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

Abstract

We present a new infinite family of Type IIB supergravity solutions preserving eight supercharges. The structure of the space is AdS2 × S2 × CY2 × S1 fibered over an interval. These solutions can be related through double analytical continuations with those recently constructed in [1]. Both types of solutions are however dual to very different superconformal quantum mechanics. We show that our solutions fit locally in the class of AdS2 × S2 × CY2 solutions fibered over a 2d Riemann surface Σ constructed by Chiodaroli, Gutperle and Krym, in the absence of D3 and D7 brane sources. We compare our solutions to the global solutions constructed by Chiodaroli, D’Hoker and Gutperle for Σ an annulus. We also construct a cohomogeneity-two family of solutions using non-Abelian T-duality. Finally, we relate the holographic central charge of our one dimensional system to a combination of electric and magnetic fluxes. We propose an extremisation principle for the central charge from a functional constructed out of the RR fluxes.

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

“…In [38], the agreement is kept since the one-dimensional quiver QMs are originated from the two-dimensional N = (0, 4) CFTs upon dimensional reduction. However, in [1,41], the equation (3.10) matches with the holographic result even though the 1d CFTs have not originated from the 2d "mother" CFTs.…”

“…The equation (3.10) was obtained in [83] for two-dimensional conformal field theories, and was determined by identifying the right-handed central charge with the U(1) R current two-point function. With the expression (3.10), both results, holographic and field theory central charge have been shown to agree for the 2d N = (0, 4) quiver CFTs constructed in [27][28][29], as well as for the AdS 2 /SCQM pairs proposed in [1,38,41]. In [38], the agreement is kept since the one-dimensional quiver QMs are originated from the two-dimensional N = (0, 4) CFTs upon dimensional reduction.…”

“…1 In [41], SL(2, R)-NATD was used to find an explicit example -with brane sources -in the class of AdS2×S 2 ×CY2 solutions fibered over a 2d Riemann surface constructed in [14]. 2 We take g µν = −Tr(t µ t ν ) in order to have (+, −, +) signature.…”

“…In a conformal quantum mechanics the energy momentum tensor has only one component, and as the theory is conformal, it must vanish. We will interpret the central charge as counting the number of vacuum states in the dual superconformal quantum mechanics, along the lines of [1,38,41].…”

“…In particular, recent progress has been reported on the construction of new AdS 3 solutions with four Poincaré supersymmetries [18,24,26,34,37] as well as on the identification of their 2d (half-maximal BPS) dual CFTs [27-29, 34, 37, 44]. In the same vein, AdS 2 /CFT 1 pairs have been explored as a natural extension of AdS 3 /CFT 2 pairs through T-duality [38] and double analytical continuation, [1,41], in each case, providing different families of quiver quantum mechanics with four Poincaré supersymmetries.…”