Clifford V. Johnson

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. @S0556-2821~99!02316-4#

Holography, thermodynamics, and fluctuations of charged AdS black holes

The physical properties of Reissner-Nordstrom black holes in (n11)-dimensional anti-de Sitter spacetime are related, by a holographic map, to the physics of a class of n-dimensional field theories coupled to a background global current. Motivated by that fact, and the recent observations of the striking similarity between the thermodynamic phase structure of these black holes ~in the canonical ensemble! and that of the van der Waals-Maxwell liquid-gas system, we explore the physics in more detail. We study fluctuations and stability within the equilibrium thermodynamics, examining the specific heats and electrical permittivity of the holes, and consider the analogue of the Clayperon equation at the phase boundaries. Consequently, we refine the phase diagrams in the canonical and grand canonical ensembles. We study the interesting physics in the neighborhood of the critical point in the canonical ensemble. There is a second order phase transition found there, and that region is characterized by a Landau-Ginzburg model with A3 potential. The holographically dual field theories provide the description of the microscopic degrees of freedom which underlie all of the thermodynamics, as can be seen by examining the form of the microscopic fluctuations. @S0556-2821~99!06820-4#

Gauge theory and the excision of repulson singularities

We study brane configurations that give rise to large-N gauge theories with eight supersymmetries and no hypermultiplets. These configurations include a variety of wrapped, fractional, and stretched branes or strings. The corresponding spacetime geometries which we study have a distinct kind of singularity known as a repulson. We find that this singularity is removed by a distinctive mechanism, leaving a smooth geometry with a core having an enhanced gauge symmetry. The spacetime geometry can be related to large-N Seiberg-Witten theory.

D-brane primer

Following is a collection of lecture notes on D-branes, which may be used by the reader as preparation for applications to modern research applications such as: the AdS/CFT and other gauge theory/geometry correspondences, Matrix Theory and stringy non-commutative geometry, etc. In attempting to be reasonably self-contained, the notes start from classical point-particles and develop the subject logically (but selectively) through classical strings, quantisation, D-branes, supergravity, superstrings, string duality, including many detailed applications. Selected focus topics feature D-branes as probes of both spacetime and gauge geometry, highlighting the role of world-volume curvature and gauge couplings, with some non-Abelian cases. Other advanced topics which are discussed are the (presently) novel tools of research such as fractional branes, the enhancon mechanism, D(ielectric)-branes and the emergence of the fuzzy/non-commutative sphere.

Aspects of type IIB theory on asymptotically locally Euclidean 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 IR×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 ‘HyperKähler 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.

A holographic superconductor in an external magnetic field

We study a system of a complex charged scalar coupled to a Reissner-Nordstr?m black hole in 3+1 dimensional anti-de Sitter spacetime, neglecting back-reaction. With suitable boundary conditions, the cases of a neutral and purely electric black hole have been studied in various limits and were shown to yield key elements of superconductivity in the dual 2+1 dimensional field theory, forming a condensate below a critical temperature. By adding magnetic charge to the black hole, we immerse the superconductor into an external magnetic field. We show that a family of condensates can form and we examine their structure. For finite magnetic field, they are localized in one dimension with a profile that is exactly solvable, since it maps to the quantum harmonic oscillator. As the magnetic field increases, the condensate shrinks in size, which is reminiscent of the Meissner effect.

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 a conjectured holographic technique for its computation. We study a thermal quench, dual to the addition of a shell of uncharged matter to four-dimensional anti-de Sitter (AdS4) 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 AdS4, 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. We briefly discuss the possible origin of the new phenomena in terms of the features of the conjectured dual field theory.

Orientifolds, Branes, and Duality of 4D Gauge Theories

Recently, a D-brane construction in type IIA string theory was shown to yield the electric/magnetic duality of four-dimensional N = 1 supersymmetric U(Nc) gauge theories with Nf flavours of quark. We present here an extension of that construction which yields the electric/magnetic duality for the SO(Nc) and USp(Nc) gauge theories with Nf quarks, by adding an orientifold plane which is consistent with the supersymmetry. Due to the intersection of the orientifold plane with the NS-NS fivebranes already present, new features arise which are crucial in determining the correct final structure of the dualities.

Entropy of 4D Extremal Black Holes

We derive the Bekenstein-Hawking entropy formula for four-dimensional Reissner- Nordstrom extremal black holes in type II string theory. The derivation is performed in two separate (T-dual) weak coupling pictures. One uses a type IIB bound state problem of D5- and D1-branes, while the other uses a bound state problem of D0- and D4-branes with macroscopic fundamental type IIA strings. In both cases, the D-brane systems are also bound to a Kaluza-Klein monopole, which then yields the four-dimensional black hole at strong coupling.

Flavoured large N gauge theory in an external magnetic field

We consider a D7-brane probe of AdS5 × S5 in the presence of pure gauge B-field. In the dual gauge theory, the B-field couples to the fundamental matter introduced by the D7-brane and acts as an external magnetic field. The B-field supports a 6-form Ramond-Ramond potential on the D7-branes world volume that breaks the supersymmetry and enables the dual gauge theory to develop a non-zero fermionic condensate. We explore the dependence of the fermionic condensate on the bare quark mass mq and show that at zero bare quark mass a chiral symmetry is spontaneously broken. A study of the meson spectrum reveals a coupling between the vector and scalar modes, and in the limit of weak magnetic field we observe Zeeman splitting of the states. We also observe the characteristic √mq dependence of the ground state corresponding to the Goldstone boson of spontaneously broken chiral symmetry.