Deformations of closed strings and topological open membranes

Christiaan Hofman, Whee Ky Ma

Research output: Contribution to journalArticlepeer-review


We study deformations of topological closed strings. A well-known example is the perturbation of a topological closed string by itself, where the associative OPE product is deformed, and which is governed by the WDVV equations. Our main interest will be closed strings that arise as the boundary theory for topological open membranes, where the boundary string is deformed by the bulk membrane operators. The main example is the topological open membrane theory with a nonzero 3-form field in the bulk. In this case the Lie bracket of the current algebra is deformed, leading in general to a correction of the Jacobi identity. We identify these deformations in terms of deformation theory. To this end we describe the deformation of the algebraic structure of the closed string, given by the BRST operator, the associative product and the Lie bracket. Quite remarkably, we find that there are three classes of deformations for the closed string, two of which are exemplified by the WDVV theory and the topological open membrane. The third class remains largely mysterious, as we have no explicit example.

Original languageEnglish (US)
Pages (from-to)XXXXIII-48
JournalJournal of High Energy Physics
Issue number6
StatePublished - 2001


  • Chern-simons theories
  • Conformai field models in string theory
  • Differential and algebraic geometry
  • Topological field theories

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


Dive into the research topics of 'Deformations of closed strings and topological open membranes'. Together they form a unique fingerprint.

Cite this