c-Extremization from toric geometry

104

We evaluate the large-N behavior of the superconformal indices of toric quiver gauge theories, and use it to find the entropy functions of the dual electrically charged rotating AdS 5 black holes. To this end, we employ the recently proposed Bethe Ansatz method, and find a certain set of solutions to the Bethe Ansatz Equations of toric theories. This, in turn, allows us to compute the large-N behavior of the index for these theories, including the infinite families Y pq , X pq and L pqr of quiver gauge theories. Our results are in perfect agreement with the predictions made recently using the Cardy-like limit of the superconformal index. We also explore the index structure in the space of chemical potentials and describe the pattern of Stokes lines arising in the conifold theory case.

Section: Introductionmentioning

confidence: 88%

“…It is therefore natural to apply this approach to theories beyond N = 4 SYM. Here, similarly to [41] we consider the superconformal index of various toric theories. In particular, we show that the basic solutions to the BAEs for N = 4 SYM used in [42] also solve the BAEs for all toric quiver theories.…”

Section: Introductionmentioning

confidence: 99%

Black hole entropy function for toric theories via Bethe Ansatz

Lanir

Nedelin

Sela

2020

104

“…Several groups have now independently reproduced the entropy function by studying the partition function or the superconformal index of N " 4 SYM [34][35][36] by slightly reinterpreting the original work in the superconformal index [26]. Further extensions for the general growth of the N " 1 superconformal index [37][38][39][40][41] including via the Bethe-Ansatz approach [42,43] have been achieved. After this important progress, the generalizations to other dimensions were also considered.…”

Section: Introductionmentioning

confidence: 99%

Microscopic entropy of rotating electrically charged AdS4 black holes from field theory localization

Nian

Zayas

2020

We employ supersymmetric localization to determine the exact partition function of 3d N " 2 gauge theories on a background given by a round S 2 fibered over a circle and certain complexified background fields. The Coulomb branch localization locus includes monopole configurations, and the partition function reduces to a matrix model. We consider the partition function of the ABJM theory on this background as an explicit case. We verify that the large-N limit of the ABJM theory partition function produces, in the Cardy limit, the entropy function of the dual rotating, electrically charged asymptotically AdS 4 supersymmetric black holes and thus provides a microscopic explanation for the Bekenstein-Hawking entropy.

“…This follows from the fact that x = 0 would lead to a singularity due to the explicit 1 x appearing in the metric. 13 Furthermore, we need that U is positive on its domain. We have four surfaces at which the metric degenerates specified by x = x ± and θ = 0, π.…”

Section: C2 Regularity Analysismentioning

confidence: 99%

“…This solution will be of the form AdS 3 × Y 7 in which Y 7 is a fibration of the Sasaki-Einstein manifold Y 5 over the Riemann surface, with self-dual five-form flux sourced by the D3-branes.The above has been successfully studied in the case that the 4d parent theory is dual to AdS 5 × Y 5 for Y 5 = S 5 [6-10], i.e. N = 4 super Yang-Mills, and for Y 5 = Y p,q [11], see also [12,13]. For the latter case of Y 5 = Y p,q , local supergravity solutions have been found in [11] but their global regularity has not been studied so far, see also [14,15].…”

mentioning

confidence: 99%

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

Couzens

Lam

Mayer

2020

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...