Twisted D3-brane and M5-brane compactifications from multi-charge spindles

Abstract

We construct families of supersymmetric AdS3 × Y7 and AdS3 × Y8 solutions to type IIB string theory and M-theory, respectively. Here Y7 is an S5 fibration over Σ, while Y8 is an S4 fibration over Σg × Σ, where Σg is a Riemann surface of genus g > 1 and Σ is a two-dimensional orbifold known as a spindle. We interpret the solutions as near-horizon limits of N D3-branes wrapped on Σ and N M5-branes wrapped on Σg × Σ, respectively. These are holographically dual to d = 2, (0, 2) SCFTs, and we show that the central charge and superconformal R-symmetry of the gravity solutions agree with dual field theory calculations.

M5-branes wrapped on a spindle

“…Notice that we are working in a specifc gauge for the "flavour" symmetry gauge field, A1 − A2, that is given by the original supergravity solution. This is analogous to the analysis of D3-branes wrapped on a spindle in[10], whereas in the same setting other gauge choices were analysed in[9], leading to the same final result for the central charge.…”

“…In fact further interesting examples have already appeared. In [9,10] the solutions of [6] were generalized from minimal D = 5 gauged supergavity to the STU model, which has three Abelian gauge fields. The solutions can be uplifted on the five-sphere to obtain solutions of type IIB supergravity describing D3-branes wrapping the spindle, which are again completely regular, and were first constructed in [7].…”

“…Furthermore the central charge of the d = 2 SCFT obtained from the gravity solution agrees exactly with the associated field theory calculation using the anomaly polynomial of N = 4 SYM theory in d = 4. In the solutions describing D3-branes wrapped on spindles in both [6] and [9,10], supersymmetry is not being realized by the topological twist; for example, it was shown by explicit construction in [6] that the Killing spinors are not constant on Σ, and moreover are in fact sections of non-trivial bundles over Σ.…”

“…In [10] a sub-class of the D = 5 solutions of the STU model were uplifted to D = 11 supergravity on Σ g × S 4 , where Σ g is a Riemann surface of genus g > 1. These are regular D = 11 solutions, first found in [11], that describe M5-branes wrapped on a product fourcycle Σ × Σ g .…”

M5-brane sources, holography, and Argyres-Douglas theories

“…This is the expected result for a disk in R 2 /Z centered at the origin. 2 Our 7d solutions can be compared to the spindle solutions of [14,15,[30][31][32]. As in those references, the 2d space Σ is not equipped with a constant curvature metric.…”