A supermatrix model for N=6 super Chern-Simons-matter theory

We construct the Wilson loop operator of N=6 super Chern-Simons-matter which is invariant under half of the supercharges of the theory and is dual to the simplest macroscopic open string in AdS_4 x CP^3. The Wilson loop couples, in addition to the gauge and scalar fields of the theory, also to the fermions in the bi-fundamental representation of the U(N) x U(M) gauge group. These ingredients are naturally combined into a superconnection whose holonomy gives the Wilson loop, which can be defined for any representation of the supergroup U(N|M). Explicit expressions for loops supported along an infinite straight line and along a circle are presented. Using the localization calculation of Kapustin et al. we show that the circular loop is computed by a supermatrix model and discuss the connection to pure Chern-Simons theory with supergroup U(N|M).Comment: 23 page

Thermal photon production in a strongly coupled anisotropic plasma

Photons produced in heavy ion collisions escape virtually unperturbed from the surrounding medium, thus representing an excellent probe of the conditions at the emission point. Using the gauge/gravity duality, we calculate the rate of photon production in an anisotropic, strongly coupled N=4 plasma with Nf<<Nc quark flavors. We consider arbitrary orientations of the photon momentum with respect to the anisotropic direction, as well as arbitrary values of the anisotropy. We present results for the correlation functions of two electromagnetic currents and for the electric conductivity. These quantities can be larger or smaller than the isotropic ones, depending on the direction of propagation and polarization of the photons. The total production rate is however always larger than the isotropic one, independently of the frequency, direction of propagation, and value of the anisotropy.Comment: 27 pages, 13 figures; v2: minor changes, added reference

Physical quantities and dimensional analysis: from mechanics to quantum gravity

Physical quantities and physical dimensions are among the first concepts encountered by students in their undergraduate career. In this pedagogical review, I will start from these concepts and, using the powerful tool of dimensional analysis, I will embark in a journey through various branches of physics, from basic mechanics to quantum gravity. I will also discuss a little bit about the fundamental constants of Nature, the so-called "cube of Physics", and the natural system of units.Comment: 20 pages, 6 figures; v2: minor changes, reference added. Pedagogical article in Portuguese addressed to undergraduate student

A profusion of 1/21/2 BPS Wilson loops in N=4\mathcal{N}=4 Chern-Simons-matter theories

We initiate the study of $1/2$ BPS Wilson loops in $\mathcal{N}=4$ Chern-Simons-matter theories in three dimensions. We consider a circular or linear quiver with Chern-Simons levels $k$, $-k$ and $0$, and focus on loops preserving one of the two $SU(2)$ subgroups of the $R$-symmetry. In the cases with no vanishing Chern-Simons levels, we find a pair of Wilson loops for each pair of adjacent nodes on the quiver connected by a hypermultiplet (nodes connected by twisted hypermultiplets have Wilson loops preserving another set of supercharges). We expect this classical pairwise degeneracy to be lifted by quantum corrections. In the case with nodes with vanishing Chern-Simons terms connected by twisted hypermultiplets, we find that the usual $1/4$ BPS Wilson loops are automatically enlarged to $1/2$ BPS, as happens also in 3-dimensional Yang-Mills theory. When the nodes with vanishing Chern-Simons levels are connected by untwisted hypermultiplets, we do not find any Wilson loops coupling to those nodes which are classically invariant. Rather, we find several loops whose supersymmetry variation, while non zero, vanishes in any correlation function, so is weakly zero. We expect only one linear combination of those Wilson loops to remain BPS when quantum corrections are included. We analyze the M-theory duals of those Wilson loops and comment on their degeneracy. We also show that these Wilson loops are cohomologically equivalent to certain $1/4$ BPS Wilson loops whose expectation value can be evaluated by the appropriate localized matrix model.Comment: 40 page

Quantum 't Hooft operators and S-duality in N=4 super Yang-Mills

We provide a quantum path integral definition of an 't Hooft loop operator, which inserts a pointlike monopole in a four dimensional gauge theory. We explicitly compute the expectation value of the circular 't Hooft operators in N=4 super Yang-Mills with arbitrary gauge group G up to next to leading order in perturbation theory. We also compute in the strong coupling expansion the expectation value of the circular Wilson loop operators. The result of the computation of an 't Hooft loop operator in the weak coupling expansion exactly reproduces the strong coupling result of the conjectured dual Wilson loop operator under the action of S-duality. This paper demonstrates - for the first time - that correlation functions in N=4 super Yang-Mills admit the action of S-duality.Comment: 38 pages; v2: references added, typos fixe

