Stephen Hwang | Halmstad University (original) (raw)

Papers by Stephen Hwang

Physics Letters B 466 227 233, 1999

The equivalence between the Chern-Simons gauge theory on a threedimensional manifold with boundar... more The equivalence between the Chern-Simons gauge theory on a threedimensional manifold with boundary and the WZNW model on the boundary is established in a simple and general way using the BRST symmetry. Our approach is based on restoring gauge invariance of the Chern-Simons theory in the presence of a boundary. This gives a correspondence to the WZNW model that does not require solving any constraints, fixing the gauge or specifying boundary conditions.

We investigate the unitarity of strings on non-trivial space-time backgrounds based on gauged WZN... more We investigate the unitarity of strings on non-trivial space-time backgrounds based on gauged WZNW models involving SO(n, 2), gauging an SO(n, 1) subgroup. As geometric coset spaces, these are Anti de Sitter spaces. Our present models are more complicated than the ones considered previously, for example those connected to Hermitian symmetric spaces. In the present case, the time-like field component is not a center of the maximal compact subalgebra, leading to several additional complications. Assuming discrete representations, it will only be possible to consider n even, resulting in odd dimensional spaces. We will prove that such models are free of ghosts for a class of discrete representations.

We propose a new general BRST approach to string and string-like theories which have a wider rang... more We propose a new general BRST approach to string and string-like theories which 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 to be expressible in terms of zeta functions from which finite values then may be extracted in a rigorous manner. The method is particular 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 details. Although we mostly rederive known results they appear in a new fashion which 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 find a new solution for d = 4.

Nuclear Physics B, 2006

The BRST-invariant formulation of the bosonic stretched membrane is considered. In this formulati... more The BRST-invariant formulation of the bosonic stretched membrane is considered. In this formulation the stretched membrane is given as a perturbation around zero-tension membranes, where the BRST-charge decomposes as a sum of a string-like BRST-charge and a perturbation. It is proven, by means of cohomology techniques, that there exists to any order in perturbation theory a canonical transformation that reduces the full BRST-charge to the string-like one. It is also shown that one may extend the results to the quantum level yielding a nilpotent charge in 27 dimensions.

Nuclear Physics B, 2009

In this paper we generalize our investigation of the unitarity of non-compact WZNW models connect... more 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.

Nuclear Physics B, 2010

The purpose of the present paper is to investigate the necessary conditions for unitarity of the ... more The purpose of the present paper is to investigate the necessary conditions for unitarity of the spectrum of non-compact gauged WZNW models to some depth. In particular, we would like to investigate the necessity of integer weights and level. We will learn that the problem is very complex and we have not found any simple and general way to formulate the necessary conditions. Instead one must resort to studying the problem almost case by case. The only nearly complete conditions that we will find, is for the case g = su(n, 1). Furthermore, the horizontal part of the case g = su(p, q) is nearly completed as well. In other cases, we will find conditions associated with certain subalgebras and nodes in the Dynkin diagram close to the one corresponding to the non-compact root. In these examples we can give conditions for the horizontal part of the algebra. As a by-product of our investigation we will prove some nice formulae of character identities and explicit branching functions for these representations.

Nuclear Physics B, 2008

In this paper we investigate the unitarity of gauged non-compact WZNW strings i.e. string theorie... more In this paper we investigate the unitarity of gauged non-compact WZNW strings i.e. string theories formulated as G/H ′ WZNW models, where G is a non-compact group. These models represent string theories on non-trivial curved space-times with one time-like component. We will prove that for the class of models connected to Hermitian symmetric spaces, and a natural set of discrete highest weight representations, the BRST formulation, in which the gauging is defined through a BRST condition, yields unitarity. Unitarity requires the level times the Dynkin index to be an integer, as well as integer valued highest weights w.r.t. the compact subalgebra. We will also show that the BRST formulation is not equivalent to the conventional GKO coset formulation, defined by imposing a highest weight condition w.r.t. H ′ . The latter leads to non-unitary physical string states. This is, to our knowledge, the first example of a fundamental difference between the two formulations.

Physics Letters B, 1998

If G is a simple non-compact Lie Group, with K its maximal compact subgroup, such that K contains... more 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. G = SL(2, R)/U(1) is the simplest example of such a space. It is only when G/K is a 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.

Nuclear Physics B, 1986

The lagrangian and hamiltonian formalisms for a free bosonic relativistic string are considered f... more The lagrangian and hamiltonian formalisms for a free bosonic relativistic string are considered for arbitrary non-orthonormal or non-conformal gauges. We show in detail how one can write an arbitrary metric tensor as a reparametrization of a conformally fiat one. By means of this decomposition, the lagrangian and hamiltonian formalisms are explicitly solved. From the result of this classical analysis we are then able to conclude that the quantization yields the same physical results as in the standard orthonormal gauge.

Physics Letters B, 1988

Interaction theory for relativistic bosonic strings in spacetime dimensions below the critical va... more Interaction theory for relativistic bosonic strings in spacetime dimensions below the critical value 26 is formulated using BRST techniques with an extra scalar field. One-loop zero-point amplitudes for closed strings are modular invariant. For a free scalar field, vertex operators ...

Physics Letters B, 1991

We investigate the question of modular invariance for a string moving on an SU (1, 1) group manif... more We investigate the question of modular invariance for a string moving on an SU (1, 1) group manifold. By including new sectors corresponding to windings around the compact time-direction, modular invariance is achieved for the discrete representations which are free of ...

Physics Letters B, 2008

This paper deals with p-branes with small but non-zero tension. We prove the existence of canonic... more This paper deals with p-branes with small but non-zero tension. We prove the existence of canonical transformations, within a perturbation theory, that link specific geometries of pbranes to solvable theories, namely string-like and particle-like theories. The specific shapes correspond to stretched configurations. For configurations linked to string-like theories one will upon quantization get a critical dimension of (25+p).

Physics Letters B, 1995

We study the cohomology arising in the BRST formulation of G/H gauged WZNW models, i.e. in which ... more We study the cohomology arising in the BRST formulation of G/H gauged WZNW models, i.e. in which the states of the gauged theory are projected out from the ungauged one by means of a BRST condition. We will derive for a general simple group H with arbitrary level, conditions for which the cohomology is non-trivial. We show, by i n troducing a small perturbation due to Jantzen, in the highest weights of the representations, how states in the cohomology, "singlet pairs", arise from unphysical states, "Kugo-Ojima quartets", as the perturbation is set to zero. This will enable us to identify and construct states in the cohomology. The ghost numbers that will occur are p, with p uniquely determined by the representations of the algebras involved. Our construction is given in terms of the current modes and relies on the explicit form of highest weight n ull-states given by Malikov, Feigen and Fuchs. 1 tfesh(fy.chalmers.se 2 hr(fy.chalmers.se

Physics Letters B, 1992

We consider a string theory based on an SU(1, 1) Wess-Zumino-Novikov-Witten model and an arbitrar... more We consider a string theory based on an SU(1, 1) Wess-Zumino-Novikov-Witten model and an arbitrary unitary conformal field theory. We show that the solutions of the Virasoro conditions, in the unitarity regime of the SU(1, 1) theory, are states which lie in the Euclidean coset SU(1, 1)/U(1). This shows the validity, at the quantum level, of a time-like type of gauge in these models.

Physics Letters B, 1999