On the universal hydrodynamics of strongly coupled CFTs with gravity duals

It is known that the solutions of pure classical 5D gravity with $AdS_5$ asymptotics can describe strongly coupled large N dynamics in a universal sector of 4D conformal gauge theories. We show that when the boundary metric is flat we can uniquely specify the solution by the boundary stress tensor. We also show that in the Fefferman-Graham coordinates all these solutions have an integer Taylor series expansion in the radial coordinate (i.e. no $log$ terms). Specifying an arbitrary stress tensor can lead to two types of pathologies, it can either destroy the asymptotic AdS boundary condition or it can produce naked singularities. We show that when solutions have no net angular momentum, all hydrodynamic stress tensors preserve the asymptotic AdS boundary condition, though they may produce naked singularities. We construct solutions corresponding to arbitrary hydrodynamic stress tensors in Fefferman-Graham coordinates using a derivative expansion. In contrast to Eddington-Finkelstein coordinates here the constraint equations simplify and at each order it is manifestly Lorentz covariant. The regularity analysis, becomes more elaborate, but we can show that there is a unique hydrodynamic stress tensor which gives us solutions free of naked singularities. In the process we write down explicit first order solutions in both Fefferman-Graham and Eddington-Finkelstein coordinates for hydrodynamic stress tensors with arbitrary $\eta/s$. Our solutions can describe arbitrary (slowly varying) velocity configurations. We point out some field-theoretic implications of our general results.Comment: 39 pages, two appendices added, in appendix A the proof of the power series solution has been detailed, in appendix B, we have commented on method of fixing $\eta/s$ by calculating curvature invariant

Ads(3)/CFT(2) to Ads(2)/CFT(1)

It has been suggested that the quantum generalization of the Wald entropy for an extremal black hole is the logarithm of the ground state degeneracy of a dual quantum mechanics in a fixed charge sector. We test this proposal for supersymmetric extremal BTZ black holes for which there is an independent definition of the quantum entropy as the logarithm of the degeneracy of appropriate states in the dual 1+1 dimensional superconformal field theory. We find that the two proposals agree. This analysis also suggests a possible route to deriving the OSV conjecture.Comment: LaTeX file, 14 pages; v2: references added; v3: comments and refernces added; v4: expanded discussion on the role of cut-of

Heat Kernels on the AdS(2) cone and Logarithmic Corrections to Extremal Black Hole Entropy

We develop new techniques to efficiently evaluate heat kernel coefficients for the Laplacian in the short-time expansion on spheres and hyperboloids with conical singularities. We then apply these techniques to explicitly compute the logarithmic contribution to black hole entropy from an N=4 vector multiplet about a Z(N) orbifold of the near-horizon geometry of quarter--BPS black holes in N=4 supergravity. We find that this vanishes, matching perfectly with the prediction from the microstate counting. We also discuss possible generalisations of our heat kernel results to higher-spin fields over Z(N) orbifolds of higher-dimensional spheres and hyperboloids.Comment: 41 page

Logarithmic Corrections to Extremal Black Hole Entropy in N = 2, 4 and 8 Supergravity

We compute the logarithmic correction to black hole entropy about exponentially suppressed saddle points of the Quantum Entropy Function corresponding to Z(N) orbifolds of the near horizon geometry of the extremal black hole under study. By carefully accounting for zero mode contributions we show that the logarithmic contributions for quarter--BPS black holes in N=4 supergravity and one--eighth BPS black holes in N=8 supergravity perfectly match with the prediction from the microstate counting. We also find that the logarithmic contribution for half--BPS black holes in N = 2 supergravity depends non-trivially on the Z(N) orbifold. Our analysis draws heavily on the results we had previously obtained for heat kernel coefficients on Z(N) orbifolds of spheres and hyperboloids in arXiv:1311.6286 and we also propose a generalization of the Plancherel formula to Z(N) orbifolds of hyperboloids to an expression involving the Harish-Chandra character of SL(2,R), a result which is of possible mathematical interest.Comment: 40 page

Supersymmetric Localization for BPS Black Hole Entropy: 1-loop Partition Function from Vector Multiplets

We use the techniques of supersymmetric localization to compute the BPS black hole entropy in N=2 supergravity. We focus on the n_v+1 vector multiplets on the black hole near horizon background which is AdS_2 x S^2 space. We find the localizing saddle point of the vector multiplets by solving the localization equations, and compute the exact one loop partition function on the saddle point. Furthermore, we propose the appropriate functional integration measure. Through this measure, the one loop determinant is written in terms of the radius of the physical metric, which depends on the localizing saddle point value of the vector multiplets. The result for the one loop determinant is consistent with the logarithmic corrections to the BPS black hole entropy from vector multiplets.Comment: 28+16 pages, improved discussion on the boundary mode in the 4.2 and conclusion sectio

ϵ\epsilon-Expansion in the Gross-Neveu Model from Conformal Field Theory

We compute the anomalous dimensions of a class of operators of the form $(\bar\psi\psi)^p$ and $(\bar\psi\psi)^p\psi$ to leading order in $\epsilon$ in the Gross-Neveu model in $2+\epsilon$ dimensions. We use the techniques developed in arXiv: 1505.00963.Comment: 16 pages, some explanations in section 2 improved, references added and typos correcte

Logarithmic Corrections to Twisted Indices from the Quantum Entropy Function

We compute logarithmic corrections to the twisted index $B^g_6$ in four-dimensional $\mathcal{N}=4$ and $\mathcal{N}=8$ string theories using the framework of the Quantum Entropy Function. We find that these vanish, matching perfectly with the large--charge expansion of the corresponding microscopic expressions.Comment: v2 : 22 pages, presentation significantly improved, published in JHE

Shell closure effects studied via cluster decay in heavy nuclei

The effects of shell closure in nuclei via the cluster decay is studied. In this context, we have made use of the Preformed Cluster Model ($PCM$) of Gupta and collaborators based on the Quantum Mechanical Fragmentation Theory. The key point in the cluster radioactivity is that it involves the interplay of close shell effects of parent and daughter. Small half life for a parent indicates shell stabilized daughter and long half life indicates the stability of the parent against the decay. In the cluster decay of trans lead nuclei observed so far, the end product is doubly magic lead or its neighbors. With this in our mind we have extended the idea of cluster radioactivity. We investigated decay of different nuclei where Zirconium is always taken as a daughter nucleus, which is very well known deformed nucleus. The branching ratio of cluster decay and $\alpha$-decay is also studied for various nuclei, leading to magic or almost doubly magic daughter nuclei. The calculated cluster decay half-life are in well agreement with the observed data. First time a possibility of cluster decay in $^{218}U$ nucleus is predicted