The Chern-Simons diffusion rate from higher curvature gravity

An important transport coefficient in the study of non-Abelian plasmas is the Chern-Simons diffusion rate, which parameterizes the rate of transition among the degenerate vacua of a gauge theory. We compute this quantity at strong coupling, via holography, using two theories of gravity with higher curvature corrections, namely Gauss-Bonnet gravity and quasi-topological gravity. We find that these corrections may either increase or decrease the result obtained from Einstein's gravity, depending on the value of the couplings. The Chern-Simons diffusion rate for Gauss-Bonnet gravity decreases as the shear viscosity over entropy ratio is increased.Comment: 9 pages, 1 figure; v2: minor changes, added reference

Holographic renormalization and anisotropic black branes in higher curvature gravity

We consider five-dimensional AdS-axion-dilaton gravity with a Gauss-Bonnet term and find a solution of the equations of motion which corresponds to a black brane exhibiting a spatial anisotropy, with the source of the anisotropy being an axion field linear in one of the horizon coordinates. Our solution is static, regular everywhere on and outside the horizon, and asymptotically AdS. It is analytic and valid in a small anisotropy expansion, but fully non-perturbative in the Gauss-Bonnet coupling. We discuss various features of this solution and use it as a gravity dual to a strongly coupled anisotropic plasma with two independent central charges, $a\neq c$. In the limit of small Gauss-Bonnet coupling, we carry out holographic renormalization of the system using (a recursive variant of) the Hamilton-Jacobi method and derive a generic expression for the boundary stress tensor, which we later specialize to our solution. Finally, we compute the shear viscosity to entropy ratios and conductivities of this anisotropic plasma.Comment: 35 pages, 1 figure; v2: references adde

Spectral curves, emergent geometry, and bubbling solutions for Wilson loops

We study the supersymmetric circular Wilson loops of N=4 super Yang-Mills in large representations of the gauge group. In particular, we obtain the spectral curves of the matrix model which captures the expectation value of the loops. These spectral curves are then proven to be precisely the hyperelliptic surfaces that characterize the bubbling solutions dual to the Wilson loops, thus yielding an example of a geometry emerging from an eigenvalue distribution. We finally discuss the Wilson loop expectation value from the matrix model and from supergravity.Comment: 27 pages, 2 figures; v2: references adde

More on thermal probes of a strongly coupled anisotropic plasma

We extend the analysis of 1211.2199, where the photon production rate of an anisotropic strongly coupled plasma with Nf<<Nc massless quarks was considered. We allow here for non-vanishing quark masses and study how these affect the spectral densities and conductivities. We also compute another important probe of the plasma, the dilepton production rate. We consider generic angles between the anisotropic direction and the photon and dilepton wave vectors, as well as arbitrary quark masses and arbitrary values of the anisotropy parameter. Generically, the anisotropy increases the production rate of both photons and dileptons, compared with an isotropic plasma at the same temperature.Comment: 41 pages, 24 figures; v2: minor changes, added references; v3: added reference. Extends arXiv:1211.219

Half-BPS Geometries and Thermodynamics of Free Fermions

Solutions of type IIB supergravity which preserve half of the supersymmetries have a dual description in terms of free fermions, as elucidated by the "bubbling AdS" construction of Lin, Lunin and Maldacena. In this paper we study the half-BPS geometry associated with a gas of free fermions in thermodynamic equilibrium obeying the Fermi-Dirac distribution. We consider both regimes of low and high temperature. In the former case, we present a detailed computation of the ADM mass of the supergravity solution and find agreement with the thermal energy of the fermions. The solution has a naked null singularity and, by general arguments, is expected to develop a finite area horizon once stringy corrections are included. By introducing a stretched horizon, we propose a way to match the entropy of the fermions with the entropy of the geometry in the low temperature regime. In the opposite limit of high temperature, the solution resembles a dilute gas of D3 branes. Also in this case the ADM mass of the geometry agrees with the thermal energy of the fermions.Comment: 37 pages, 2 figures, latex; v2: minor corrections, references adde