Two-dimensional SCFTs from D3-branes

Abstract

We find a large class of two-dimensional N = (0, 2) SCFTs obtained by compactifying four-dimensional N = 1 quiver gauge theories on a Riemann surface. We study these theories using anomalies and c-extremization. The gravitational duals to these fixed points are new AdS 3 solutions of IIB supergravity which we exhibit explicitly. Along the way we uncover a universal relation between the conformal anomaly coefficients of fourdimensional and two-dimensional SCFTs connected by an RG flow across dimensions. We also observe an interesting novel phenomenon in which the superconformal R-symmetry mixes with baryonic symmetries along the RG flow.

Betti multiplets, flows across dimensions and c-extremization

“…Finding an explicit gravitational flow usually requires the knowledge of the full 10 dimensional geometry. A rich variety of examples has been worked out in the literature, see for example [2][3][4][5][6][7][8][9][10][11][12][13][14][15]. For classifications of AdS 3 solutions with uplift in 10d and 11d see [16] and [17].…”

“…In particular in [12] the authors studied the gravity dual of an infinite set of quiver gauge theories, namely Y pq theories [18]. They arise by the worldvolume gauge theory living on a stack of N D3 branes probing the tip of a three dimensional Calabi-Yau cone with a five dimensional Sasaki Einstein (SE 5 ) base, in this case a Y pq manifold [19].…”

“…A feature of these models is that the baryonic symmetry does not contribute to the mixing, 1 namely the exact R-current in 4d is a linear combination of the UV R-current and of the (mesonic) flavor symmetries only. However, after the compactification of the theories on Σ g the baryonic symmetry in general contributes to the exact R-current of the 2d theory [12]. The mixing coefficient is computed by extremizing the two dimensional central charge.…”

“…In this section we discuss some aspects of the flow across dimensions discussed in [12]. More concretely we sketchily review the derivation of the central charge c 2d from 4d SCFTs on two dimensional compact Riemann surfaces with a partial topological twist along the abelian symmetries.…”

“…One turns on the external fluxes as F i = T i vol Σg , where vol Σg is the volume form, normalized such that dvol Σg = 2πη Σ and η Σ = 2|g−1| for g = 1 and η Σ = 1 for g = 1. Such fluxes are subject to opportune Dirac quantization conditions (see [8,12] for details).…”