AdS2 geometries and non-Abelian T-duality in non-compact spaces

Anayeli Ramirez

doi:10.1007/jhep10(2021)020

Abstract

We obtain an AdS2 solution to Type IIA supergravity with 4 Poincaré supersymmetries, via non-Abelian T-duality with respect to a freely acting SL(2,R) isometry group, operating on the AdS3×S3×CY2 solution to Type IIB. That is, non-Abelian T-duality on AdS3. The dual background obtained fits in the class of AdS2×S3×CY2 solutions to massive Type IIA constructed in [1]. We propose and study a quiver quantum mechanics dual to this solution that we interpret as describing the backreaction of the baryon vertex of a D4-D8 brane intersection.

Highlights

Groups the path integral approach to Abelian T-duality put forward in [46]
We propose and study a quiver quantum mechanics dual to this solution that we interpret as describing the backreaction of the baryon vertex of a D4-D8 brane intersection
We address the construction of the brane set-up, Page charges and holographic central charge of the resulting background and propose a quiver quantum mechanics that flows in the IR to the superconformal quantum mechanics dual to our solution

Summary

Brane set-up and charges

Non-Abelian T-dualisation under a freely acting SU(2) subgroup of an SO(4) symmetry reduces the isometry group to SU(2). The S3 is replaced by its Lie algebra, R3, which is locally R×S2 This isometry is reflected in the dual fields, for instance a B2 over the S2 is generated after the dualisation, which is ρ dependent (like the B2 in (2.17)). B2| remains in the fundamental region as we move in the ρ direction This argument was developed in [64, 66, 74] where the non-compactness in the ρ coordinate — in backgrounds like (2.17) — was addressed with the introduction of large gauge transformations in the dual geometry. The background (2.17) fits in the class of solutions presented in [1], that we briefly summarise In such geometries, the D0 and D4-branes are interpreted in the dual field theory as instantons carrying electric charge. In the interval [0, ρk] there are k F1-strings

Holographic central charge

The dual superconformal quantum mechanics

SCQM dual to the non-Abelian T-dual solution

Completed NATD solution

Conclusions