Quantum corrections to central charges and supersymmetric Casimir energy in AdS3/CFT2

We study the dependence of supersymmetric partition functions on continuous parameters for the flavor symmetry group, G F , for 2d N = (0, 2) and 4d N = 1 supersymmetric quantum field theories. In any diffeomorphism-invariant scheme and in the presence of G F 't Hooft anomalies, the supersymmetric Ward identities imply that the partition function has a non-holomorphic dependence on the flavor parameters. We show this explicitly for the 2d torus partition function, Z T 2 , and for a large class of 4d partition functions on half-BPS four-manifolds, Z M 4in particular, for M 4 = S 3 × S 1 and M 4 = Σ g × T 2 . We propose a new expression for Z M d−1 ×S 1 , which differs from earlier holomorphic results by the introduction of a non-holomorphic "Casimir" pre-factor. The latter is fixed by studying the "high temperature" limit of the partition function. Our proposal agrees with the supersymmetric Ward identities, and with explicit calculations of the absolute value of the partition function using a gauge-invariant zeta-function regularization.

Section: The Supersymmetric T 2 Partition Function Revisitedsupporting

confidence: 69%

’t Hooft anomalies and the holomorphy of supersymmetric partition functions

Closset

Pietro

Kim

2019

“…which are the central charges of the theory without the center of mass modes and is consistent with the results in [49,50] for |Γ| = 1.…”

Section: γ Gauge Multiplets Hypermultipletssupporting

confidence: 89%

Black holes and (0,4) SCFTs from type IIB on K3

Couzens

Lam

Mayer

2019

We study the central charges and levels of 2d N = (0, 4) superconformal field theories that are dual to four-and five-dimensional BPS black holes in compactifications of type IIB string theory on a K3 surface. They arise from wrapping a D3-brane on a curve C inside K3 and have transverse space either an ALE or ALF space. These D3-branes have an AdS 3 × S 3 /Γ near horizon geometry where Γ is a discrete subgroup of SU(2). We compute the central charges and levels of the 2d SCFTs both in the microscopic picture and from six-dimensional N = (2, 0) supergravity. These quantities determine the black hole entropy via Cardy's formula. We find agreement between the microscopic and macroscopic computations. The contributions from one-loop quantum corrections to the macroscopic result are crucial for this matching. c.a.couzens@uu.nl h.hetlam@uu.nl k.mayer@uu.nl s.j.g.vandoren@uu.nl IntroductionThe microscopic counting of the Bekenstein-Hawking entropy of BPS black holes in string theory has had a long and rich history since its inception in [1]. The authors of [1] considered five-dimensional non-spinning black holes arising from the compactification of type II string theory on K3×S 1 , matching the entropy of the macroscopic configuration with the microscopic one. This was later extended to five-dimensional non-spinning black holes in M-theory on a Calabi-Yau threefold [2] and four-dimensional black holes in Mtheory on the product of a Calabi-Yau threefold with a circle by MSW [3]. More recently black holes in F-theory [4] have been given further consideration in [5][6][7] for example.In this paper we are interested in compactifications of type IIB string theory on K3 and the black strings emerging in this theory. The goal is to match macroscopic data with a complimentary microscopic description. The literature on the topic is vast, in particular for black holes arising from the D1-D5-(p) system [1,8]. We shall instead concern ourselves with black strings arising from wrapping D3-branes on a curve inside K3, which, in comparison to the D1-D5-(p) system, has been far less studied. Explicitly we shall consider D3-branes in an asymptotic geometry R × S 1 × M × K3 where the D3branes are wrapped on S 1 × C with C a curve in K3 and probe the transverse space M. The equations of motion and supersymmetry preservation imply that the four-manifold M is a Ricci-flat hyper-Kähler manifold which we take to be non-compact. We consider two families of such manifolds M = M Γ : asymptotically locally Euclidean (ALE) and asymptotically locally flat (ALF) spaces, both of which may be defined by a choice of discrete subgroup Γ ⊂ SU(2) as we review in section 2. Different choices of Γ lead to black strings with different charges, some of which have not been considered before in the literature. In particular, black strings arising from D3-branes probing M Γ corresponding to the D-and E-series within the ADE-classification of discrete subgroups of SU(2) have not been studied previously. Microscopically the strings are dual to (0,4) superconforma...

“…The bulk Brown-Henneaux central charge will be obtained via the standard argument involving the near-horizon limit of the brane system [6,8]. The quantum correction to the Brown-Henneaux central charge, on the other hand, is extracted from the hightemperature asymptotics of the bulk one-particle superconformal index [9], also known as the one-particle NSNS elliptic genus. This procedure, which we will review in section 2, was recently imported into AdS 3 /CFT 2 from the AdS 5 /CFT 4 context where similar prescriptions were introduced in [10,11].…”

Section: Jhep02(2022)188mentioning

confidence: 99%

“…The one-particle indices that we need were computed in [3] (and the computation will be further elucidated for the ES case in appendix A). Their asymptotics yield [9] δc ES = 3, and δc HS = 0, (…”

Section: Jhep02(2022)188mentioning

confidence: 99%

Central charges, elliptic genera, and Bekenstein-Hawking entropy in $$ \mathcal{N} $$ = (2, 2) AdS3/CFT2

Ardehali

Jiang

Zhao

2022

Self Cite

We consider $$ \mathcal{N} $$ N = (2, 2) AdS3/CFT2 dualities proposed in the large central charge limit (c → ∞) by Eberhardt. Here we propose the associated D1-D5 systems to be orbifolds of the standard $$ \mathcal{N} $$ N = (4, 4) systems, thereby elevating the dualities to the finite-c level on the boundary and to the quantum level in the bulk. In particular, we show that our brane systems yield low-energy sigma models whose subleading central charges match earlier predictions from bulk one-loop supergravity computations. In the case involving the Enriques surface, the finite-c sigma model has a non-trivial elliptic genus which we use to microscopically explain both the Bekenstein-Hawking entropy and the subleading logarithmic correction to it for the associated macroscopic black brane.