Betti multiplets, flows across dimensions and c-extremization

Abstract

We consider 4d N=1 SCFTs, topologically twisted on compact constant curvature Riemann surfaces, giving rise to 2d N=(0,2) SCFTs. The exact R-current of these 2d SCFT extremizes the central charge c_{2d}, similarly to the 4d picture, where the exact R-current maximizes the central charge a_{4d}. There are global currents that do not mix with the R-current in 4d but their mixing becomes non trivial in 2d. In this paper we study the holographic dual of this process by analyzing a 5d N=2 truncation of T^{1,1} with one Betti vector multiplet, dual to the baryonic current on the CFT side. The holographic realization of the flow across dimensions connects AdS_5 to AdS_3 vacua in the supergravity picture. We verify the existence of the flow to AdS_3 solutions and we retrieve the field theory results for the mixing of the Betti vector with the graviphoton. Moreover, we extract the central charge from the Brown-Henneaux formula, matching with the results obtained in field theory. We develop a general formalism to obtain the central charge of a 2d SCFT from 5d N=2 gauged supergravity with a generic number of vector multiplets, showing that its extremization corresponds to an attractor mechanism for the scalars in the supergravity picture.

28 pages, 5 figures, typos fixed and additional explanations added

References in corpus (18)

• Four-Dimensional SCFTs from M5-Branes
• Gauged supergravity from type IIB string theory on Y^{p,q} manifolds
• Large $N$ matrix models for 3d $\mathcal{N}=2$ theories: twisted index, free energy and black holes
• A supersymmetric consistent truncation for conifold solutions
• Compactifications of the Klebanov-Witten CFT and new $Ad{S}_3$ backgrounds
• Large $N$ topologically twisted index: necklace quivers, dualities, and Sasaki-Einstein spaces
• All homogeneous N=2 M-theory truncations with supersymmetric AdS4 vacua
• Supersymmetric Consistent Truncations of IIB on T(1,1)
• F-theory and 2d (0,2) Theories
• (0,2) SCFTs from the Leigh-Strassler Fixed Point
• UV Completions for Non-Critical Strings
• Higher Derivative Corrections and Central Charges from Wrapped M5-branes
• Global geometry of the supersymmetric AdS_3/CFT_2 correspondence in M-theory
• Comments on a-maximization from gauged supergravity
• Supersymmetric Vacua in N=2 Supergravity
• Flowing from $Ad{S}_5$ to $Ad{S}_3$ with $T^{1,1}$
• Black string first order flow in N=2, d=5 abelian gauged supergravity
• Superconformal Symmetry in the Kaluza-Klein Spectrum of Warped AdS(3)

Cited by in corpus (19)

• An extremization principle for the entropy of rotating BPS black holes in AdS${}_5$
• Holographic microstate counting for AdS${}_4$ black holes in massive IIA supergravity
• Topologically twisted indices in five dimensions and holography
• Anomalies, Black strings and the charged Cardy formula
• Proving the equivalence of $c$-extremization and its gravitational dual for all toric quivers
• Microstates of rotating AdS${}_5$ strings
• 4d F(4) gauged supergravity and black holes of class $\mathcal{F}$
• AdS${}_5$ black strings in the stu model of FI-gauged $N=2$ supergravity
• Supersymmetric $Ad{S}_5$ black holes and strings from 5D $N=4$ gauged supergravity
• Five-branes wrapped on topological disks from 7D N=2 gauged supergravity
• $T^{1,1}$ truncation on the spindle
• Twisted compactifications of 6D field theories from maximal 7D gauged supergravity
• Two-dimensional SCFTs from matter-coupled 7D N=2 gauged supergravity
• From N=2 in four dimensions to (0,2) in two dimensions
• Magnetically-charged supersymmetric flows of gauged $\mathcal{N}=8$ supergravity in five dimensions
• New supersymmetric $Ad{S}_5$ black strings from 5D $N=4$ gauged supergravity
• Kerr-Newman black holes from $\mathcal{N}=1^{\ast }$
• Wrapped D4-branes from maximal 6D gauged supergravity
• Holographic solutions from 5D $SO(2)\times ISO(3)$ $N=4$ gauged supergravity