On the partition functions of higher spin black holes

We reconsider black hole solutions of D = 3 higher-spin gravity in the $hs[\lambda]\oplus hs[\lambda]$ Chern-Simons formulation. A suitable generalisation of the BTZ black hole has a spin-3 chemical potential $\alpha$, and non-zero values of all the conserved charges associated with the asymptotic $\mathcal W_\infty[\lambda]$ symmetry. We extend the available perturbative expansion of the partition function to order $\mathcal O(\alpha^{18})$ for generic values of the $\lambda$ parameter. The result matches the CFT prediction at $\lambda=0$ and at $\lambda=1$ where we provide the exact all-order expansion of the partition function. The perturbative series is then analysed in the interesting non-trivial limit $\lambda\to\infty$ and we derive the exact analytical expressions of the partition function and the spin-4 charge in closed form as functions of $\alpha$. Also, the first subleading correction at large $\lambda$ is shown to be simply related to the leading contribution.Comment: 15 pages, 4 figures. v2: more comments and reference

Y-system for Z_S Orbifolds of N=4 SYM

We propose a twisted Y-system for the calculation of leading wrapping corrections to physical states of general Z_S orbifold projections of N=4 super Yang-Mills theory. Agreement with available thermodynamical Bethe Ansatz results is achieved in the non supersymmetric case. Various examples of new computations, including other supersymmetric orbifolds are illustrated.Comment: 21 pages, 1 eps figur

Resummation of scalar correlator in higher spin black hole background

We consider the proposal that predicts holographic duality between certain 2D minimal models at large central charge and Vasiliev 3D higher spin gravity with a single complex field. We compute the scalar correlator in the background of a higher spin black hole at order $\mathcal O(\alpha^{5})$ in the chemical potential $\alpha$ associated with the spin-3 charge. The calculation is performed at generic values of the symmetry algebra \mbox{hs}[\lambda] parameter $\lambda$ and for the scalar in three different representations. We then study the perturbative data in the large $\lambda$ limit and discover remarkable regularities. This leads to formulate a closed formula for the resummation of the leading and subleading terms that scale like $\mathcal O(\alpha^{n}\lambda^{2n})$ and $\mathcal O(\alpha^{n}\,\lambda^{2n-1})$ respectively.Comment: 18 page

Reciprocity of higher conserved charges in the sl(2) sector of N=4 SYM

We extend the anlysis of the generalized Gribov-Lipatov reciprocity to the higher conserved charges of type IIB superstring on AdS5 x S5. The property is shown to hold for twist 2, and 3 operators in the sl(2) subsector.Comment: 5 pages. Poster presented at 'Nonlinear Physics. Theory and Experiment VI', Gallipoli (Italy) - June 23 - July 3, 201

Analysis of higher spin black holes with spin-4 chemical potential

We consider the $AdS_{3}/CFT_{2}$ duality between certain coset WZW theories at large central charge and Vasiliev 3D higher spin gravity with a single complex field. On the gravity side, we discuss a higher spin black hole solution with chemical potential coupled to the spin-4 charge. We compute the perturbative expansion of the higher spin charges and of the partition function at high order in the chemical potential. The result is obtained with its exact dependence on the parameter $\lambda$ characterising the symmetry algebra \mbox{hs}[\lambda]. The cases of $\lambda=0,1$ are successfully compared with a CFT calculation. The special point $\lambda=\infty$, the Bergshoeff-Blencowe-Stelle limit, is also solved in terms of the exact generating function for the partition function. The thermodynamics of both the spin-4 and the usual spin-3 black holes is studied in order to discuss the $\lambda$ dependence of the BTZ critical temperature $T_{\rm BTZ}(\lambda)$. In the spin-3 case, it is shown that $T_{\rm BTZ}(\lambda)$ converges for large $\lambda$ to the critical point of the $\lambda=\infty$ known partition function previously found by the authors. In the spin-4 black hole, the picture is qualitatively similar and $T_{\rm BTZ}(\infty)$ is accurately determined by various numerical methods.Comment: 27 pages, 6 figures, one more referenc

