International Journal of Modern Physics A

We study algebraic aspects of Kontsevich integrals as generating functions for intersection theory over moduli space and review the derivation of Virasoro and KdV constraints.

We show that certain vanishing couplings in the affine Toda field theories remain vanishing even after higher-order corrections are included. This is a requisite property for the Lagrangian formulation of the theory. We develop a new perturbative formulation and treat affine Toda field theories as a massless theory with exponential interaction terms. We show that the nonrenormalization comes from the Dynkin automorphism of the Lie algebra associated with these theories. A charge balance condition plays an important role in our scheme. The all-order nonrenormalization of vanishing couplings in affine Toda field theory is also proved in a standard massive scheme.

The Lagrangian field-antifield (BV) and Hamiltonian (BFV) BRST formalisms for the general quadratic systems with open gauge algebra are considered. The equivalence between the Lagrangian and Hamiltonian formalisms is proven.

All space-time supersymmetric non-Abelian orbifolds produced by finite subgroups of SU(2) whose gauge groups are of minimal rank are systematically classified for the heterotic string. Also, we discuss a novel method of removing global anomalies in the operator formalism.

There exist various formulations to discuss the 2d effective gravity: (i) light-cone gauge formulation; (ii) geometrical formulation; (iii) formulation by the constrained WZWN model; and (iv) conformal gauge formulation. In the formulations other than the last one, quantization of the 2d effective gravity is not complete in the sense that either the central charges of both sectors are not known, or one of them is known but not the other. We will provide a thorough argument on quantization of the 2d effective gravity in the formulation (ii). The argument will allow us to complete the quantization in the formulation (iii), and establish the relations among the formulations (ii)-(iv) at the quantum level.

The radial form of the partition function of a two-matrix model is formally given in terms of a spherical function for matrices representing any Euclidean symmetric space. An explicit expression is obtained by constructing the spherical function by the method of intertwining. The reduction of two-matrix models based on Lie algebras is an elementary application. A model based on the rank one symmetric space isomorphic to R^N is less trivial and is treated in detail. This model may be interpreted as an Ising model on a random branched polymer. It has the unusual feature that the maximum order of criticality is different in the planar and double-scaling limits.

Starting from the quantum field theory of nonrelativistic matter on a torus interacting with Chern-Simons gauge fields, we derive the Schrödinger equation for an anyon system. The nonintegrable phases of the Wilson line integrals on a torus play an essential role. In addition to generating degenerate vacua, they enter in the definition of a many-body Schrödinger wave function in quantum mechanics, which can be defined as a regular function of the coordinates of anyons. It obeys a non-Abelian representation of the braid group algebra, being related to Einarsson’s wave function by a singular gauge transformation.

The principal attraction of the Fock-Schwinger (FS) gauge is that the gauge potentials are completely determined in terms of the electromagnetic fields by an inversion formula once the condition x·A=0 is fixed. We have reformulated the FS gauge propagator, first derived by Kummer and Weiser, in a more useful and manageable form and applied it to perturbation calculations in spinor and scalar QED and QCD. In that way we have been able to verify the on-mass-shell equivalence of these calculations to the covariant Feynman gauge.

In a previous work, a straighforward canonical approach to the source-free quantum Chern—Simons dynamics was developed. It makes use of neither gauge conditions nor functional integrals and needs only ideas known from QCD and quantum gravity. It gives Witten’s conformal edge states in a simple way when the spatial slice is a disc. Here we extend the formalism by including sources as well. The quantum states of a source with a fixed spatial location are shown to be those of a conformal family, a result also discovered first by Witten. The internal states of a source are not thus associated with just a single ray of a Hilbert space. Vertex operators for both abelian and nonabelian sources are constructed. The regularized abelian Wilson line is proved to be a vertex operator. We also argue in favor of a similar nonabelian result. The spin-statistics theorem is established for Chern-Simons dynamics even though the sources are not described by relativistic quantum fields. The proof employs geometrical methods which we find are strikingly transparent and pleasing. It is based on the research of European physicists about “fields localized on cones.”

Supernova 1987A constraints on the decay mode (χ ≡ Majoron) is discussed for the case where the ν_τ mass is assumed to be 17 keV. Its implications for theoretical models of a 17 keV ν_τ are considered.

We perform one-loop calculations in chiral induced W₃ gravity in momentum space. Unlike a previous one-loop calculation in x space, which reduced the problem to one in local field theory, we work directly with the nonlocal action. We use Polyakov’s exponential regularization, and obtain agreement with the x-space calculation. We discuss the extension of our methods to higher-loop calculations in more-general chiral nonlocal field theories.