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Topological Aspects of Chiral Fields in Two Dimensions and Superstring Vertices
Author(s) -
Dick Rainer
Publication year - 1992
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190400602
Subject(s) - superstring theory , riemann surface , cohomology , topological quantum field theory , field (mathematics) , physics , topology (electrical circuits) , pure mathematics , mathematics , lie algebra , algebra over a field , mathematical physics , supersymmetry , combinatorics
Abstract In this paper we present in detail the construction of mode expansions of chiral fields on Riemann surfaces. The results are then applied to solve the linear equations of motion of the superstring for non‐trivial topology, thus permitting for the kinematical and dynamical description of superstring vertices, and implications on the development of quantum field theory on higher genus Riemann surfaces are outlined. Furthermore, the cohomological investigation of Lie algebras is extended to a cohomology of Lie algebra modules and it is shown that there exist up to four central charges in two‐dimensional quantum field theories.