Operator counting for $ \mathcal{N} = {2} $ Chern-Simons gauge theories with chiral-like matter fields

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Recently it was discovered that twisted superconformal index I can be used to understand the Bekenstein-Hawking entropy of magnetically charged black holes in AdS spacetime. In this paper we apply the so-called I-extremization procedure to threedimensional gauge field theories and their geometric dual, focusing in particular on the seven-dimensional Sasaki-Einstein manifold M 1,1,1 . We generalize recent studies on relations among toric geometry, variational principles, and black hole entropy to the case of AdS 2 × Y 9 , where Y 9 is a fibration of toric Sasaki-Einstein manifold M 1,1,1 over a twodimensional Riemann surface Σ g . The nine-dimensional variational problem is given in terms of an entropy functional. In order to illustrate the computations as explicitly as possible, we consider cases where either only mesonic or baryonic fluxes are turned on. By employing the operator counting method, we calculate the S 3 free energy and the topologically twisted index I at large-N . The result for I, it turns out, can be also obtained from the variational principle of the entropy functional with mesonic fluxes. We also study asymptotically AdS 4 black holes which are magnetically charged with respect to the vector field in the Betti multiplet. By extremizing the entropy functional with baryonic flux, we compute the entropy and find that it agrees with the entropy of an explicit solution in a four-dimensional gauged supergravity which is a consistent truncation of eleven-dimensional supergravity in AdS 4 × M 1,1,1 . arXiv:1904.05344v2 [hep-th]

Section: Discussionmentioning

confidence: 95%

Black holes with baryonic charge and $$ \mathcal{I} $$ -extremization

Kim

2019

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“…This fact might indicate some problem in taking the large-N limit or, more drastically, it can mean that these theories do not describe SCFTs on M2-branes. The answer is still inconclusive, even though some partial results pointing in the first direction have appeared in the literature [31,48,49,50]. One of the main purposes of this paper is, in the spirit of similar calculations for 4d SCFTs (SCFT 4 ) [51,52,53,54], to explicitly show the agreement between the field theoretic and gravity determinations of the free energy in infinite classes of models with an arbitrarily large number of gauge groups.…”

Section: Introductionmentioning

confidence: 85%

Free energy v.s. Sasaki-Einstein volume for infinite families of M2-brane theories

Amariti

Franco

2012

Abstract:We investigate infinite families of 3d N = 2 superconformal Chern-Simons quivers with an arbitrarily large number of gauge groups arising on M2-branes over toric CY 4 's. These theories have the same matter content and superpotential of those on D3-branes probing cones over L a,b,a Sasaki-Einstein manifolds. For all these infinite families, we explicitly show the correspondence between the free energy F on S 3 and the volume of the 7-dimensional base of the associated CY 4 , even before extremization. Symmetries of the toric diagram are exploited for reducing the dimensionality of the space over which the volume of the Sasaki-Einstein manifold is extremized. Similarly, the space of trial Rcharges of the gauge theory is constrained using symmetries of the quiver. Our results add to those existing in the literature, providing further support for the correspondence. We develop a lifting algorithm, based on the Type IIB realization of these theories, that takes from CY 3 's to CY 4 's and we use it to efficiently generate the models studied in the paper. Finally, we show that in all the infinite families we consider F 2 can be expressed, even offshell, as a quartic function in R-charges associated to certain 5-cycles. This suggests that a quartic formula on R-charges, analogous to a similar cubic function for the central charge a in 4d, exists for all toric toric CY 4 's and we present some ideas regarding its general form.

“…Hence, we integrate * 11 F 4 + 1 2 A 3 ∧ F 4 over various seven-cycles and calculate the so-called Page charge, which is the correct quantity to be quantized [47]. 28 Let us begin with the ansatz for the three-form potential (2.5)…”

Section: Jhep03(2021)108mentioning

confidence: 99%

“…For N = 2 Chern-Simons theories with chiral quiver, it is known that the matrix model to calculate the free energy on S 3 is not working[25]. An alternative prescription for calculating the free energy was proposed by[26,27] and further studied in[11,28] 3. Recently, S SUSY for rotating AdS4 black holes is constructed in[40].…”

mentioning

confidence: 99%

Uplifting dyonic AdS4 black holes on seven-dimensional Sasaki-Einstein manifolds

Kim

2021

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We revisit non-rotating, dyonically charged, and supersymmetric AdS4 black holes, which are solutions of $$ \mathcal{N} $$ N = 2 gauged supergravity with vector- and hyper-multiplets. Uplifting the near horizon solutions to D = 11 supergravity on seven-dimensional Sasaki-Einstein manifolds, we show that dyonic AdS4 black holes correspond to AdS2 solutions with electric and magnetic baryonic fluxes in D = 11 supergravity. We identify the off-shell AdS4 black hole solutions with parameters of D = 11 AdS2 solutions without imposing the equations of motion. We calculate the entropy of dyonic black holes, carefully analyzing the Page charge quantization conditions.