Worldline Approach of Topological BF Theory

Abstract

We present a worldline description of topological non-abelian BF theory in arbitrary space-time dimensions. It is shown that starting with a trivial classical action defined on the worldline, the BRST cohomology has a natural representation as the sum of the de Rham cohomology. Based on this observation, we construct a second-quantized action of the BF theory. Interestingly enough, this theory naturally gives us a minimal solution to the Batalin-Vilkovisky master equation of the BF theory. Our formalism sheds some light not only on an interplay between the Witten-type and the Schwarz-type topological quantum field theories but also on the role of the Batalin-Vilkovisky antifields and ghosts as geometrical and elementary objects.

12 pages, no figures, references added

References in corpus (5)

• Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the Superstring
• Covariant One-Loop Amplitudes in D=11
• Relating the Green-Schwarz and Pure Spinor Formalisms for the Superstring
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Cited by in corpus (7)

• Pure Spinor Formalism as an N=2 Topological String
• Y-formalism and $b$ ghost in the Non-minimal Pure Spinor Formalism of Superstrings
• Higher genus superstring amplitudes from the geometry of moduli spaces
• Quantum Field Theory as Effective BV Theory from Chern-Simons
• Perturbative BF theory
• Emergence of Superstring from Pure Spinor
• Effective Lagrangian for Non-Abelian Two-Dimensional Topological Field Theory