Perturbatively renormalized vertex operator, highest-weight representations of Virasoro algebra, and string dynamics in curved space
String dynamics is considered from the viewpoint of conformally invariant field theory. We discuss the renormalization of a general scalar field in the target space of a two-dimensional nonlinear sigma model. Counterterms are constructed to leading order in the slope parameter. The renormalized operator contains exponential factors that give rise to correct scaling properties as a function of the infrared cutoff. The requirement that the operator be a primary conformal field with scaling dimension (h,h-bar) = (1,1) (i.e., a vertex operator satisfying the Virasoro gauge conditions) determines the vertex function which describes tachyon emission from the string Iand Rthe equations for the background fields, which in our case are the metric and the dilaton. This then is an explicit, perturbative construction of a representation of the Virasoro algebra. In the Becchi-Rouet-Stora-Tyutin (BRST) formulation the backgrounds and the physical spectrum are solutions of the equation Qpsi = 0, where Q is the BRST change.
- Research Organization:
- Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
- OSTI ID:
- 5890625
- Journal Information:
- Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 35:10; ISSN PRVDA
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COMPOSITE MODELS
CONFORMAL INVARIANCE
DIFFERENTIAL EQUATIONS
ENERGY-MOMENTUM TENSOR
EQUATIONS
EQUATIONS OF MOTION
EXTENDED PARTICLE MODEL
FIELD THEORIES
FUNCTIONS
INVARIANCE PRINCIPLES
MATHEMATICAL MODELS
MATRICES
METRICS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE MODELS
PERTURBATION THEORY
QUARK MODEL
RENORMALIZATION
S MATRIX
SCALAR FIELDS
SIGMA MODEL
SPACE-TIME
STRING MODELS
TENSORS
TWO-DIMENSIONAL CALCULATIONS
VERTEX FUNCTIONS
WAVE FUNCTIONS