arXiv subjects

Stephen Hwang

Publications and source records attributed to Stephen Hwang.

22 records · Page 2Linked to original sources

arXiv1994

General branching functions of affine Lie algebras

Explicit expressions are presented for general branching functions for cosets of affine Lie algebras $\hat{g}$ with respect to subalgebras $\hat{g}^\prime$ for the cases where the corresponding finite dimensional algebras $g$ and $g^\prime$ are such that $g$ is simple and $g^\prime$ is either simple or sums of $u(1)$ terms. A special case of the latter yields the string functions. Our derivation is purely algebraical and has its origin in the results on the BRST cohomology presented by us earlier. We will here give an independent and simple proof of the validity our results. The method presented here generalizes in a straightforward way to more complicated $g$ and $g^\prime$ such as {\it e g } sums of simple and $u(1)$ terms.

hep-th↗

arXiv1993

The BRST formulation of G/H WZNW models

We consider a BRST approach to G/H coset WZNW models, {\it i.e.} a formulation in which the coset is defined by a BRST condition. We will give the precise ingrediences needed for this formulation. Then we will prove the equivalence of this approach to the conventional coset formulation by solving the the BRST cohomology. This will reveal a remarkable connection between integrable representations and a class of non-integrable representations for negative levels. The latter representations are also connected to string theories based on non-compact WZNW models. The partition functions of G/H cosets are also considered. The BRST approach enables a covariant construction of these, which does not rely on the decomposition of G as $G/H\times H$. We show that for the well-studied examples of $SU(2)_k \times SU(2)_1/SU(2)_{k+1}$ and $SU(2)_k/U(1)$, we exactly reproduce the previously known results.

hep-th↗

arXiv1992

Interaction and modular invariance of strings on curved manifolds

We review and present new results for a string moving on an $SU(1,1)$ group manifold. We discuss two classes of theories which use discrete representations. For these theories the representations forbidden by unitarity decouple and, in addition, one can construct modular invariant partition functions. The partion functions do, however, contain divergencies due to the time-like direction of the $SU(1,1)$ manifold. The two classes of theories have the corresponding central charges $c=9,6,5,9/2,\ldots$ and $c=9,15,21,27,\ldots$. Subtracting two from the latter series of central charges we get the Gervais-Neveu series $c-2=7,13,19,25$. This suggests a relationship between the $SU(1,1)$ string and the Liouville theory, similar to the one found in the $c=1$ string. Modular invariance is also demonstrated for the principal continous representations. Furthermore, we present new results for the Euclidean coset $SU(1,1)/U(1)$. The same two classes of theories will be possible here and will have central charges $c=8,5,4,\dots$ and $c=8,14,20,26,\ldots$, where the latter class includes the critical 2d black hole. The partition functions for the coset theory are convergent.(Talk presented by S.H. at the 16'th Johns Hopkins' Workshop, Göteborg, Sweden, June 8-10, 1992)

hep-th↗

arXiv1991

Cosets as gauge slices in SU(1,1) strings

We consider a string theory based on an SU(1,1) Wess-Zumino-Novikov-Witten model and an arbitrary unitary conformal fild 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.

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