International Journal of Modern Physics A

The perturbative computation of the gravitational anomaly in curved space–time and in 1+1 dimensions is considered. This determination is obtained by a known method of complexification of the action variables applied to the fermionic effective action. Our result gives an exact definition of the Lorentz anomaly and it is introductory to a nonambiguous nonperturbative determination of the gravitational anomaly on curved manifolds. The quantum variation of the effective action, or Weyl determinant, is regularized with the help of the ζ-function technique, by extending the local algebra of infinitesimal current generators to complex values. Some ambiguities in the definition and computation of gauge anomalies are hopefully clarified.

The u-plane integrals of topologically twisted N=2 supersymmetric gauge theories generally contain contact terms of nonlocal topological observables. This paper proposes an interpretation of these contact terms from the point of view of integrable hierarchies and their Whitham deformations. This is inspired by Mariño and Moore's remark that the blowup formula of the u-plane integral contains a piece that can be interpreted as a single-time tau function of an integrable hierarchy. This single-time tau function can be extended to a multitime version without spoiling the modular invariance of the blowup formula. The multitime tau function is comprised of a Gaussian factor e^{Q(t₁,t₂,…)} and a theta function. The time variables t_n play the role of physical coupling constants of two-observables I_n(B) carried by the exceptional divisor B. The coefficients q_mn of the Gaussian part are identified to be the contact terms of these two-observables. This identification is further examined in the language of Whitham equations. All relevant quantities are written in the form of derivatives of the prepotential.

We study the BPS black hole solutions of the (truncated) action for heterotic string theory compactified on a six-torus. The O(3,Z) duality symmetry of the theory, together with the bound state interpretation of extreme black holes, is used to generate the whole spectrum of the solutions. The corresponding space–time structures, written in terms of the string metric, are analyzed in detail. In particular, we show that only the elementary solutions present naked singularities. The bound states have either null singularities (electric solutions) or are regular (magnetic or dyonic solutions) with near-horizon geometries given by the product of two 2d spaces of constant curvature. The behavior of some of these solutions as supersymmetric attractors is discussed. We also show that our approach is very useful to understand some of the puzzling features of charged black hole solutions in string theory.

The cosmological compactification of D=10, N=1 supergravity–super-Yang–Mills theory obtained from superstring theory is studied. The constraint of unbroken N=1 supersymmetry is imposed. A duality transformation is performed on the resulting consistency conditions. The original equations as well as the transformed equations are solved numerically to obtain new configurations with a nontrivial scale factor and a dynamical dilaton. It is shown that various classes of solutions are possible, which include cosmological solutions with no initial singularity.

We have determined constraints on the SU(5)_C × SU(2)_L × U(1)′ model in terms of the extra mixing angle ϕ in the neutral gauge boson sector and Δρ_M, the deviation of the Standard Model ρ parameter from unity at the tree level, using the recent precision measurements at LEP on electroweak parameters at the Z peak. The lower bound of the extra Z′ boson mass has also been determined.

In this paper, we discuss the behavior of conformal field theories interacting at a single point. The edge states of the quantum Hall effect (QHE) system give rise to a particular representation of a chiral Kac–Moody current algebra. We show that in the case of QHE systems interacting at one point we obtain a "twisted" representation of the current algebra. The condition for stationarity of currents is the same as the classical Kirchoff's law applied to the currents at the interaction point. We find that in the case of two discs touching at one point, since the currents are chiral, they are not stationary and one obtains current oscillations between the two discs. We determine the frequency of these oscillations in terms of an effective parameter characterizing the interaction. The chiral conformal field theories can be represented in terms of bosonic Lagrangians with a boundary interaction. We discuss how these one-point interactions can be represented as boundary conditions on fields, and how the requirement of chirality leads to restrictions on the interactions described by these Lagrangians. By gauging these models we find that the theory is naturally coupled to a Chern–Simons gauge theory in 2+1 dimensions, and this coupling is completely determined by the requirement of anomaly cancellation.

A symplectic structure of classical field theory and its application to the canonical geometric quantization procedure are presented. The developed formalism can be treated in two ways: as a prequantization procedure in the usual sense or as a quantization procedure in a stochastic quantum mechanics approach on a phase space.

The trajectory and Copenhagen representations render different predictions for impulsive perturbations. The different predictions are due to the different roles that causality plays in the trajectory and Copenhagen interpretations. We investigate a small perturbing impulse acting on the ground state of an infinitely deep square well. For the two representations, the first-order perturbation calculations for the temporal change in energy differ. This temporal change in energy for the trajectory representation is dependent upon the microstate of the wave function. We show that even under Copenhagen epistemology, the two representations predict different theoretical results.

We introduce a lattice model with local U(1) gauge symmetry which incorporates explicit frustration in d>2. The form of the action is inspired from the loop expansion of the fermionic determinant in standard lattice QED. We study through numerical simulations the phase diagram of the model, revealing the existence of a frustrated (antiferromagnetic) phase for d=3 and d=4, once an appropriate order parameter is identified.

Duality symmetries are discussed for nonlinear gauge theories of (n-1)th rank antisymmetric tensor fields in general even dimensions d=2n. When there are M field strengths and no scalar fields, the duality symmetry groups should be compact. We find conditions on the Lagrangian required by compact duality symmetries and show an example of duality invariant nonlinear theories. We also discuss how to enlarge the duality symmetries to noncompact groups by coupling scalar fields described by nonlinear sigma models.