Warped AdS6 × S2 in Type IIB supergravity III. Global solutions with seven-branes

Abstract

We extend our previous construction of global solutions to Type IIB supergravity that are invariant under the superalgebra F (4) and are realized on a spacetime of the form AdS 6 × S 2 warped over a Riemann surface Σ by allowing the supergravity fields to have non-trivial SL(2, R) monodromy at isolated punctures on Σ. We obtain explicit solutions for the case where Σ is a disc, and the monodromy generators are parabolic elements of SL(2, R) physically corresponding to the monodromy allowed in Type IIB string theory. On the boundary of Σ the solutions exhibit singularities at isolated points which correspond to semi-infinite five-branes, as is familiar from the global solutions without monodromy. In the interior of Σ, the solutions are everywhere regular, except at the punctures where SL(2, R) monodromy resides and which physically correspond to the locations of [p, q] seven-branes. The solutions have a compelling physical interpretation corresponding to fully localized five-brane intersections with additional seven-branes, and provide candidate holographic duals to the five-dimensional superconformal field theories realized on such intersections.

Type IIB 7-branes in warped AdS6: partition functions, brane webs and probe limit

“…This motivates a corresponding extension of the construction of supergravity solutions. In [22] the construction of supergravity solutions has indeed been extended to incorporate punctures with non-trivial SL(2, R) monodromy, signaling the presence of additional 7-branes. However, while the map between supergravity solutions and 5-brane webs appeared very clearly and naturally in the case without monodromy, where a given 5-brane intersection is entirely characterized by the charges of the external 5-branes, a corresponding map is less automatic in the case with additional 7-branes.…”

“…The solutions in [22] are constructed in terms of two locally holomorphic functions A ± on the Riemann surface Σ, which is a disc or equivalently the upper half plane. The differentials of these functions have common poles on the boundary of Σ, at which the entire solution approaches that for a (p, q) 5-brane, as constructed in [23], with p − iq identified with the residue at the pole.…”

“…For solutions with monodromy, the differentials in addition have a number of branch points in the interior of Σ with associated branch cuts, across which the supergravity fields undergo a parabolic SL(2, R) transformation. The regularity conditions for the supergravity solutions as constructed in [22] constrain each puncture to lie on a curve in Σ. This leaves one real parameter in addition to the orientation of the branch cut for a puncture with fixed monodromy.…”

“…Similarly, one may wonder whether solutions with punctures at different points in Σ can be related by 7-brane moves with the associated Hanany-Witten brane creation effect [24], or whether punctures at different points correspond to genuinely different brane webs. An unambiguous brane web interpretation for the solutions constructed in [22] is…”

“…In the present paper we will expand on the interpretation of the solutions in [22] in several ways and address these questions. We will constrain the monodromy around the punctures to realize the SL(2, R) transformation appropriate for D7 branes for simplicity, but the results immediately generalize to other 7-branes by globally conjugating with suitable SL(2, R) elements.…”