Holographic duals of five-dimensional SCFTs on a Riemann surface

Abstract

We study the twisted compactifications of five-dimensional Seiberg SCFTs, with SU M (2) × E N f +1 flavor symmetry, on a generic Riemann surface that preserves four supercharges. The five-dimensional SCFTs are obtained from the decoupling limit of N D4-branes probing a geometry of N f < 8 D8-branes and an O8-plane. In addition to the R-symmetry, we can also twist the flavor symmetry by turning on background flux on the Riemann surface. In particular, in the string theory construction of the five-dimensional SCFTs, the background flux for the SU M (2) has a geometric origin, similar to the topological twist of the R-symmetry. We argue that the resulting low-energy three-dimensional theories describe the dynamics on the world-volume of the N D4-branes wrapped on the Riemann surface in the O8/D8 background. The Riemann surface can be described as a curve in a Calabi-Yau three-fold that is a sum of two line bundles over it. This allows for an explicit construction of AdS 4 solutions in massive IIA supergravity dual to the worldvolume theories, thereby providing strong evidence that the three-dimensional SCFTs exist in the low-energy limit of the compactification of the five-dimensional SCFTs. We compute observables such as the free energy and the scaling dimensions of operators dual to D2-brane probes; these have non-trivial dependence on the twist parameter for the U (1) in SU M (2). The free energy exhibits the N 5/2 scaling that is emblematic of five-dimensional SCFTs.1 See also [5] for further studies and generalizations of the Seiberg SCFTs. 2 Holographic duals of twisted compactifications of five-dimensional SCFTs were also studied in [16] using six-dimensional F (4) supergravity. There, twist of a U (1) flavor symmetry was considered by adding a vector multiplet to the theory. However it was not proven that the theory considered is a consistent truncation of massive IIA supergravity.

6D attractors and black hole microstates

“…We believe that after all this simplification the theory is a consistent truncation of massive type IIA supergravity on the warped background AdS 6 × S 4 . We give evidence for this in section 4 where we match the ten-dimensional result found in [43].…”

“…As a warm-up, and to test the consistency of the truncation, we consider the background AdS 4 × Σ g which corresponds to a twisted compactification of the five-dimensional field theory on Σ g . We successfully compare the free energy of the solution with the field theory computation in [33] and the ten-dimensional gravity computation in [43].…”

“…In section 3 we discuss the AdS 6 vacuum and an interesting partially off-shell version of its free energy that we relate to its field theory counterpart. In section 4 we consider the background AdS 4 × Σ g with a topological twist on Σ g and we successfully compare the free energy of the solution with the field theory computation in [33] and the ten-dimensional gravity computation in [43]. In section 5 we obtain a two-parameter family of black hole horizons AdS 2 × Σ g 1 × Σ g 2 and successfully reproduce their entropy using the topologically twisted index.…”

Universal spinning black holes and theories of class $$ \mathcal{R} $$

“…Upon a twisted compactification on a Riemann surface Σ g of genus g one obtains a 3d N = 2 theory whose S 3 partition function can be computed via the localization results of [8] where a universal relation to the free energy on S 5 was derived; we comment on this further in Section 5. These 3d N = 2 SCFTs admit a bulk description in terms of warped AdS 4 vacua of massive IIA or IIB supergravity, see for example [26] and [67]. We conjecture that these supergravity compactifications should admit a consistent truncation to minimal 4d gauged supergravity.…”

Exact results for 5d SCFTs of long quiver type

“…These theories have been studied extensively e.g. in [15][16][17][18][19][20][21][22][23][24][25][26][27][28]. However, many more 5d gauge theories are believed to have strongly-coupled UV fixed points, and indeed many more theories can be engineered in Type IIB string theory using 5-brane webs [3][4][5], 5-brane webs with 7-branes [29] and further generalizations [30][31][32][33].…”