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Vanishing of BV cohomology

Banff International Research Station for Mathematical Innovation and Discovery

Consider the BV cohomology associated to a solution of the BV master equation for field theory on a d-dimensional world sheet. When d=0, Felder and Kazhdan have suggested the additional axiom that the cohomology for a physically relevant theory vanish below dimension 0. The natural generalization of this to d>0 is that the cohomology vanish below dimension d. In earlier work, we have shown that this axiom is violated for the spinning particle, which is a toy model of a supersymmetric field coupled to supergravity in d=1. Sean Pohorence and I have shown that in contrast, the axiom holds for the superparticle, which is a toy model of the Green- Schwartz superstring in d=1. This theory exhibits some interesting features: there is an infinite tower of ghosts, so it is important to work with the correct completion of the space of local observables, and also one must work with Cech cochains at every stage of the calculation.

Mathematics; Category theory; homological algebra; Quantum theory; Mathematical physics

video/mp4

Author affiliation: Northwestern University

2017-12-07

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63852

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/