Universal Holographic Chiral Dynamics in an External Magnetic Field

In this work we further extend the investigation of holographic gauge theories in external magnetic fields, continuing earlier work. We study the phenomenon of magnetic catalysis of mass generation in 1+3 and 1+2 dimensions, using D3/D7- and D3/D5-brane systems, respectively. We obtain the low energy effective actions of the corresponding pseudo Goldstone bosons and study their dispersion relations. The D3/D7 system exhibits the usual Gell-Mann--Oakes--Renner (GMOR) relation and a relativistic dispersion relation, while the D3/D5 system exhibits a quadratic non-relativistic dispersion relation and a modified linear GMOR relation. The low energy effective action of the D3/D5 system is related to that describing magnon excitations in a ferromagnet. We also study properties of general Dp/Dq systems in an external magnetic field and verify the universality of the magnetic catalysis of dynamical symmetry breaking.Comment: 41 pages, 11 figures, references adde

Evolution of Holographic Entanglement Entropy after Thermal and Electromagnetic Quenches

We study the evolution and scaling of the entanglement entropy after two types of quenches for a 2+1 field theory, using holographic techniques. We study a thermal quench, dual to the addition of a shell of uncharged matter to four dimensional Anti-de Sitter (AdS_4) spacetime, and study the subsequent formation of a Schwarzschild black hole. We also study an electromagnetic quench, dual to the addition of a shell of charged sources to AdS_4, following the subsequent formation of an extremal dyonic black hole. In these backgrounds we consider the entanglement entropy of two types of geometries, the infinite strip and the round disc, and find distinct behavior for each. Some of our findings naturally supply results analogous to observations made in the literature for lower dimensions, but we also uncover several new phenomena, such as (in some cases) a discontinuity in the time derivative of the entanglement entropy as it nears saturation, and for the electromagnetic quench, a logarithmic growth in the entanglement entropy with time for both the disc and strip, before settling to saturation.Comment: 30 pages, 19 figures. Corrected typos and added some discussion. To appear in New J. Phy

Taub--NUT Dyons in Heterotic String Theory

Starting with the Taub--NUT solution to Einstein's equations, together with a constant dilaton, a dyonic Taub--NUT solution of low energy heterotic string theory with non--trivial dilaton, axion and $U(1)$ gauge fields is constructed by employing $O(1,1)$ transformations. The electromagnetic dual of this solution is constructed, using SL(2,\rline) transformations. By an appropriate change to scaled variables, the extremal limit of the dual solution is shown to correspond to the low energy limit of an exact conformal field theory presented previously.Comment: 16 pages (plain TEX), (Revised version has curvature singularities correctly identified), IASSNS-HEP-94/50, McGill/94-2

Aspects of Type IIB Theory on ALE Spaces

D-brane technology and strong/weak coupling duality supplement traditional orbifold techniques by making certain background geometries more accessible. In this spirit, we consider some of the geometric properties of the type IIB theory on R^6 \times M where M is an `Asymptotically Locally Euclidean (ALE)' gravitational instanton. Given the self-duality of the theory, we can extract the geometry (both singular and resolved) seen by the weakly coupled IIB string by studying the physics of a D1-brane probe. The construction is both amusing and instructive, as the physics of the probe completely captures the mathematics of the construction of ALE instantons via `HyperKahler Quotients', as presented by Kronheimer. This relation has been noted by Douglas and Moore for the A-series. We extend the explicit construction to the case of the D- and E-series -- uncovering a quite beautiful structure -- and highlight how all of the elements of the mathematical construction find their counterparts in the physics of the type IIB D-string. We discuss the explicit ALE metrics which may be obtained using these techniques, and comment on the role duality plays in relating gauged linear sigma models to conformal field theories.Comment: 27 pages, three figures. Uses harvmac.tex and epsf.tex (sentences corrected on pages 13+14, reference added, small addition to final remarks

Penrose Limits, Deformed pp-Waves and the String Duals of N=1 Large n Gauge Theory

A certain conformally invariant N=1 supersymmetric SU(n) gauge theory has a description as an infra-red fixed point obtained by deforming the N=4 supersymmetric Yang-Mills theory by giving a mass to one of its N=1 chiral multiplets. We study the Penrose limit of the supergravity dual of the large n limit of this N=1 gauge theory. The limit gives a pp-wave with R-R five-form flux and both R-R and NS-NS three-form flux. We discover that this new solution preserves twenty supercharges and that, in the light-cone gauge, string theory on this background is exactly solvable. Correspondingly, this latter is the stringy dual of a particular large charge limit of the large n gauge theory. We are able to identify which operators in the field theory survive the limit to form the string's ground state and some of the spacetime excitations. The full string model, which we exhibit, contains a family of non-trivial predictions for the properties of the gauge theory operators which survive the limit.Comment: 39 pages, Late

