Conformal symmetry and string theories

Thesis/Dissertation · Thu Jan 01 04:00:00 EST 1987

OSTI ID:5145337

Kumar, A

This thesis is devoted to the study of various aspects of the 2-dimensional conformal field theory and its applications to strings. We make a short review of the conformal field theory and its supersymmetric extension, called superconformal field theory. We present an elegant superspace formulation of these theories and solve the condition for the closure of the superconformal algebra. The we go on to classify the superconformal field theories according to these solutions. We prove that N {ge} 5 superconformal algebra, with N being the number of supersymmetries, does not have central charge. We find the primary representations of all the interesting superconformal algebra. We study the quantization of the superconformal theories and derive the constraints on the central charge of the algebra that has to be satisfied for a consistent quantum theory. This quantization process also determines the ground state energy of the system and the spectrum of the model. We study the global aspects of the conformal symmetry and its role in the construction of consistent heterotic string theories. We prove the uniqueness of heterotic superstring theories in 10 dimensions in the fermionic constructions. We show how the vertex operators are closely associated with the primary field representation of the conformal algebra. We utilize these vertex operator constructions to obtain tree amplitudes in the 10-dimensional heterotic string theory. We show by explicit calculation at the 3-point level that the scattering amplitudes derived from the heterotic superstring are same as the ones obtained from 10-dimensional supergravity theories.

• Research Organization: Maryland Univ., College Park, MD (USA)
• OSTI ID: 5145337
• Country of Publication: United States
• Language: English

Related Subjects

645400 -- High Energy Physics-- Field Theory
657000* -- Theoretical & Mathematical Physics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CALCULATION METHODS
COMPOSITE MODELS
CONFORMAL INVARIANCE
EXTENDED PARTICLE MODEL
FIELD THEORIES
FUNCTIONS
INVARIANCE PRINCIPLES
MATHEMATICAL MODELS
PARTICLE MODELS
QUARK MODEL
STRING MODELS
TWO-DIMENSIONAL CALCULATIONS
VERTEX FUNCTIONS