Conformally exact metric and dilaton in string theory on curved spacetime

• Published in: Physical review. D, Particles and fields Particles and fields, 1992-11, Vol.46 (10), p.4510-4519
• Main Authors: BARS, I, SFETSOS, K
• Format: Article
• Language: English
• Subjects: 661100 - Classical & Quantum Mechanics- (1992-); 662110 - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-); 662120 - General Theory of Particles & Fields- Symmetry, Conservation Laws, Currents & Their Properties- (1992-); BOSON-EXCHANGE MODELS; BOSONS; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPOSITE MODELS; Exact sciences and technology; EXTENDED PARTICLE MODEL; FUNCTIONS; GAUGE INVARIANCE; General theory of fields and particles; HAMILTONIANS; INVARIANCE PRINCIPLES; LAGRANGIAN FUNCTION; LIE GROUPS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; MECHANICS; METRICS; PARTICLE MODELS; PERIPHERAL MODELS; PERTURBATION THEORY; Physics; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; QUANTUM MECHANICS; QUANTUM OPERATORS; QUARK MODEL; RENORMALIZATION; SEMICLASSICAL APPROXIMATION; SIGMA MODEL; SO GROUPS; SPACE-TIME; STRING MODELS; SYMMETRY GROUPS; The physics of elementary particles and fields; Theory of fundamental strings; UNIVERSE
• ISSN: 0556-2821; 1089-4918
• DOI: 10.1103/PhysRevD.46.4510

Using a Hamiltonian approach to gauged Wess-Zumino-Witten models, we present a general method for computing the conformally exact metric and dilaton, to all orders in the 1/{ital k} expansion, for any bosonic, heterotic, or type-II superstring model based on a coset {ital G}/{ital H}. We prove the following relations: (i) For type-II superstrings the conformally exact metric and dilaton are identical to those of the nonsupersymmetric {ital semiclassical} bosonic model except for an overall renormalization of the metric obtained by {ital k}{r arrow}{ital k}{minus}{ital g}. (ii) The exact expressions for the heterotic superstring are derived from their exact bosonic string counterparts by shifting the central extension {ital k}{r arrow}2{ital k}{minus}{ital h} (but an overall factor ({ital k}{minus}{ital g}) remains unshifted). (iii) The combination {ital e}{sup {Phi}} {radical}{minus}{ital G} is independent of {ital k} and therefore can be computed in/p lowest-order perturbation theory. The general formalism is applied to the coset models SO({ital d}{minus}1,2){sub {minus}{ital k}}/SO({ital d}{minus}1,1){sub {minus}{ital k}} that are relevant for string theory on curved spacetime. Explicit expressions for the conformally exact metric and dilaton for the cases {ital d}=2,3,4 are given. In the semiclassical limit ({ital k}{r arrow}{infinity}) our results agree with those obtained with the Lagrangian method up to one loop in perturbation theory.