Stephen Hwang

Nonsemisimple Fusion Algebras and the Verlinde Formula

Abstract:We find a nonsemisimple fusion algebra associated with each (1, p) Virasoro model. We present a nonsemisimple generalization of the Verlinde formula which allows us to derive from modular transformations of characters.

Logarithmic conformal field theories via logarithmic deformations

We construct logarithmic conformal field theories starting from an ordinary conformal field theory -- with a chiral algebra C and the corresponding space of states V -- via a two-step construction: ...

Unitarity of strings and non-compact Hermitian symmetric spaces

Abstract If G is a simple non-compact Lie Group, with K its maximal compact subgroup, such that K contains a one-dimensional center C , then the coset space G / K is an Hermitian symmetric non-compact space. SL(2, R )/U(1) is the simplest example of such a space. It is only when G / K is an Hermitian symmetric space that there exists unitary discrete representations of G . We will here study string theories defined as G / K ′, K ′= K / C , WZNW models. We will establish unitarity for such string theories for certain discrete representations. This proof generalizes earlier results on SL(2, R ) , which is the simplest example of this class of theories. We will also prove unitarity of G / K conformal field theories generalizing results for SL(2, R )/U(1) . We will show that the physical space of states lie in a subspace of the G / K state space.

Equivalence of Chern-Simons gauge theory and WZNW model using a BRST symmetry

The equivalence between the Chern-Simons gauge theory on a three-dimensional manifold with boundary and the WZNW model on the boundary is established in a simple and general way using the BRST symm ...

Sectors of solutions in three-dimensional gravity and black holes

We examine the connection between three dimensional gravity with negative cosmological constant and two-dimensional CFT via the Chern-Simons formulation. A set of generalized spectral flow transfor ...

On the unitarity of gauged non-compact WZNW strings

This thesis deals with different aspects of string and /p/-brane theories. One of the motivations for string theory is to unify the forces in nature and produce a quantum theory of gravity. /p/-branes and related objects arise in string theory and are related to a non-perturbative definition of the theory. The results of this thesis might help in understanding string theory better. The first part of the thesis introduces and discusses relevant topics for the second part of the thesis which consists of five papers. In the three first papers we develop and treat a perturbative approach to relativistic /p/-branes around stretched geometries. The unperturbed theory is described by a string- or particle-like theory. The theory is solved, within perturbation theory, by constructing successive canonical transformations which map the theory to the unperturbed one order by order. The result is used to define a quantum theory which requires for consistency d = 25 + p dimensions for the bosonic /p/-branes and d = 11 for the supermembrane. This is one of the first quantum results for extended objects beyond string theory and is a confirmation of the expectation of an eleven-dimensional quantum membrane. The two last papers deal with a gauged WZNW-approach to strings moving on non-trivial space-times. The groups used in the formulation of these models are connected to Hermitian symmetric spaces of non-compact type. We have found that the GKO-construction does not yield a unitary spectrum. We will show that there exists, however, a different approach, the BRST approach, which gives unitarity under certain conditions. This is the first example of a difference between the GKO- and BRST construction. This is one of the first proofs of unitarity of a string theory in a non-trivial non-compact space-time. Furthermore, new critical string theories in dimensions less then 26 or 10 is found for the bosonic and supersymmetric string, respectively.

A general BRST approach to string theories with zeta function regularizations

We propose a new general BRST approach to string and string-like theories that have a wider range of applicability than, e.g., the conventional conformal field theory method. The method involves a simple general regularization of all basic commutators, which makes all divergent sums expressible in terms of zeta functions from which finite values then may be extracted in a rigorous manner. The method is particularly useful in order to investigate possible state space representations to a given model. The method is applied to three string models: The ordinary bosonic string, the tensionless string, and the conformal tensionless string. We also investigate different state spaces for these models. The tensionless string models are treated in detail. Although we mostly rederive known results, they appear in a new fashion that deepens our understanding of these models. Furthermore, we believe that our treatment is more rigorous than most of the previous ones. In the case of the conformal tensionless string we f...

On the unitarity of gauged non-compact world-sheet supersymmetric WZNW models

Abstract In this paper we generalize our investigation of the unitarity of non-compact WZNW models connected to Hermitian symmetric spaces to the N = 1 world-sheet supersymmetric extension of these models. We will prove that these models have a unitary spectrum in a BRST approach for antidominant highest weight representations if the level and weights of the gauged subalgebra are integers. We will find new critical string theories in 7 and 9 space–time dimensions.

No-ghost theorem for the bosonic Nappi-Witten string

We prove a no-ghost theorem for a bosonic string propagating in Nappi-Witten spacetime. This is achieved in two steps. We first demonstrate unitarity for a class of NW/U(1) modules: the norm of any ...

The membrane as a perturbation around string-like configurations

Abstract The bosonic membrane in a partial gauge, where one space dimension is eliminated, is formulated as a perturbation theory around an exact free string-like solution. This perturbative regime corresponds to a situation where one of the world-volume space-like dimensions is much greater than the other, so that the membrane has the form of a narrow band or large hoop with string excitations being transverse to the widest dimension. The perturbative equations of motion are studied and solved to first order. Furthermore, for the open or semi-open cases and to any order in perturbation theory, we construct a canonical transformation that will transform the membrane Hamiltonian into a free string-like Hamiltonian and a boundary Hamiltonian. Thus the membrane dynamics in our perturbation scheme is essentially captured by an interacting boundary theory defined on a two-dimensional world-sheet. A possible implication of this to M-theory is discussed.