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

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

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

Closed Form Effective Conformal Anomaly Actions in D≥\geq4

I present, in any D$\geq$4, closed-form type B conformal anomaly effective actions incorporating the logarithmic scaling cutoff dependence that generates these anomalies. Their construction is based on a novel class of Weyl-invariant tensor operators. The only known type A actions in D$\geq$4 are extensions of the Polyakov integral in D=2; despite contrary appearances, we show that their nonlocality does not conflict with general anomaly requirements. They are, however, physically unsatisfactory, prompting a brief attempt at better versions.Comment: 8 pages. Improved discussion of type A actions. Some references adde

Isospin diffusion in thermal AdS/CFT with flavor

We study the gauge/gravity dual of a finite temperature field theory at finite isospin chemical potential by considering a probe of two coincident D7-branes embedded in the AdS-Schwarzschild black hole background. The isospin chemical potential is obtained by giving a vev to the time component of the non-Abelian gauge field on the brane. The fluctuations of the non-Abelian gauge field on the brane are dual to the SU(2) flavor current in the field theory. For the embedding corresponding to vanishing quark mass, we calculate all Green functions corresponding to the components of the flavor current correlator. We discuss the physical properties of these Green functions, which go beyond linear response theory. In particular, we show that the isospin chemical potential leads to a frequency-dependent isospin diffusion coefficient.Comment: 26 pages, 8 figures, typos correcte