Applied Conformal Field Theory
Paul Ginsparg
TL;DR
This paper provides an elementary introduction to conformal field theory, covering its mathematical structure and applications to statistical mechanics and string theory, with emphasis on 2D theories and algebraic methods.
Contribution
It offers a comprehensive overview of conformal field theory concepts, including Virasoro algebra, Kac determinant, and applications to critical models, serving as an educational resource.
Findings
Identification of the m=3 model with the critical Ising model
Analysis of free bosons and fermions on tori
Application of affine Kac-Moody algebras in conformal theories
Abstract
These lectures consisted of an elementary introduction to conformal field theory, with some applications to statistical mechanical systems, and fewer to string theory. Contents: 1. Conformal theories in d dimensions 2. Conformal theories in 2 dimensions 3. The central charge and the Virasoro algebra 4. Kac determinant and unitarity 5. Identication of m = 3 with the critical Ising model 6. Free bosons and fermions 7. Free fermions on a torus 8. Free bosons on a torus 9. Affine Kac-Moody algebras and coset constructions 10. Advanced applications
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Black Holes and Theoretical Physics · Theoretical and Computational Physics