Abstract:We construct the black hole geometry dual to the deconfined phase of the BMN matrix model at strong 't Hooft coupling. We approach this solution from the limit of large temperature where it is approximately that of the non-extremal D0-brane geometry with a spherical S 8 horizon. This geometry preserves the SO(9) symmetry of the matrix model trivial vacuum. As the temperature decreases the horizon becomes deformed and breaks the SO(9) to the SO(6) × SO(3) symmetry of the matrix model. When the black hole free energy crosses zero the system undergoes a phase transition to the confined phase described by a Lin-Maldacena geometry. We determine this critical temperature, whose computation is also within reach of Monte Carlo simulations of the matrix model.

We consider solutions in Einstein-Maxwell theory with a negative cosmological constant that asymptote to global AdS 4 with conformal boundary S 2 × R t . At the sphere at infinity we turn on a space-dependent electrostatic potential, which does not destroy the asymptotic AdS behaviour. For simplicity we focus on the case of a dipolar electrostatic potential. We find two new geometries: (i) an AdS soliton that includes the full backreaction of the electric field on the AdS geometry; (ii) a polarised neutral black hole that is deformed by the electric field, accumulating opposite charges in each hemisphere. For both geometries we study boundary data such as the charge density and the stress tensor. For the black hole we also study the horizon charge density and area, and further verify a Smarr formula. Then we consider this system at finite temperature and compute the Gibbs free energy for both AdS soliton and black hole phases. The corresponding phase diagram generalizes the Hawking-Page phase transition. The AdS soliton dominates the low temperature phase and the black hole the high temperature phase, with a critical temperature that decreases as the external electric field increases. Finally, we consider the simple case of a free charged scalar field on S 2 × R t with conformal coupling. For a field in the SU (N ) adjoint representation we compare the phase diagram with the above gravitational system. arXiv:1511.08505v1 [hep-th] 26 Nov 2015 ✓ AdS Boundary AdS Soliton ✓ Black Hole

We numerically construct asymptotically AdS 4 solutions to Einstein-Maxwell-dilaton theory. These have a dipolar electrostatic potential turned on at the conformal boundary S 2 × R t . We find two classes of geometries: AdS soliton solutions that encode the full backreaction of the electric field on the AdS geometry without a horizon, and neutral black holes that are "polarised" by the dipolar potential. For a certain range of the electric field E, we find two distinct branches of the AdS soliton that exist for the same value of E. For the black hole, we find either two or four branches depending on the value of the electric field and horizon temperature. These branches meet at critical values of the electric field and impose a maximum value of E that should be reflected in the dual field theory. For both the soliton and black hole geometries, we study boundary data such as the stress tensor. For the black hole, we also consider horizon observables such as the entropy. At finite temperature, we consider the Gibbs free energy for both phases and determine the phase transition between them. We find that the AdS soliton dominates at low temperature for an electric field up to the maximum value. Using the gauge/gravity duality, we propose that these solutions are dual to deformed ABJM theory and compute the corresponding weak coupling phase diagram.1 In the notation of [3] we set Φ 1 = Φ, Φ 2 = Φ 3 = 0, A = A 1 = −A 2 and A 3 = A 4 = 0.

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Based on string theory's framework, the gauge/gravity duality, also known as holography, has the ability to solve practical problems in low energy physical systems like metals and fluids. Holographic applications open a path for conversation and collaboration between the theorydriven, high energy culture of string theory and fields like nuclear and condensed matter physics, which in contrast place great emphasis on the empirical evidence that experiment provides. This paper takes a look at holography's history, from its roots in string theory to its present-day applications that are challenging the cultural identity of the field. I will focus on two of these applications: holographic QCD and holographic superconductivity, highlighting some of the (often incompatible) historical influences, motives, and epistemic values at play, as well as the subcultural shifts that help the collaborations work. The extent to which holographic research -arguably string theory's most successful and prolific area -must change its subcultural identity in order to function in fields outside of string theory reflects its changing nature and the uncertain future of the field. Does string theory lose its identity in the low-energy applications that holography provides? Does holography still belong under string theory's umbrella, or is it destined to form new subcultures with each of its fields of application? I find that the answers to these questions are dynamic, interconnected, and highly dependent on string theory's relationship with its field of application. In some cases, holography can maintain the goals and values it inherited from string theory. In others, it instead adopts the goals and values of the field in which it is applied. These examples highlight a growing need for the STS community to expand its treatment of string theory regarding its relationship with empiricism and role as a theory of quantum gravity.