arXiv subjects
Publications and source records attributed to Clifford V. Johnson.
Using the AdS/CFT correspondence, we show that the Anti-de Sitter (AdS) rotating (Kerr) black holes in five and seven dimensions provide us with examples of non-trivial field theories which are scale, but not conformally invariant. This is demonstrated by our computation of the actions and the stress-energy tensors of the four and six dimensional field theories residing on the boundary of these Kerr-AdS black holes spacetimes.
The presentation at Strings 2000 was intended to be in two main parts, but there was only time for part one. However both parts appeared on the online proceedings, and are also included in this document. The first part concerns an exploration of the connection between the physics of the `enhancon' geometry arising from wrapping N D6-branes on the K3 manifold in Type IIA string theory and that of a charge N BPS multi-monopole. This also relates to the physics of 2+1 dimensional SU(N) gauge theory with eight supercharges. The main results uncovered by this exploration are: a) better insight into the non-perturbative geometry of the enhancon; b) the structure of the moduli space geometry, and its characterisation in terms of generalisations of an Atiyah-Hitchin-like manifold; c) the use of Nahm data to describe aspects of the geometry, showing that the enhancon locus itself has a description as a fuzzy sphere. Part two discusses the addition of extra D2-branes into the geometry. Two probe computations show the difference between the geometry as seen by D2-branes and that seen by wrapped D6-branes, and the accompanying gauge theory interpretations are discussed.
Using the counterterm subtraction technique we calculatehe stress-energy tensor, action, and other physical quantities for Kerr-AdS black holes in various dimensions. For Kerr-AdS_5 with both rotation parameters non-zero, we demonstrate that stress-energy tensor, in the zero mass parameter limit, is equal to the stress tensor of the weakly coupled four dimensional dual field theory. As a result, the total energy of the generalKerr-AdS_5 black hole at zero mass parameter, exactly matches the Casimir energy of the dual field theory. We show that at high temperature, the general Kerr-AdS_5 and perturbative field theory stress-energy tensors are equal, up to the usual factor of 3/4. We also use the counterterm technique to calculate the stress tensors and actions for Kerr-AdS_6, and Kerr-AdS_7 black holes, with one rotation parameter, and we display the results. We discuss the conformal anomalies of the field theories dual to the Kerr-AdS_5 and Kerr-AdS_7 spacetimes. In these two field theories, we show that the rotation parameters break conformal invariance but not scale invariance, a novel result for a non-trivial field theory. For Kerr-AdS_7 the conformal anomalies calculated on the gravity side and the dual (0,2) tensor multiplet theory are equal up to 4/7 factor. We expect that the Casimir energy of the free field theory is the same as the energy of the Kerr-AdS_7 black hole (with zero mass parameter), up to that factor.
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.
We study the family of ten dimensional type IIB supergravity solutions corresponding to renormalisation group flows from N=4 to N=2 supersymmetric Yang-Mills theory. Part of the solution set corresponds to a submanifold of the Coulomb branch of the gauge theory, and we use a D3-brane probe to uncover details of this physics. At generic places where supergravity is singular, the smooth physics of the probe yields the correct one-loop form of the effective low energy gauge coupling. The probe becomes tensionless on a ring at finite radius. Supergravity flows which end on this ``enhancon'' ring correspond to the vacua where extra massless degrees of freedom appear in the gauge theory, and the gauge coupling diverges there. We identify an SL(2,Z) duality action on the enhancon ring which relates the special vacua, and comment on the massless dyons within them. We propose that the supergravity solution inside the enhancon ring should be excised, since the probe's tension is unphysical there.
We study the `enhancon', a spherical hypersurface apparently made of D-branes, which arises in string theory studies of large N SU(N) pure gauge theories with eight supercharges. When the gauge theory is 2+1 dimensional, the enhancon is an S^2. A relation to charge N BPS multi-monopoles is exploited to uncover many of its detailed properties. It is simply a spherical slice through an Atiyah-Hitchin-like submanifold of the charge $N$ BPS monopole moduli space. In the form of Nahm data, it is built from the N dimensional irreducible representation of SU(2). In this sense the enhancon is a non-commutative sphere, reminiscent of the spherical `dielectric' branes of Myers.
We present two examples of non-trivial field theories which are scale invariant, but not conformally invariant. This is done by placing certain field theories, which are conformally invariant in flat space, onto curved backgrounds of a specific type. We define this using the AdS/CFT correspondence, which relates the physics of gravity in asymptotically Anti-de Sitter (AdS) spacetimes to that of a conformal field theory (CFT) in one dimension fewer. The AdS rotating (Kerr) black holes in five and seven dimensions provide us with the examples, since by the correspondence we are able to define and compute the action and stress tensor of four and six dimensional field theories residing on rotating Einstein universes, using the ``boundary counterterm'' method. The rotation breaks conformal but not scale invariance. The AdS/CFT framework is therefore a natural arena for generating such examples of non-trivial scale invariant theories which are not conformally invariant.
