Cohomology and the Operator Formalism
نویسندگان
چکیده
This letter points a close parallel between the operator formalism for string theory and the action of a Lie algebra on a differential complex. The construction of conformal field theories can then be regarded as a cohomology problem; we suggest that this viewpoint may survive the generalization beyond finite genus Riemann surfaces. Disciplines Physical Sciences and Mathematics | Physics This journal article is available at ScholarlyCommons: http://repository.upenn.edu/physics_papers/575
منابع مشابه
Cohomology in the Pure Spinor Formalism for the Superstring
A manifestly super-Poincaré covariant formalism for the superstring has recently been constructed using a pure spinor variable. Unlike the covariant Green-Schwarz formalism, this new formalism is easily quantized with a BRST operator and tree-level scattering amplitudes have been evaluated in a manifestly covariant manner. In this paper, the cohomology of the BRST operator in the pure spinor fo...
متن کاملep - t h / 93 02 11 4 v 1 2 4 Fe b 19 93 KCL - TH - 93 - 2 THE COVARIANT SCATTERING AND COHOMOLOGY OF W 3 STRINGS
A general formalism for covariant W 3 string scattering is given. It is found necessary to use screening charges that are constructed from the W 3 fields including ghosts. The scattering amplitudes so constructed contain within them Ising model correlation functions and agree with those found previously by the authors. Using the screening charge and a picture changing operator, an infinite numb...
متن کاملA New First Class Algebra, Homological Perturbation and Extension of Pure Spinor Formalism for Superstring
Based on a novel first class algebra, we develop an extension of the pure spinor (PS) formalism of Berkovits, in which the PS constraints are removed. By using the homological perturbation theory in an essential way, the BRST-like charge Q of the conventional PS formalism is promoted to a bona fide nilpotent charge Q̂, the cohomology of which is equivalent to the constrained cohomology of Q. Thi...
متن کاملDe Rham Cohomology of the Supermanifolds and Superstring BRST Cohomology
We show that the BRST operator of Neveu-Schwarz-Ramond superstring is closely related to de Rham differential on the moduli space of decorated super-Riemann surfaces P. We develop formalism where superstring amplitudes are computed via integration of some differential forms over a section of P over the super moduli space M. We show that the result of integration does not depend on the choice of...
متن کاملHamiltonian Reduction and Topological Conformal Algebra in c ≤ 1 Non - critical Strings
We study the hamiltonian reduction of affine Lie superalgebra sl(2|1)(1). Based on a scalar Lax operator formalism, we derive the free field realization of the classical topological topological algebra which appears in the c ≤ 1 non-critical strings. In the quantum case, we analyze the BRST cohomology to get the quantum free field expression of the algebra.
متن کامل