On the cusp anomalous dimension in the ladder limit of N=4\mathcal N=4 SYM

We analyze the cusp anomalous dimension in the (leading) ladder limit of $\mathcal N=4$ SYM and present new results for its higher-order perturbative expansion. We study two different limits with respect to the cusp angle $\phi$. The first is the light-like regime where $x = e^{i\,\phi}\to 0$. This limit is characterised by a non-trivial expansion of the cusp anomaly as a sum of powers of $\log x$, where the maximum exponent increases with the loop order. The coefficients of this expansion have remarkable transcendentality features and can be expressed by products of single zeta values. We show that the whole logarithmic expansion is fully captured by a solvable Woods-Saxon like one-dimensional potential. From the exact solution, we extract generating functions for the cusp anomaly as well as for the various specific transcendental structures appearing therein. The second limit that we discuss is the regime of small cusp angle. In this somewhat simpler case, we show how to organise the quantum mechanical perturbation theory in a novel efficient way by means of a suitable all-order Ansatz for the ground state of the associated Schr\"odinger problem. Our perturbative setup allows to systematically derive higher-order perturbative corrections in powers of the cusp angle as explicit non-perturbative functions of the effective coupling. This series approximation is compared with the numerical solution of the Schr\"odinger equation to show that we can achieve very good accuracy over the whole range of coupling and cusp angle. Our results have been obtained by relatively simple techniques. Nevertheless, they provide several non-trivial tests useful to check the application of Quantum Spectral Curve methods to the ladder approximation at non zero $\phi$, in the two limits we studied.Comment: 21 pages, 3 figure

Supergravity one-loop corrections on AdS_7 and AdS_3, higher spins and AdS/CFT

As was shown earlier, one-loop correction in 10d supergravity on AdS_5 x S^5 corresponds to the contributions to the vacuum energy and boundary 4d conformal anomaly which are minus the values for one n=4 Maxwell supermultiplet, thus reproducing the subleading term in their N^2-1 coefficient in the dual SU(N) SYM theory. We perform similar one-loop computations in 11d supergravity on AdS_7 x S^4 and 10d supergravity on AdS_3 x S^3 x T^4. In the AdS_7 case we find that the corrections to the 6d conformal anomaly a-coefficient and the vacuum energy are again minus the ones for one (2,0) tensor multiplet, suggesting that the total a-anomaly coefficient for the dual (2,0) theory is 4 N^3 - 9/4 N - 7/4 and thus vanishes for N=1. In the AdS_3 case the one-loop correction to the vacuum energy or 2d central charge turns out to be equal to that of one free (4,4) scalar multiplet, i.e. is c=+6. This reproduces the subleading term in the central charge c= 6(Q_1 Q_5 +1) of the dual 2d CFT describing decoupling limit of D5-D1 system. We also present the expressions for the 6d anomaly a-coefficient and vacuum energy for a general-symmetry higher spin field in AdS_7 and consider their application to tests of vectorial AdS/CFT with the boundary conformal 6d theory represented by free scalars, spinors or rank 2 antisymmetric tensors.Comment: 28 pages, v2 minor addition

Chiral trace relations in Ω\Omega-deformed N=2\mathcal N=2 theories

We consider $\mathcal N=2$ $SU(2)$ gauge theories in four dimensions (pure or mass deformed) and discuss the properties of the simplest chiral observables in the presence of a generic $\Omega$-deformation. We compute them by equivariant localization and analyze the structure of the exact instanton corrections to the classical chiral ring relations. We predict exact relations valid at all instanton number among the traces $\langle\text{Tr}\varphi^{n}\rangle$, where $\varphi$ is the scalar field in the gauge multiplet. In the Nekrasov-Shatashvili limit, such relations may be explained in terms of the available quantized Seiberg-Witten curves. Instead, the full two-parameter deformation enjoys novel features and the ring relations require non trivial additional derivative terms with respect to the modular parameter. Higher rank groups are briefly discussed emphasizing non-factorization of correlators due to the $\Omega$-deformation. Finally, the structure of the deformed ring relations in the $\mathcal N=2^{\star}$ theory is analyzed from the point of view of the Alday-Gaiotto-Tachikawa correspondence proving consistency as well as some interesting universality properties.Comment: 36 pages. v2 references adde

Reactive immunization on complex networks

Epidemic spreading on complex networks depends on the topological structure as well as on the dynamical properties of the infection itself. Generally speaking, highly connected individuals play the role of hubs and are crucial to channel information across the network. On the other hand, static topological quantities measuring the connectivity structure are independent on the dynamical mechanisms of the infection. A natural question is therefore how to improve the topological analysis by some kind of dynamical information that may be extracted from the ongoing infection itself. In this spirit, we propose a novel vaccination scheme that exploits information from the details of the infection pattern at the moment when the vaccination strategy is applied. Numerical simulations of the infection process show that the proposed immunization strategy is effective and robust on a wide class of complex networks