Global half-BPS AdS2 × S6 solutions in Type IIB

Abstract

We investigate half-BPS Type IIB supergravity solutions with spacetime geometry AdS 2 × S 6 warped over a Riemann surface Σ. The general local solution was obtained in earlier work in terms of two holomorphic functions A ± on Σ. In the first part of this paper we seek global solutions corresponding to the near-horizon behavior of (p, q)string junctions. We identify the type of singularity in A ± needed at the boundary of Σ to match the solutions locally onto the classic (p, q)-string solution. We construct solutions with multiple (p, q)-strings, but the existence of geodesically complete solutions remains unsettled. In a second part we construct multi-parameter families of non-compact globally regular and geodesically complete solutions with asymptotic regions and an AdS 2 throat which caps off smoothly.

Warped AdS2 and SU(1, 1|4) symmetry in Type IIB

“…the complex 3form G or the 5-form field strength F (5) is the SO(2, 1) ⊕ SO(6) ⊕ SO(2) symmetry. For example, in [1][2][3][4] and [5,6] the two-and six-form potentials (respectively) were ultimately valuable indicators of brane and string sources for the physically regular solutions. But for the present case, we found that the relations following from the reduction of the BPS equations imply that G = 0 while the coefficient of F (5) is constant, thus precluding the existence of non-trivial sources for such half-BPS solutions.…”

“…The residual supersymmetries, if any, of a configuration of purely bosonic Type IIB supergravity fields are governed by the BPS equations of (2.9). In [1][2][3][4] and [5,6], the Ansatz for the supergravity fields and supersymmetry spinor which satisfies the BPS equations also solves the Bianchi identities and field equations, and thus automatically provides a half-BPS solution to Type IIB supergravity. In the present case however, we will show that no non-trivial half-BPS solutions exist.…”

“…It is shown that there exist a finite number of such subalgebras H, and thus one obtains a classification of half-BPS solutions with the above asymptotics. Among these are the special classes of exact solutions previously found in [10] and [11], while those of [1][2][3][4] and [5,6] are absent since neither F (4) nor any of its real forms are subalgebras of PSU (2, 2|4).…”

“…In the study of half-BPS solutions to Type IIB supergravity, recent progress was made on spacetimes with the following factors warped over a two-dimensional Riemann surface Σ: AdS 6 × S 2 [1][2][3][4] and AdS 2 × S 6 [5,6]. In the former case, globally regular and geodesically complete solutions were obtained which provide the near-horizon geometry of (p, q) fivebrane webs [7,8].…”

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

“…A natural extension is the study of backgrounds with an AdS 2 factor [57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72]. These should be dual to superconformal quantum mechanics (SCQM).…”