Exact results for 5d SCFTs of long quiver type

Abstract

Exact results are derived for 5d SCFTs with holographic duals in Type IIB supergravity. These theories have relevant deformations that flow to linear quiver gauge theories, with the number of nodes large in the large-N limits described by supergravity. Starting from a suitable formulation of the matrix models resulting from supersymmetric localization of the squashed S 5 partition functions, the saddle point equations are solved for generic quivers with N f = 2N at all interior nodes, which includes the T N theories, and for a sample of theories with N f = 2N nodes including theories with Chern-Simons terms. The resulting exact expressions for the free energies and conformal central charges are consistent with supergravity predictions and, where available, with previous numerical field theory analyses. CONTENTS

AdS6/CFT5 with O7-planes

“…the quartic scaling characteristic of the 5d SCFTs with holographic duals in Type IIB and follows the pattern that the results for solutions with punctures involve polylogarithms of degree up to 5 [50]. O7 + / O7 − + 8 D7 Figure 7.…”

“…For the theories corresponding to 5-brane webs with D7-branes these are linear quiver theories with SU(•) nodes connected by bifundamental hypermultiplets, possibly involving Chern-Simons terms and additional fundamental hypermultiplets. The S 5 free energies for such theories were matched between supergravity and field theory computations in [48,49] and in [50], where the general form of the quivers is discussed in detail. The 5d SCFTs dual to the supergravity solutions with localized O7-planes have deformations to linear quiver gauge theories of the aforementioned type, but, depending on the type of O7 and whether or not fractional NS5-branes are involved, isolated nodes in addition have hypermultiplets in symmetric or antisymmetric representations or are replaced by SO(•) or USp(•) nodes.…”

“…the set of interior gauge nodes, consists of SU(•) nodes with only fundamental matter and possibly Chern-Simons terms. The matrix models computing the partition functions for such quivers and their saddle point evaluation capturing the free energy at large L were discussed in [50]. The (bulk) requirement for non-trivial saddle points fixes the scaling of the eigenvalues to be linear in L, and the saddle point equations take the form of an electrostatics problem with certain boundary conditions.…”

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

“…Five-dimensional SCFTs can be constructed in string theory from a system of D4-D8-O8 branes in massive type IIA string theory [58,59], studied holographically in [60,61]. Alternatively one can utilize (p, q)-fivebrane webs in type IIB string theory [62][63][64], which was studied holographically in [65,66]. 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.…”

Supersymmetric AdS6 black holes from F(4) gauged supergravity

“…See also [16]. Although the dual field theory of the non-Abelian T-dual of the Brandhuber-Oz solutions is still unclear [17,18], the infinite family of AdS 6 solutions was shown to be dual of five-brane web theories, e.g., 5d T N theories, [19,20,21,22].…”