One-loop effective multi-gluon Lagrangian in arbitrary dimensions

We exhibit the one-loop multi-gluon effective Lagrangian in any dimension for a field theory with a quasilocal background, using the background-field formalism. Specific results, including counter terms (up to 12 spacetime dimensions), have been derived, applied to the Yang-Mills theory and found to be in agreement with other string-inspired approaches.Comment: 16 pages, LaTe

Twenty Years of the Weyl Anomaly

In 1973 two Salam prot\'{e}g\'{e}s (Derek Capper and the author) discovered that the conformal invariance under Weyl rescalings of the metric tensor $g_{\mu\nu}(x)\rightarrow\Omega^2(x)g_{\mu\nu}(x)$ displayed by classical massless field systems in interaction with gravity no longer survives in the quantum theory. Since then these Weyl anomalies have found a variety of applications in black hole physics, cosmology, string theory and statistical mechanics. We give a nostalgic review. (Talk given at the {\it Salamfest}, ICTP, Trieste, March 1993.)Comment: 43 page

Exact Absorption Probability in the Extremal Six-Dimensional Dyonic String Background

We show that the minimally coupled massless scalar wave equation in the background of an six-dimensional extremal dyonic string (or D1-D5 brane intersection) is exactly solvable, in terms of Mathieu functions. Using this fact, we calculate absorption probabilities for these scalar waves, and present the explicit results for the first few low energy corrections to the leading-order expressions. For a specific tuning of the dyonic charges one can reach a domain where the low energy absorption probability goes to zero with inverse powers of the logarithm of the energy. This is a dividing domain between the regime where the low energy absorption probability approaches zero with positive powers of energy and the regime where the probability is an oscillatory function of the logarithm of the energy. By the conjectured AdS/CFT correspondence, these results shed novel light on the strongly coupled two-dimensional field theory away from its infrared conformally invariant fixed point (the strongly coupled ``non-critical'' string).Comment: Latex (3 times), 23 page

Quantum Theory of Black Holes

A solvable 2-dimensional conformally invariant midi-superspace model for black holes is obtained by imposing spherical symmetry in 4-dimensional conformally invariant Einstein gravity. The Wheeler-DeWitt equation for the theory is solved exactly to obtain the unique quantum wave functional for an isolated black hole with fixed mass. By suitably relaxing the boundary conditions, a non-perturbative ansatz is obtained for the wave functional of a black hole interacting with its surroundings.Comment: Plain-TeX, 13 pages, no figures, WIN-92-9, UNB Tech. Rep. 92-0

Effective actions with fixed points, (error in derivation of coefficient corrected)

The specific form of the constant term in the asymptotic expansion of the heat-kernel on an axially-symmetric space with a codimension two fixed-point set of conical singularities is used to determine the associated conformal change of the effective action in four dimensions. Another derivation of the relevant coefficient is presented.Comment: 10p,uses JyTeX,MUTP/94/1

Black holes admitting a Freudenthal dual

The quantised charges x of four dimensional stringy black holes may be assigned to elements of an integral Freudenthal triple system whose automorphism group is the corresponding U-duality and whose U-invariant quartic norm Delta(x) determines the lowest order entropy. Here we introduce a Freudenthal duality x -> \tilde{x}, for which \tilde{\tilde{x}}=-x. Although distinct from U-duality it nevertheless leaves Delta(x) invariant. However, the requirement that \tilde{x} be integer restricts us to the subset of black holes for which Delta(x) is necessarily a perfect square. The issue of higher-order corrections remains open as some, but not all, of the discrete U-duality invariants are Freudenthal invariant. Similarly, the quantised charges A of five dimensional black holes and strings may be assigned to elements of an integral Jordan algebra, whose cubic norm N(A) determines the lowest order entropy. We introduce an analogous Jordan dual A*, with N(A) necessarily a perfect cube, for which A**=A and which leaves N(A) invariant. The two dualities are related by a 4D/5D lift.Comment: 32 pages revtex, 10 tables; minor corrections, references adde

Partition Functions for the Rigid String and Membrane at Any Temperature

Exact expressions for the partition functions of the rigid string and membrane at any temperature are obtained in terms of hypergeometric functions. By using zeta function regularization methods, the results are analytically continued and written as asymptotic sums of Riemann-Hurwitz zeta functions, which provide very good numerical approximations with just a few first terms. This allows to obtain systematic corrections to the results of Polchinski et al., corresponding to the limits $T\rightarrow 0$ and $T\rightarrow \infty$ of the rigid string, and to analyze the intermediate range of temperatures. In particular, a way to obtain the Hagedorn temperature for the rigid membrane is thus found.Comment: 20 pages, LaTeX file, UB-ECM-PF 93/

Spherical and planar three-dimensional anti-de Sitter black holes

The technique of dimensional reduction was used in a recent paper (Zanchin et al, Phys. Rev. D66, 064022,(2002)) where a three-dimensional (3D) Einstein-Maxwell-Dilaton theory was built from the usual four-dimensional (4D) Einstein-Maxwell-Hilbert action for general relativity. Starting from a class of 4D toroidal black holes in asymptotically anti-de Sitter (AdS) spacetimes several 3D black holes were obtained and studied in such a context. In the present work we choose a particular case of the 3D action which presents Maxwell field, dilaton field and an extra scalar field, besides gravity field and a negative cosmological constant, and obtain new 3D static black hole solutions whose horizons may have spherical or planar topology. We show that there is a 3D static spherically symmetric solution analogous to the 4D Reissner-Nordstr\"om-AdS black hole, and obtain other new 3D black holes with planar topology. From the static spherical solutions, new rotating 3D black holes are also obtained and analyzed in some detail.Comment: 27 pages, uses "iopclass" files (Latex2e

Universal Features of Holographic Anomalies

We study the mechanism by which gravitational actions reproduce the trace anomalies of the holographically related conformal field theories. Two universal features emerge: a) the ratios of type B trace anomalies in any even dimension are independent of the gravitational action, being uniquely determined by the underlying algebraic structure b) the normalization of the type A and the overall normalization of the type B anomalies are given by action dependent expressions with the dimension dependence completely fixed.Comment: 17 pages, harvma

The aa-theorem and the Asymptotics of 4D Quantum Field Theory

We study the possible IR and UV asymptotics of 4D Lorentz invariant unitary quantum field theory. Our main tool is a generalization of the Komargodski-Schwimmer proof for the $a$-theorem. We use this to rule out a large class of renormalization group flows that do not asymptote to conformal field theories in the UV and IR. We show that if the IR (UV) asymptotics is described by perturbation theory, all beta functions must vanish faster than $(1/|\ln\mu|)^{1/2}$ as $\mu \to 0$ ($\mu \to \infty$). This implies that the only possible asymptotics within perturbation theory is conformal field theory. In particular, it rules out perturbative theories with scale but not conformal invariance, which are equivalent to theories with renormalization group pseudocycles. Our arguments hold even for theories with gravitational anomalies. We also give a non-perturbative argument that excludes theories with scale but not conformal invariance. This argument holds for theories in which the stress-energy tensor is sufficiently nontrivial in a technical sense that we make precise.Comment: 41 pages, 2 figures. v2: Arguments clarified, some side comments corrected, connection to previous work by Jack and Osborn described, conclusions unaffecte