Black holes in vector-tensor theories and their thermodynamics

In this paper, we study Einstein gravity either minimally or non-minimally coupled to a vector field which breaks the gauge symmetry explicitly in general dimensions. We first consider a minimal theory which is simply the Einstein-Proca theory extended with a quartic self-interaction term for the vector field. We obtain its general static maximally symmetric black hole solution and study the thermodynamics using Wald formalism. The aspects of the solution are much like a Reissner-Nordstrøm black hole in spite of that a global charge cannot be defined for the vector. For non-minimal theories, we obtain a lot of exact black hole solutions, depending on the parameters of the theories. In particular, many of the solutions are general static and have maximal symmetry. However, there are some subtleties and ambiguities in the derivation of the first laws because the existence of an algebraic degree of freedom of the vector in general invalids the Wald entropy formula. The thermodynamics of these solutions deserves further studies.     

Thermalization of strongly coupled field theories

Using the holographic mapping to a gravity dual, we calculate 2-point functions, Wilson loops, and entanglement entropy in strongly coupled field theories in d=2, 3, and 4 to probe the scale dependence of thermalization following a sudden injection of energy. For homogeneous initial conditions, the entanglement entropy thermalizes slowest and sets a time scale for equilibration that saturates a causality bound. The growth rate of entanglement entropy density is nearly volume-independent for small volumes but slows for larger volumes. In this setting, the UV thermalizes first.     

Integrability of coupled conformal field theories

The massive phase of two-layer integrable systems is studied by means of RSOS restrictions of affine Toda theories. A general classification of all possible integrable perturbations of coupled minimal models is pursued by an analysis of the (extended) Dynkin diagrams. The models considered in most detail are coupled minimal models which interpolate between magnetically coupled Ising models and Heisenberg spin ladders along the c < 1 discrete series.     

A note on the minimally coupled Bhabha field

The Bhabha field with multimass and maximum spin S, a system transforming reducibly under a representation of the homogenous Lorentz group is considered. The field is quantized in the presence of a minimally coupled electromagnetic field. The relation $\text{ψ(x)=ψ(}\text{x}\text{σ}\text{)}$ does not hold for the case of S integer contrary to the half-integer S or lower spin (S<) case, but the usual difficulties of high spin field theories seem to be absent. The propagation of the interacting (classical) equations is casual, since their principal part is unaffected by the introduction of an interaction, analogous to the lower spin case. This good nature of the Bhabha field equations appears due to the absence of secondary constraints. This is further supported with a similar example of a vector-spinor field.     

Disordered loop model and coupled conformal field theories

A family of models for fluctuating loops in a two-dimensional random background is analyzed. The models are formulated as O(n) spin models with quenched inhomogeneous interactions. Using the replica method, the models are mapped to the M→0 limits of M-layered O(n) models coupled each other via _1,3 primary fields. The renormalization group flow is calculated in the vicinity of the decoupled critical point, by an epsilon expansion around the Ising point (n=1), varying n as a continuous parameter. The one-loop beta function suggests the existence of a strongly coupled phase (0<n<n_*) near the self-avoiding walk point (n=0) and a line of infrared fixed points (n_*<n<1) near the Ising point. For the fixed points, the effective central charges are calculated. The scaling dimensions of the energy operator and the spin operator are obtained up to two-loop order. The relation to the random-bond q-state Potts model is briefly discussed.     

On the single point field theories

A systematic approach to reduce the dynamical degrees of freedom is presented. Certain field theory models with non-trivial large-N limit defined in the infinite volume are shown to be reduced to theories defined at a single point in space-time when N → ∞.     

