CFT(4) Partition Functions and the Heat Kernel on AdS(5)

We explicitly reorganise the partition function of an arbitrary CFT in four spacetime dimensions into a heat kernel form for the dual string spectrum on AdS(5). On very general grounds, the heat kernel answer can be expressed in terms of a convolution of the one-particle partition function of the four-dimensional CFT. Our methods are general and would apply for arbitrary dimensions, which we comment on.Comment: 15 page

Logarithmic Corrections to Entropy of Magnetically Charged AdS4 Black Holes

We compute logarithmic corrections to the entropy of a magnetically charged extremal black hole in AdS4 x S7 using the quantum entropy function and discuss the possibility of matching against recently derived microscopic expressions.Comment: 14 page

On the Holography of Free Yang-Mills

We study the AdS$_5$/CFT$_4$ duality where the boundary CFT is free Yang-Mills theory with gauge group SU(N). At the planar level we use the spectrum and correlation functions of the boundary theory to explicate features of the bulk theory. Further, by computing the one-loop partition function of the bulk theory using the methods of arXiv:1603.05387, we argue that the bulk coupling constant should be shifted to $N^2$ from $N^2-1$. Similar conclusions are reached by studying the dualities in thermal AdS$_5$ with $S^1\times S^3$ boundary.Comment: 44 pages, version to appear in JHE

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

Exploring Free Matrix CFT Holographies at One-Loop

We extend our recent study on the duality between stringy higher spin theories and free CFTs in the $SU(N)$ adjoint representation to other matrix models namely the free $SO(N)$ and $Sp(N)$ adjoint models as well as the free $U(N)\times U(M)$ bi-fundamental and $O(N)\times O(M)$ bi-vector models. After determining the spectrum of the theories in the planar limit by Polya counting, we compute the one loop vacuum energy and Casimir energy for their respective bulk duals by means of the CIRZ method that we have introduced recently. We also elaborate on possible ambiguities in the application of this method.Comment: 37 pages, 7 figure

The Next-to-Simplest Quantum Field Theories

We describe new on-shell recursion relations for tree-amplitudes in N=1 and N=2 gauge theories and use these to show that the structure of the S-matrix in pure N=1 and N=2 gauge theories resembles that of pure Yang-Mills. We proceed to study gluon scattering in gauge theories coupled to matter in arbitrary representations. The contribution of matter to individual bubble and triangle coefficients can depend on the fourth and sixth order Indices of the matter representation respectively. So, the condition that one-loop amplitudes be free of bubbles and triangles can be written as a set of linear Diophantine equations involving these higher-order Indices. These equations simplify for supersymmetric theories. We present new examples of supersymmetric theories that have only boxes (and no triangles or bubbles at one-loop) and non-supersymmetric theories that are free of bubbles. In particular, our results indicate that one-loop scattering amplitudes in the N=2, SU(K) theory with a symmetric tensor hypermultiplet and an anti-symmetric tensor hypermultiplet are simple like those in the N=4 theory.Comment: 53 pages; (v2) reference to gravity dual and subsection on large N adde

Character Integral Representation of Zeta function in AdSd+1_{d+1}: II. Application to partially-massless higher-spin gravities

We compute the one-loop free energies of the type-A$_\ell$ and type-B$_\ell$ higher-spin gravities in $(d+1)$-dimensional anti-de Sitter (AdS$_{d+1}$) spacetime. For large $d$ and $\ell$, these theories have a complicated field content, and hence it is difficult to compute their zeta functions using the usual methods. Applying the character integral representation of zeta function developed in the companion paper arXiv:1805.05646 to these theories, we show how the computation of their zeta function can be shortened considerably. We find that the results previously obtained for the massless theories ($\ell=1$) generalize to their partially-massless counterparts (arbitrary $\ell$) in arbitrary dimensions.Comment: 39 pages; v2: references and subsection 6.3 on SU(N) matrix model added; v3: typo corrected in subsection 5.3.