N=2 structures in all string theories

Abstract

The BRST cohomology of any topological conformal field theory admits the structure of a Batalin--Vilkovisky algebra, and string theories are no exception. Let us say that two topological conformal field theories are ``cohomologically equivalent'' if their BRST cohomologies are isomorphic as Batalin--Vilkovisky algebras. What we show in this paper is that any string theory (regardless of the matter background) is cohomologically equivalent to some twisted N=2 superconformal field theory. We discuss three string theories in detail: the bosonic string, the NSR string and the W_3 string. In each case the way the cohomological equivalence is constructed can be understood as coupling the topological conformal field theory to topological gravity. These results lend further supporting evidence to the conjecture that _any_ topological conformal field theory is cohomologically equivalent to some topologically twisted N=2 superconformal field theory. We end the paper with some comments on different notions of equivalence for topological conformal field theories and this leads to an improved conjecture.

23 pages (12 physical pages), .dvi.uu (+ some hyperlinks)

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Cited by in corpus (8)

• Multiparticle SYM equations of motion and pure spinor BRST blocks
• The Quantum Superstring as a WZNW Model with N=2 Superconformal Symmetry
• Cohomology foundations of one-loop amplitudes in pure spinor superspace
• N=1 and N=2 cosets from gauged supersymmetric WZW models
• N=4 Superconformal Symmetry for the Covariant Quantum Superstring
• The BRST quantisation of chiral BMS-like field theories
• Pure spinor formulation of the superstring and its applications
• Untwisting Topological Field Theories