6−D4−D2 Hanany-Witten brane setups. We choose an appropriate string embedding and use differential Galois theory on its associated Hamiltonian system, intending to produce the conditions under which Liouvillian solutions may occur. By constraining the parameters of the system according to the consistency of the associate brane setups we prove that no such conditions exist, yielding the complete non-integrability of these vacua. That is, up to the trivial cases where the background reduces to the Abelian and non-Abelian T-dual of AdS 3 × S 3 × T 4 .

AdS2 × S2 × CY2 solutions in Type IIB with 8 supersymmetries

“…By the same token, it would be interesting to study the integrability (or not) of the backgrounds presented here, as well as those in [1,39]. Integrable string backgrounds dual to field theories described by linear quivers in dimensions d = 2, 4, 6, have been found in [57][58][59][60]. Similar techniques should probably apply for the d = 1 case.…”

AdS2 duals to ADHM quivers with Wilson lines

“…Major recent progress has been achieved in the classification of AdS 3 geometries with N = (0, 4) supersymmetries and SU(2) structure [15,28]. Remarkably, the 2d CFTs dual to subsets of these solutions have been identified [40][41][42] (see also [43][44][45]), thus providing for explicit AdS 3 /CFT 2 pairs where the microscopical description of 5d black holes can be addressed. Generalising recent developments in five dimensional BPS black holes (see for instance [46][47][48]) to these new set-ups constitutes a promising new avenue that is still awaiting for further development.…”

New AdS2 backgrounds and $$ \mathcal{N} $$ = 4 conformal quantum mechanics

“…The case of two-dimensional SCFTs and their AdS 3 duals is very attractive, not only for the rich landscape of two dimensional CFTs, but also for the connection with the Physics of black holes. In this case, recent progress was reported for half-maximal supersymmetric (for AdS 3 ) backgrounds, see for example [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56]. All these solutions geometrise various perturbative and non-perturbative aspects of conformal field theories in diverse dimensions.…”

“…These should be dual to superconformal quantum mechanics (SCQM). The similarities between the superconformal algebras in one and two dimensions or, by duality, the geometric relations between AdS 2 and AdS 3 -spaces, suggest in particular that the studies of [49][50][51][52][53][54][55][56] could be extended to the AdS 2 case. Some studies involving AdS 2 geometries were motivated by developments in black holes Physics, whilst others drew inspiration from a purely geometric or field theoretical viewpoint, or both [73][74][75][76][77][78][79][80][81][82][83][84][85].…”