Zero Temperature Limit of Holographic Superconductors

We consider holographic superconductors whose bulk description consists of gravity minimally coupled to a Maxwell field and charged scalar field with general potential. We give an analytic argument that there is no "hard gap": the real part of the conductivity at low frequency remains nonzero (although typically exponentially small) even at zero temperature. We also numerically construct the gravitational dual of the ground state of some holographic superconductors. Depending on the charge and dimension of the condensate, the infrared theory can have emergent conformal or just Poincare symmetry. In all cases studied, the area of the horizon of the dual black hole goes to zero in the extremal limit, consistent with a nondegenerate ground state.Comment: 27 pages, 8 figure

On (multi-)center branes and exact string vacua

Multicenter supergravity solutions corresponding to Higgs phases of supersymmetric Yang-Mills theories are considered. For NS5 branes we identify three cases where there is a description in terms of exact conformal field theories. Other supergravity solutions, such as D3-branes with angular momentum, are understood as special limits of multicenter ones. Within our context we also consider 4-dim gravitational multi-instantons.Comment: 9 pages, latex; To be published in the proceedings of the Quantum Aspects of Gauge Theories, Supersymmetry and Unification, Corfu, Greece, 20-26 September 199

Gauge Theory Correlators from Non-Critical String Theory

We suggest a means of obtaining certain Green's functions in 3+1-dimensional ${\cal N} = 4$ supersymmetric Yang-Mills theory with a large number of colors via non-critical string theory. The non-critical string theory is related to critical string theory in anti-deSitter background. We introduce a boundary of the anti-deSitter space analogous to a cut-off on the Liouville coordinate of the two-dimensional string theory. Correlation functions of operators in the gauge theory are related to the dependence of the supergravity action on the boundary conditions. From the quadratic terms in supergravity we read off the anomalous dimensions. For operators that couple to massless string states it has been established through absorption calculations that the anomalous dimensions vanish, and we rederive this result. The operators that couple to massive string states at level $n$ acquire anomalous dimensions that grow as 2\left (n g_{YM} \sqrt {2 N} )^{1/2} for large `t Hooft coupling. This is a new prediction about the strong coupling behavior of large $N$ SYM theory.Comment: 15 pages, harvmac with btxmac; minor revisions, 1 reference added, the version to appear in Physics Letters

Tachyon Condensation and Black Strings

We show that under certain conditions, closed string tachyon condensation produces a topology changing transition from black strings to Kaluza-Klein "bubbles of nothing." This can occur when the curvature at the horizon is much smaller than the string scale, so the black string is far from the correspondence point when it would make a transition to an excited fundamental string. This provides a dramatic new endpoint to Hawking evaporation. A similar transition occurs for black p-branes, and can be viewed as a nonextremal version of a geometric transition. Applications to AdS black holes and the AdS soliton are also discussed.Comment: 23 pages, 1 figure, v2: references adde

Introduction to Holographic Superconductors

These lectures give an introduction to the theory of holographic superconductors. These are superconductors that have a dual gravitational description using gauge/gravity duality. After introducing a suitable gravitational theory, we discuss its properties in various regimes: the probe limit, the effects of backreaction, the zero temperature limit, and the addition of magnetic fields. Using the gauge/gravity dictionary, these properties reproduce many of the standard features of superconductors. Some familiarity with gauge/gravity duality is assumed. A list of open problems is included at the end.Comment: 34 pages, 10 figures, to appear in the proceedings of the 5th Aegean Summer School, "From Gravity to Thermal Gauge Theories: the AdS/CFT Correspondence"; v2: references adde

Vector Meson Propagator and Baryon Current Conservation

If baryons couple only with $\omega$-mesons, one found the baryon spectral function may be negative. We show this unacceptable result is caused by the $k_\mu k_\nu$-terms in the $\omega$-meson propagator. Their contribution may not vanish in approximate calculations which violate the baryon current conserves. A rule is suggested, by which the calculated baryon spectral function is well behaved.Comment: 9 pages (LaTeX file), 3 figures (PostScript file

Negative Energy, Superluminosity and Holography

The holographic connection between large $N$ Super Yang Mills theory and gravity in anti deSitter space requires unfamiliar behavior of the SYM theory in the limit that the curvature of the AdS geometry becomes small. The paradoxical behavior includes superluminal oscillations and negative energy density. These effects typically occur in the SYM description of events which take place far from the boundary of AdS when the signal from the event arrives at the boundary. The paradoxes can be resolved by assuming a very rich collection of hidden degrees of freedom of the SYM theory which store information but give rise to no local energy density. These degrees of freedom, called precursors, are needed to make possible sudden apparently acausal energy momentum flows. Such behavior would be impossible in classical field theory as a consequence of the positivity of the energy density. However we show that these effects are not only allowed in quantum field theory but that we can model them in free quantum field theory.Comment: Expanded version replacing earlier hep-th/990218

Stability of the non-extremal enhancon solution I: perturbation equations

We consider the stability of the two branches of non-extremal enhancon solutions. We argue that one would expect a transition between the two branches at some value of the non-extremality, which should manifest itself in some instability. We study small perturbations of these solutions, constructing a sufficiently general ansatz for linearised perturbations of the non-extremal solutions, and show that the linearised equations are consistent. We show that the simplest kind of perturbation does not lead to any instability. We reduce the problem of studying the more general spherically symmetric perturbation to solving a set of three coupled second-order differential equations.Comment: 20 pages, 1 figure, references added, typos fixed, version to appear in PR

Rotating nonuniform black string solutions

We explore via linearized perturbation theory the Gregory-Laflamme instability of rotating black strings with equal magnitude angular momenta. Our results indicate that the Gregory-Laflamme instability persists up to extremality for all even dimensions between six and fourteen. We construct rotating nonuniform black strings with two equal magnitude angular momenta in six dimensions. We see a first indication for the occurrence of a topology changing transition, associated with such rotating nonuniform black strings. Charged nonuniform black string configurations in heterotic string theory are also constructed by employing a solution generation technique.Comment: 36 pages, 10 figures, final versio

Black Holes on Cylinders

We take steps toward constructing explicit solutions that describe non-extremal charged dilatonic branes of string/M-theory with a transverse circle. Using a new coordinate system we find an ansatz for the solutions with only one unknown function. We show that this function is independent of the charge and our ansatz can therefore also be used to construct neutral black holes on cylinders and near-extremal charged dilatonic branes with a transverse circle. For sufficiently large mass $M > M_c$ these solutions have a horizon that connects across the cylinder but they are not translationally invariant along the circle direction. We argue that the neutral solution has larger entropy than the neutral black string for any given mass. This means that for $M > M_c$ the neutral black string can gain entropy by redistributing its mass to a solution that breaks translational invariance along the circle, despite the fact that it is classically stable. We furthermore explain how our construction can be used to study the thermodynamics of Little String Theory.Comment: latex, 68 pages, 4 figures. v2: Typos fixed, argument about \chi corrected in sec. 7.4, discussion of space of physical solutions corrected and clarified in sec. 9; v3: v=\pi clarified, typos fixed, figure 1 change