On general-relativistic and gauge field theories

The fundamental open questions of general relativity theory are the unification of the gravitational field with other fields, aiming at a unified geometrization of physics, as well as the renormalization of relativistic gravitational theory in order to obtain their self-consistent solutions. These solutions are to furnish field-theoretic particle models—a problem first discussed by Einstein. In addition, we are confronted with the issue of a coupling between gravitational and matter fields determined (not only) by Einstein's principle of equivalence, and also with the question of the geometric meaning of a gravitational quantum theory. In our view, all these problems are so closely related that they warrant a general solution. We treat mainly the concepts suggested by Einstein and Weyl.     

On topological field theories and duality

Topologically non-trivial effects appearing in the discussion of duality transformations in higher genus manifolds are discussed in a simple example. Their relation with the properties of Topological Field Theories is established.     

On characteristic integrals of Toda field theories

Characteristic integrals of Toda field theories associated to general simple Lie algebras are constructed using systematic techniques, and complete mathematical proofs are provided. Plenty of examples illustrating the results are presented in explicit forms.     

On nonlinear field theories of elementary particles

A nonlinear field equation has been derived from a gauge formalism. It has been shown that a soluble nonlinear equation, the sine-Gordon equation, can be obtained from the general nonlinear equation. The physical interpretation is given.Work supported by the National Research Council of Canada.Talk given at the Third International Workshop On Weak Interactions with Very High Energy Beams, Columbus, Ohio, U.S.A., September 3–13, 1975.     

On the classification of rational conformal field theories

We propose a method for classifying rational conformal field theories in terms of the differential equation satisfied by their characters.     

On the energy-momentum tensor in gauge field theories

The energy-momentum tensor in spontaneously broken non-Abelian gauge field theories is studied. The motivation is to show that recent results on the finiteness and gauge independence of S-matrix elements in gauge theories extends to observable amplitudes for transitions in a gravitational field. Path integral methods and dimensional regularization are used throughout. Green's functions Γ_μν^(j)(q; p₁,…,p_j) involving the energy-momentum tensor and j particle fields are proved finite to all orders in perturbation theory to zero and first order in q, and finite to one loop order for general q. Amputated Green's functions of the energy momentum tensor are proved to be gauge independent on mass shell.     

On local field products in special Wightman theories

We shall try to define local field products under assumptions imposed only on the four-point-function. This idea is based on the work of Schlieder and Seiler [1]. In our framework we shall prove that the two-point-function carries the strongest singularity whenever two arguments in a Wightman function coincide. This will be generalized to the case when more arguments coincide. We shall define “regulated”n-point-functions and study their properties in detail. This will lead us to the definition of arbitrarily high powers of the field-operators as operator-valued distributions overD(?⁴) in the center coordinate with a dense domain of definition.     

On theories of gravitation with higher-order field equations

Weyl and Eddington suggested three alternative general relativistic theories of gravitation with fourth-order field equations which in empty space admit the Schwarzschild metric as a solution. These theories, Like Einstein's, follow from a variational principle and thus imply differential identities. If, as in Einstein's theory, the sources are taken to be proportional to the energy-momentum tensorT , these identities imply the vanishing of the covariant divergence ofT ^v. It is shown here that in the presence of extended sources, Weyl's and Eddington's theories (as well as all other higher-order metric theories derivable from an action principle) contradict Newton's law of gravitation in the nonrelativistic limit. To entail this law would require a modification of the source term of the field equations which in general is not compatible withT ^v _;v alternatively, one could require only asymptotic agreement with Newton's law, which is compatible with supplementary higher-order terms in Einstein's equations, but which requires the introduction of universal constants of the dimensions of length. None of the generalizations of Einstein's equations considered here admits Birkhoff's theorem.Dedicated to Achille Papapetrou on the occasion of his retirement.     

On the alleged equivalence of certain field theories

We critically examine some recent claims that certain field theories with and without boson kinetic energy terms are equivalent. We point out that the crucial element in these claims is the finiteness or otherwise of the boson wavefunction renormalisation constant. We show that when this constant is finite, the equivalence proof offered in the literature fails in a direct way. When the constant is divergent, the claimed equivalence is only a consequence of improper use of divergent quantities.