Non-local observables at finite temperature in AdS/CFT

Within gauge/gravity duality, we consider the AdS-Schwarzschild metric in arbitrary dimensions. We obtain analytical closed-form results for the two-point function, Wilson loop and entanglement entropy for strip geometries in the finite-temperature field-theory dual. According to the duality, these are given by the area of minimal surfaces of different dimension in the gravity background. Our analytical results involve generalised hypergeometric functions. We show that they reproduce known numerical results to great accuracy. Our results allow to identify new physical behaviour: For instance, we consider the entanglement density, i.e. the difference of entanglement entropies at finite and vanishing temperature divided by the volume of the entangling region. For field theories of dimension seven or higher, we find that the entanglement density displays non-monotonic behaviour as function of l*T, with l the strip width and T the temperature. This implies that the area theorem, proven for RG flows in general dimensions, does not apply here. This may signal the emergence of new degrees of freedom for AdS Schwarzschild black holes in eight or more dimensions.Comment: 42 pages + appendi

Superconductivity from gauge/gravity duality with flavor

We consider thermal strongly-coupled N=2 SYM theory with fundamental matter at finite isospin chemical potential. Using gauge/gravity duality, i.e. a probe of two flavor D7-branes embedded in the AdS black hole background, we find a critical temperature at which the system undergoes a second order phase transition. The critical exponent of this transition is one half and coincides with the result from mean field theory. In the thermodynamically favored phase, a flavor current acquires a vev and breaks an Abelian symmetry spontaneously. This new phase shows signatures known from superconductivity, such as an infinite dc conductivity and a gap in the frequency-dependent conductivity. The gravity setup allows for an explicit identification of the degrees of freedom in the dual field theory, as well as for a dual string picture of the condensation process.Comment: 11 pages, 5 figure

Information geometry in quantum field theory: lessons from simple examples

Motivated by the increasing connections between information theory and high-energy physics, particularly in the context of the AdS/CFT correspondence, we explore the information geometry associated to a variety of simple systems. By studying their Fisher metrics, we derive some general lessons that may have important implications for the application of information geometry in holography. We begin by demonstrating that the symmetries of the physical theory under study play a strong role in the resulting geometry, and that the appearance of an AdS metric is a relatively general feature. We then investigate what information the Fisher metric retains about the physics of the underlying theory by studying the geometry for both the classical 2d Ising model and the corresponding 1d free fermion theory, and find that the curvature diverges precisely at the phase transition on both sides. We discuss the differences that result from placing a metric on the space of theories vs. states, using the example of coherent free fermion states. We compare the latter to the metric on the space of coherent free boson states and show that in both cases the metric is determined by the symmetries of the corresponding density matrix. We also clarify some misconceptions in the literature pertaining to different notions of flatness associated to metric and non-metric connections, with implications for how one interprets the curvature of the geometry. Our results indicate that in general, caution is needed when connecting the AdS geometry arising from certain models with the AdS/CFT correspondence, and seek to provide a useful collection of guidelines for future progress in this exciting area.Comment: 36 pages, 2 figures; added new section and appendix, miscellaneous improvement

Superconformal Ward Identities for Green Functions with Multiple Supercurrent Insertions

Superconformal Ward identities for N=1 supersymmetric quantum field theories in four dimensions are convenienty obtained in the superfield formalism by combining diffeomorphisms and Weyl transformations on curved superspace. Using this approach we study the superconformal transformation properties of Green functions with one or more insertions of the supercurrent to all orders in perturbation theory. For the case of two insertions we pay particular attention to fixing the additional counterterms present, as well as to the purely geometrical anomalies which contribute to the transformation behaviour. Moreover we show in a scheme-independent way how the quasi-local terms in the Ward identities are related to similar terms which contribute to the supercurrent two and three point functions. Furthermore we relate our superfield approach to similar studies which use the component formalism by discussing the implications of our approach for the components of the supercurrent and of the supergravity prepotentials.Comment: 35 pages, AMSLaTeX Problems with older LaTeX versions fixed, no change of conten

The Perfect Atom: Bound States of Supersymmetric Quantum Electrodynamics

We study hydrogen-like atoms in N=1 supersymmetric quantum electrodynamics with an electronic and a muonic family. These atoms are bound states of an anti-muon and an electron or their superpartners. The exchange of a photino converts different bound states into each other. We determine the energy eigenstates and calculate the spectrum to fourth order in the fine structure constant. A difference between these perfect atoms and non-supersymmetric ones is the absence of hyperfine structure. We organize the eigenstates into super multiplets of the underlying symmetry algebra.Comment: 30 pages, 2 figures. v2: mistake associated with gauge choice fixed, references added. v3: comment about super-positronium added, published versio