Holographic Studies of Entanglement Entropy in Superconductors

We present the results of our studies of the entanglement entropy of a superconducting system described holographically as a fully back-reacted gravity system, with a stable ground state. We use the holographic prescription for the entanglement entropy. We uncover the behavior of the entropy across the superconducting phase transition, showing the reorganization of the degrees of freedom of the system. We exhibit the behaviour of the entanglement entropy from the superconducting transition all the way down to the ground state at T=0. In some cases, we also observe a novel transition in the entanglement entropy at intermediate temperatures, resulting from the detection of an additional length scale.Comment: 21 pages, 14 figures. v2:Clarified some remarks concerning stability. v3: Updated to the version that appears in JHE

Large N Phases, Gravitational Instantons and the Nuts and Bolts of AdS Holography

Recent results in the literature concerning holography indicate that the thermodynamics of quantum gravity (at least with a negative cosmological constant) can be modeled by the large N thermodynamics of quantum field theory. We emphasize that this suggests a completely unitary evolution of processes in quantum gravity, including black hole formation and decay; and even more extreme examples involving topology change. As concrete examples which show that this correspondence holds even when the space-time is only locally asymptotically AdS, we compute the thermodynamical phase structure of the AdS-Taub-NUT and AdS-Taub-Bolt spacetimes, and compare them to a 2+1 dimensional conformal field theory (at large N) compactified on a squashed three sphere, and on the twisted plane.Comment: 20 pages, three figures. (uses harvmac.tex and epsf.tex

Surface Terms as Counterterms in the AdS/CFT Correspondence

We examine the recently proposed technique of adding boundary counterterms to the gravitational action for spacetimes which are locally asymptotic to anti-de Sitter. In particular, we explicitly identify higher order counterterms, which allow us to consider spacetimes of dimensions d<=7. As the counterterms eliminate the need of ``background subtraction'' in calculating the action, we apply this technique to study examples where the appropriate background was ambiguous or unknown: topological black holes, Taub-NUT-AdS and Taub-Bolt-AdS. We also identify certain cases where the covariant counterterms fail to render the action finite, and we comment on the dual field theory interpretation of this result. In some examples, the case of vanishing cosmological constant may be recovered in a limit, which allows us to check results and resolve ambiguities in certain asymptotically flat spacetime computations in the literature.Comment: Revtex, 18 pages. References updated and few typo's fixed. Final versio

Charged AdS Black Holes and Catastrophic Holography

We compute the properties of a class of charged black holes in anti-de Sitter space-time, in diverse dimensions. These black holes are solutions of consistent Einstein-Maxwell truncations of gauged supergravities, which are shown to arise from the inclusion of rotation in the transverse space. We uncover rich thermodynamic phase structures for these systems, which display classic critical phenomena, including structures isomorphic to the van der Waals-Maxwell liquid-gas system. In that case, the phases are controlled by the universal `cusp' and `swallowtail' shapes familiar from catastrophe theory. All of the thermodynamics is consistent with field theory interpretations via holography, where the dual field theories can sometimes be found on the world volumes of coincident rotating branes.Comment: 19 pages, revtex, psfig, 6 multicomponent figures, typos, references and a few remarks have been repaired, and adde

A Conformal Field Theory of a Rotating Dyon

A conformal field theory representing a four-dimensional classical solution of heterotic string theory is presented. The low-energy limit of this solution has U(1) electric and magnetic charges, and also nontrivial axion and dilaton fields. The low-energy metric contains mass, NUT and rotation parameters. We demonstrate that this solution corresponds to part of an extremal limit of the Kerr-Taub-NUT dyon solution. This limit displays interesting `remnant' behaviour, in that asymptotically far away from the dyon the angular momentum vanishes, but far down the infinite throat in the neighbourhood of the horizon (described by our CFT) there is a non-zero angular velocity. A further natural generalization of the CFT to include an additional parameter is presented, but the full physical interpretation of its role in the resulting low energy solution is unclear.Comment: 43 pages, Plain TEX + epsf.tex for one uuencoded figure