Twisted $$ \mathcal{N} $$ = 1 SCFTs and their AdS3 duals

Abstract

We study compactifications of an infinite family of four-dimensional N = 1 SCFTs on a Riemann surface in the presence of arbitrary background fluxes for global symmetries. The four-dimensional parent theories have holographic Sasaki-Einstein duals in type IIB string theory. We compute central charges and R-charges of baryonic operators in the resulting twodimensional N = (0, 2) theories in three distinct ways: from the field theory side utilizing c-extremization, its recently discovered geometric dual formulation, and holographically using new AdS 3 duals of two-dimensional field theories. c.a.couzens@uu.nl h.hetlam@uu.nl k.mayer@uu.nl arXiv:1912.07605v2 [hep-th] 23 Dec 2019Since the advent of AdS/CFT in [1] many examples of dual pairs have been conjectured. The first (and most studied) was AdS 5 ×S 5 with five-form flux in type IIB and is proposed to be dual to four-dimensional N = 4 supersymmetric Yang-Mills [1]. The five-sphere can be replaced by an arbitrary five-dimensional Sasaki-Einstein manifold Y 5 and gives rise to AdS 5 ×Y 5 spaces dual to 4d N = 1 quiver gauge theories. In general, it is hard to find explicit metrics for these spaces and this makes it difficult to obtain evidence for new dualities. 1 Despite the difficulties, the infinite family of explicit Sasaki-Einstein metrics Y 5 = Y p,q [4] and its generalization Y 5 = L a,b,c [5] have been discovered. These manifolds are toric and specified by coprime integers p and q, and a, b and c respectively. The duality can be understood via its construction using D3-branes probing the Calabi-Yau cone singularity with base Y 5 . The 4d theory is the worldvolume theory on these D3-branes whilst AdS 5 × Y 5 is the near horizon geometry of the type IIB D3-brane solution.Of course, one can also study the correspondence in lower dimensions. One way is to take the aforementioned four-dimensional theories and compactify them on a (smooth) Riemann surface Σ g with genus g performing a topological twist to preserve supersymmetry. Additionally, background magnetic fluxes for the continuous flavour symmetries in the 4d theory can be turned on. Since these fluxes are quantized, every 4d theory leads to a discrete family of 2d theories. In the IR one expects these theories to flow to a 2d superconformal field theory (SCFT), however proving the existence of this flow is in general challenging. Assuming the existence of the SCFT one can compute its central charges and R-charges from UV data using the technique of c-extremization [6,7] which is based on anomaly considerations. In this scenario we are not considering a conventional RG flow from a 2d UV theory to the 2d IR theory but instead we consider an RG flow across dimensions. One can obtain evidence for the existence of the 2d SCFT using holography by finding an explicit supergravity solution with the same central charges and R-charges. Employing the D3-brane picture, one expects the solution to correspond to the near horizon geometry of a D3-brane compactified on the Riemann surface. This solution will be of the fo...

$\mathcal{I}$/$c$-extremization in M/F-duality

“…From the point of view of the 4d N = 4 Super-Yang-Mills (SYM) theory on the D3-branes, this corresponds to a varying complexified coupling, and the 2d SCFT is obtained by a duality-twist [13][14][15][16]. Generalizations of these Ftheory solutions were obtained in [17][18][19][20] and the dual field theories were studied in [21,22].…”

“…20) can be extremized with respect to the remaining variables in ξ and [J 8 ]. This is a necessary condition for the geometry Y τ 9 to be on-shell, i.e.…”

$$ \mathcal{N} $$ = (0, 2) AdS3 solutions of type IIB and F-theory with generic fluxes

“…By making a suitable ansatz later, they find a class of N = (0, 2) solutions generalizing [7,9,12], this class will be recovered as a special case of our results. Solutions of these various classifications can also be found in [14][15][16][17], see also [18] for some TsT-dual solutions.…”

Anomalies of (0,4) SCFTs from F-theory

“…Further work in type IIA (and also type IIB) can be found in [12] where solutions preserving the large N = (0, 4) supersymmetry algebra were found. 1 Type IIB and F-theory N = (0, 4) solutions were discussed in [14], whilst further work on AdS 3 solutions in type IIB, with varying amounts of supersymmetry, can be found in [15][16][17][18][19][20][21][22][23][24].…”