Surveying 4d SCFTs twisted on Riemann surfaces

“…For the case of transverse ALE space we utilize the results of [20,21] to determine the worldvolume theory on D3-branes probing an ADE singularity. By placing the resultant four-dimensional SCFTs on R 1,1 ×C and performing a suitable topological twist [19,23,45,46] we obtain 2d N = (0, 4) SCFTs, whose central charges and levels we may compute via a spectrum computation and anomaly arguments. In the ALF case it is convenient to use a dual M-theory description for the A-series.…”

Section: Microscopics Of 6d Stringsmentioning

confidence: 99%

“…In order to preserve N = (0, 4) in the 2d theory we must perform a topological twist with respect to U(1) r [19,23,45,46]. The unique twist preserving N = (0, 4) in 2d, up to redefinition, is implemented by defining the generator of U(1) ′ C to be…”

Section: γ Gauge Multiplets Hypermultipletsmentioning

confidence: 99%

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

Couzens

Lam

Mayer

2019

J. High Energ. Phys.

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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...

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“…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%

“…We have excluded values where c = d since this is in fact the Y p,q limit and we make further comments about this in appendix C. In particular we show how to take this limit for the local solution 12. Y p,q are again, in abuse of notation, the analogues of the Sasaki-Einstein manifolds Y p,q .…”

mentioning

confidence: 99%

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

Couzens

Lam

Mayer

2020

J. High Energ. Phys.

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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...

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Surveying 4d SCFTs twisted on Riemann surfaces

Cited by 17 publications

References 40 publications

N $$ \mathcal{N} $$ =1 Lagrangians for generalized Argyres-Douglas theories

N $$ \mathcal{N} $$ =1 Lagrangians for generalized Argyres-Douglas theories

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

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

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