On Exactly Marginal Deformations Dual to BB-Field Moduli of IIB Theory on SE5_5

The complex dimension of the space of exactly marginal deformations for quiver CFTs dual to IIB theory compactified on $Y^{p,q}$ is known to be generically three. Simple general formulas already exist for two of the exactly marginal directions in the space of couplings, one of which corresponds to the sum of the (inverse squared of) gauge couplings, and the other to the $\beta$-deformation. Here we identify the third exactly marginal direction, which is dual to the modulus $\int B_{2}$ on the gravity side. This identification leads to a relation between the field theory gauge couplings and the vacuum expectation value of the gravity modulus that we further support by a computation related to the chiral anomaly induced by added fractional branes. We also present a simple algorithm for finding similar exactly marginal directions in any CFT described by brane tiling, and demonstrate it for the quiver CFTs dual to IIB theory compactified on $L^{1,5,2}$ and the Suspended Pinch Point.Comment: 28 pages, JHEP style. v2: minor corrections, added references and acknowledgements. v3: a number of speculative comments regarding the application of the Konishi anomaly equation to our problem are removed. v4: the proposal in Eq. (2.4) added back as a conjectur

Constraints on chiral operators in N=2 SCFTs

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Superconformal indices at large N and the entropy of AdS5 x SE5 black holes

The large N limit of the four-dimensional superconformal index was computed and successfully compared to the entropy of a class of AdS5 black holes only in the particular case of equal angular momenta. Using the Bethe ansatz formulation, we compute the index at large N with arbitrary chemical potentials for all charges and angular momenta, for general four-dimensional conformal theories with a holographic dual. We conjecture and bring some evidence that a particular universal contribution to the sum over Bethe vacua dominates the index at large N. For SYM, this contribution correctly leads to the entropy of BPS Kerr-Newman black holes in AdS5 x S5 for arbitrary values of the conserved charges, thus completing the microscopic derivation of their microstates. We also consider theories dual to AdS5 x SE5, where SE5 is a Sasaki-Einstein manifold. We first check our results against the so-called universal black hole. We then explicitly construct the near-horizon geometry of BPS Kerr-Newman black holes in AdS5 T^{1,1}, charged under the baryonic symmetry of the conifold theory and with equal angular momenta. We compute the entropy of these black holes using the attractor mechanism and find complete agreement with the field theory predictions

Holographic renormalization and supersymmetry

Holographic renormalization is a systematic procedure for regulating divergences in observables in asymptotically locally AdS spacetimes. For dual boundary field theories which are supersymmetric it is natural to ask whether this defines a supersymmetric renormalization scheme. Recent results in localization have brought this question into sharp focus: rigid supersymmetry on a curved boundary requires specific geometric structures, and general arguments imply that BPS observables, such as the partition function, are invariant under certain deformations of these structures. One can then ask if the dual holographic observables are similarly invariant. We study this question in minimal N = 2 gauged supergravity in four and five dimensions. In four dimensions we show that holographic renormalization precisely reproduces the expected field theory results. In five dimensions we find that no choice of standard holographic counterterms is compatible with supersymmetry, which leads us to introduce novel finite boundary terms. For a class of solutions satisfying certain topological assumptions we provide some independent tests of these new boundary terms, in particular showing that they reproduce the expected VEVs of conserved charges.Comment: 70 pages; corrected typo