International Journal of Modern Physics A

We present a general method of constructing manifestly world-volume supersymmetric actions of super p-branes, starting from some higher-dimensional field theories in which the partial breaking of global supersymmetry (PBGS) comes about. Our approach is based upon a substitution of the superspace coordinates which relates linear and nonlinear realizations of PBGS. As instructive examples we consider the massive d=2 superparticle (p=0) and d=4 superstring (p=1). The relevant world-line and world-sheet superfied actions naturally appear as a long-wavelength limit of the superfield actions of some two- and four-dimensional supersymmetric field theories possessing topologically nontrivial soliton solutions. The corresponding topological charges prove to enter the super p-brane actions as the coupling constants. We also give a new general Wess-Zumino-type representation of the d=2 superparticle action via the world-line superfields. It respects invariances both under the target space Poincaré supersymmetry and the gauge group of general reparametrizations of the world-line superspace. In one gauge, it is reduced to the standard PBGS form while in another, it gives rise to a very simple action which displays manifest world-line superconformal symmetry and is directly related to the familiar component action of the superparticle. The fermionic κ-symmetry of the latter can be identified with the odd sector of superconformal symmetry. This identity suggests a simple recipe for building higher-order κ-invariant corrections to the minimal superparticle action.

We show that Landau-Ginzburg models with modality one are equivalent to Z_N orbifold models on two-dimensional tori. The identification of the primary field content is given and the operator product coefficients of the twisted sectors are computed explicitly.

Two-dimensional Wess-Zumino-Novikov-Witten theory is extended to three dimensions, where it becomes a scalar gauge theory of the singleton type. The three-dimensional formulation involves a scalar field valued in a compact group G, a Nakanishi-Lautrup field valued in Lie (G) and Faddeev-Popov ghosts. The physical sector, characterized by the vanishing of the Nakanishi-Lautrup field, coincides with the WZNW theory of the group G. Three-dimensional space-time structure involves a generalized metric, but only its boundary values are of consequence. An alternative formulation in terms of left and right movers (in three dimensions!) is also possible.

A general method for the construction of modular invariant partition functions of Kač-Moody algebras using a covariant lattice approach is presented. The A-D-E series for conformal invariant theories and partition functions of are constructed explicitly to demonstrate the technique.

We describe the embedding structure of the Verma modules of the W₃ algebra using the free field representation (FFR) in the lattice approach. This structure is expressed by a set of intertwining diagrams. In particular, we show how these diagrams can be used to achieve the Bernstein-Gel’fand-Gel’fand (BGG) resolution of the irreducible highest weight representation (IHWR) in terms of the Verma modules. As an application of prime importance, we show how the character of the W₃ IHWR can be readily derived using the Rocha-Caridi procedure.

New modular invariant partition functions for tensor products of affine Lie algebras are presented. These exceptional modular invariants can be understood in terms of automorphisms of the fusion rules of the affine algebra or of its extensions. There are three isolated cases, as well as an infinite series of new invariants. As an application, the new modular invariants are employed to produce new Gepner type compactifications of the heterotic string.

We present a covariant path integral quantization of supersymmetric chiral bosons (leftons and rightons). An infinite set of auxiliary scalar superfields are introduced to convert the second-class chiral constraint into first-class ones. Our gauge-fixed action has an extended BRST symmetry described by the graded algebra GL(1|1). A regularization respecting this symmetry is proposed to deal with the contributions of the infinite towers of auxiliary fields and associated ghosts and is verified to lead to the desired partition function. We apply our formulation to give a covariant quantization of the heterotic-type NSR strings, and show that (super)conformal anomalies from all unphysical degrees of freedom are cancelled, even in noncritical dimensions. Our treatment does not suffer from Siegel gauge anomaly, because of the use of linear chiral constraints.

A derivation of the loop equation for two-dimensional quantum gravity from the KdV equations and the string equation of the one-matrix model has been recently given. The loop equation was found to be equivalent to an infinite set of linear constraints on the square root of the partition function satisfying the Virasoro algebra. Starting from the equations expressing these constraints, we are able to rederive the equations of the KdV hierarchy using the vertex operator construction of the infinite dimensional twisted Kac-Moody algebra. From these considerations it follows that the solutions of the string equation of the one-matrix model are given by a subset of the solutions of the KdV hierarchy.

We discuss some physical aspects of W gravities and W strings. We identify global characteristics in W gravities (in addition to the usual Euler characteristic) and show how the dependence of the partition function on the various chemical potentials involves these quantities. We find the operators which create physical states in W₃ and W₄ gravities and discuss their relationship with screening operators. W strings are discussed in the framework of a natural way of coupling “matter” to W gravity, and the issues of extra dimensions and critical dimensions are clarified. We find a remarkable relationship between pure W gravities and ordinary gravity coupled to c<1 unitary minimal models.

We investigate the nonperturbative physics of the zero-dimensional random Hermitian matrix model, using semiclassical analysis as well as orthogonal polynomials. Finite-N tunneling leads to a unique equilibration of the Dyson gas of eigenvalues and dissolves a fictitious family of N=∞ saddle points. We present a mean-field potential for the limiting multiple-arc eigenvalue distribution. The sequence of the orthogonal-polynomial recursion coefficients R_k is characterized by the critical points of the matrix potential. Its large-N limit can show regions of smooth, quasi-periodic and seemingly chaotic behavior. The tunneling competition between nondegenerate potential wells is the origin of the unpredictability.

Massless scalar fields coupled to gravity produces two kinds of wormhole instantons, the Giddings-Strominger wormhole and the Tolman-Hawking wormhole. A new type of coupling between gravity and a massless scalar field is discussed which produces a different wormhole-like solution, . It is seen that these three solutions can be related to each other by means of suitable conformal transformations. The Wheeler DeWitt equation corresponding to a fourth-order gravity theory minimally coupled to an axionic field is obtained and some of its particular solutions are discussed.