We extend our analysis of a IIB supergravity solution dual to a spatially anisotropic finitetemperature N = 4 super Yang-Mills plasma. The solution is static, possesses an anisotropic horizon, and is completely regular. The full geometry can be viewed as a renormalization group flow from an AdS geometry in the ultraviolet to a Lifshitz-like geometry in the infrared. The anisotropy can be equivalently understood as resulting from a position-dependent θ-term or from a non-zero number density of dissolved D7-branes. The holographic stress tensor is conserved and anisotropic. The presence of a conformal anomaly plays an important role in the thermodynamics. The phase diagram exhibits homogeneous and inhomogeneous (i.e. mixed) phases. In some regions the homogeneous phase displays instabilities reminiscent of those of weakly coupled plasmas. We comment on similarities with QCD at finite baryon density and with the phenomenon of cavitation.

We present a IIB supergravity solution dual to a spatially anisotropic finite-temperature N = 4 super Yang-Mills plasma. The solution is static and completely regular. The full geometry can be viewed as a renormalization group flow from an ultraviolet AdS geometry to an infrared Lifshitz-like geometry. The anisotropy can be equivalently understood as resulting from a position-dependent θ-term or from a non-zero number density of dissolved D7-branes. The holographic stress tensor is conserved and anisotropic. The presence of a conformal anomaly plays an important role in the thermodynamics. The phase diagram exhibits homogeneous and inhomogeneous (i.e. mixed) phases. In some regions the homogeneous phase displays instabilities reminiscent of those of weakly coupled plasmas. We comment on similarities with QCD at finite baryon density and with the phenomenon of cavitation.1. Introduction. The realization that the quark-gluon plasma (QGP) produced in heavy ion collisions (HIC) is strongly coupled [1] has provided motivation for understanding the dynamics of strongly coupled non-Abelian plasmas through the gauge/string duality [2] (see [3] for a review of applications to the QGP). The simplest example of the duality is the equivalence between fourdimensional N = 4 SU (N c ) super Yang-Mills (SYM) theory and IIB string theory on AdS 5 × S 5 . Here we extend this example to the case in which the SYM plasma is spatially anisotropic. For accessibility by a broad audience, details will appear elsewhere [4]. Previous holographic studies of anisotropic plasmas include [5,6]. One important difference with the gravity solution of [6] is that the latter possesses a naked singularity, whereas our solution is completely regular.

We present a large new family of Wilson loop operators in N = 4 supersymmetric Yang-Mills theory. For an arbitrary curve on the three dimensional sphere one can add certain scalar couplings to the Wilson loop so it preserves at least two supercharges. Some previously known loops, notably the 1/2 BPS circle, belong to this class, but we point out many more special cases which were not known before and could provide further tests of the AdS/CFT correspondence.

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We study the isotropization of a homogeneous, strongly coupled, non-abelian plasma by means of its gravity dual. We compare the time evolution of a large number of initially anisotropic states as determined, on the one hand, by the full nonlinear Einstein's equations and, on the other, by the Einstein's equations linearized around the final equilibrium state. The linear approximation works remarkably well even for states that exhibit large anisotropies. For example, it predicts with a 20% accuracy the isotropization time, which is of the order of t(iso)≲1/T, with T the final equilibrium temperature. We comment on possible extensions to less symmetric situations.

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 × 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 ) × 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 ).

We analyze several aspects of the recent construction of three-dimensional conformal gauge theories by Aharony et al. in various regimes. We pay special attention to understanding how the M-theory geometry and interpretation can be extracted from the analysis of the field theory. We revisit the calculations of the moduli space of vacua and the complete characterization of chiral ring operators by analyzing the field theory compactified on a 2-sphere. We show that many of the states dual to these operators can be interpreted as D-brane states in the weak coupling limit.Also, various features of the dual AdS geometry can be obtained by performing a strong coupling expansion around moduli space configurations, even though one is not taking the planar expansion. In particular, we show that at strong coupling the corresponding weak coupling D-brane states of the chiral ring localize on particular submanifolds of the dual geometry that match the M-theory interpretation. We also study the massive spectrum of fields in the moduli space. We use this to investigate the dispersion relation of giant magnons from the field theory point of view. Our analysis predicts the exact functional form of the dispersion relation as a function of the world-sheet momentum, independently of integrability assumptions, but not the exact form with respect to the 't Hooft coupling. We also get the dispersion relation of bound states of giant magnons from first principles, providing evidence for the full integrability of the corresponding spin chain model at strong 't Hooft coupling.

We consider certain 1/4 BPS Wilson loop operators in SU(N) ${\cal N}=4$ supersymmetric Yang-Mills theory, whose expectation value can be computed exactly via supersymmetric localization. Holographically, these operators are mapped to fundamental strings in AdS5 x S5. The string on-shell action reproduces the large N and large coupling limit of the gauge theory expectation value and, according to the AdS/CFT correspondence, there should also be a precise match between subleading corrections to these limits. We perform a test of such match at next-to-leading order in string theory, by deriving the spectrum of quantum fluctuations around the classical string solution and by computing the corresponding 1-loop effective action. We discuss in detail the supermultiplet structure of the fluctuations. To remove a possible source of ambiguity in the ghost zero mode measure, we compare the 1/4 BPS configuration with the 1/2 BPS one, dual to a circular Wilson loop. We find a discrepancy between the string theory result and the gauge theory prediction, confirming a previous result in the literature. We are able to track the modes from which this discrepancy originates, as well as the modes that by themselves would give the expected result.Comment: 5 pages; v2: 43 pages, long version fixing a mistake and altering the conclusion