We use the counterterm subtraction method to calculate the action and stress-energy-momentum tensor for the (Kerr) rotating black holes in AdS_{n+1}, for n=2, 3 and 4. We demonstrate that the expressions for the total energy for the Kerr-AdS_3 and Kerr-AdS_5 spacetimes, in the limit of vanishing black hole mass, are equal to the Casimir energies of the holographically dual n-dimensional conformal field theories. In particular, for Kerr-AdS_5, dual to the case of four dimensional N=4 supersymmetric Yang-Mills theory on the rotating Einstein universe, we explicitly verify the equality of the zero mass stress tensor from the two sides of the correspondence, and present the result for general mass as a prediction from gravity. Amusingly, it is observed in four dimensions that while the trace of the stress tensor defined using the standard counterterms does not vanish, its integral does, thereby keeping the action free of ultraviolet divergences. Using a different regularisation scheme another stress tensor can be defined, which is traceless.
Supergravity solutions related to large N SU(N) pure gauge theories with eight supercharges have recently been shown to give rise to an ``enhancon'', a new type of hypersurface made of D-branes. We show that enhancons also arise in similar situations pertaining to SO(2N+1), USp(2N) and SO(2N) gauge theories, using orientifolds. Enhancons therefore appear to come in types A, B, C, and D. The latter three differ globally from type A by having an extra Z_2 identification, and are distinguished locally by their subleading behaviour in large N. We focus mainly on 2+1 dimensional gauge theory, where a relation to M-theory and the Atiyah-Hitchin and Taub-NUT manifolds enables the construction of the smooth supergravity solution and the study of some of the 1/N corrections. The role of the enhancon in eleven dimensional supergravity is also uncovered. There is a close relation to certain multi-monopole moduli space problems.
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.
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.
The physical properties of Reissner-Nordstrom black holes in (n+1)-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 neighbourhood 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 A_3 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.
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.
This is a short arrangement of notes on D-branes, offered as an embellishment of five lectures which were presented at the 1998 Trieste Spring School entitled ``Non-Perturbative Aspects of String Theory and Supersymmetric Gauge Theory''. There is a good number of collections of pedagogical notes on D-branes in the literature, and since space here is limited, no attempt will be made to cover all of the introductory material again. Instead, the notes cover selected topics and themes in string theory and M-theory, emphasizing how certain technical aspects of D-branes play a role. The subject is developed mainly from the perspective of non-perturbative string theory, touching on aspects of the old matrix model, string duality, the new matrix model, the AdS/CFT correspondence and other gauge theory/geometry correspondences.
In SO(32) heterotic string theory, the space-time at the core of N coincident NS-fivebranes is an infinite throat, R x S^3. As shown by Witten, the throat signals a singularity in the usual heterotic string conformal field theory and a non--perturbative USp(2N) gauge group appears, due to the N small instantons at the fivebranes' core. Nevertheless, we look for some trace of the non-perturbative physics in a description of the heterotic string infinitely far down the throat. Our guide is a D1-brane probing N D5-branes in type I, which yields a 1+1 dimensional (0,4) supersymmetric model with ADHM data in its couplings, as shown by Douglas. The neighbourhood of the classical boundary of the hypermultiplet moduli space of the theory flows to an exact conformal field theory description of the throat theory. Ironically, the remnant of the non-perturbative symmetry is indeed found in the conformal field theory, lurking in the structure of the partition function, and encoded in a family of deformations of the theory along flat directions. The deformations have an explicit description using the flow from the type I theory, and have a hyperKahler structure. Similar results hold true for the analogous (4,4) supersymmetric situation in the type IIB theory, as is evident in the work of Diaconescu and Seiberg.
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.
The four six-dimensional ``little string'' theories are all described in the infinite momentum frame (IMF) as matrix theories by non-trivial 1+1 dimensional infra-red fixed points. We characterize these fixed points using supergravity. Starting from the matrix theory definition of M5-branes, we derive an associated dual supergravity description of the fixed point theories, arising as the near horizon geometry of certain brane configurations. These supergravity solutions are all smooth, and involve three dimensional Anti-de Sitter space AdS_3. They therefore provide a complete description of the fixed point theories, and hence the IMF little string theories, if the AdS/CFT correspondence holds.
We study the origins of the five ten-dimensional ``matrix superstring'' theories, supplementing old results with new ones, and find that they all fit into a unified framework. In all cases the matrix definition of the string in the limit of vanishingly small coupling is a trivial 1+1 dimensional infra-red fixed point (an orbifold conformal field theory) characterized uniquely by matrix versions of the appropriate Green-Schwarz action. The Fock space of the matrix string is built out of winding T-dual strings. There is an associated dual supergravity description in terms of the near horizon geometry of the fundamental string solution of those T-dual strings. The singularity at their core is related to the orbifold target space in the matrix theory. At intermediate coupling, for the IIB and SO(32) systems, the matrix string description is in terms of non-trivial 2+1 dimensional fixed points. Their supergravity duals involve Anti de-Sitter space (or an orbifold thereof) and are well-defined everywhere, providing a complete description of the fixed point theory. In the case of the type IIB system, the two extra organizational dimensions normally found in F-theory appear here as well. The fact that they are non-dynamical has a natural interpretation in terms of holography.