# Spectral sequences and Batalin-Vilkovisky formalism

I have been studying the BRST quantization in quantum field theory recently and noticed that the subject is very much related to algebraic topology and cohomology. A quick google search led me to the paper Local BRST cohomology in gauge theories Indeed, there are even applications of spectral spectral sequences in this subject, as can be found here Simplifying Local BRST Cohomology Calculation via Spectral Sequence. I know that there exists a generalization of the BRST quantization to supersymmetric gauge theories, namely the Batalin-Vilkovisky formalism. Does algebraic topology, and in particular spectral sequences show up in this area of physics as well? (and if so, how?)

• I would voice a disagreement with a premise in this question, which is that "cohomology + spectral sequences = algebraic topology". Cohomology and various mathematical tools related to it make up the so-called subject of "homological algebra", essentially an advanced extension of what is considered elementary linear algebra. It may have originated in algebraic topology, but has since then transcended that subject and has found many applications in other branches of mathematics. In particular, you have noted that it has applications in mathematical physics, in quantization of gauge theories. Commented Feb 10, 2015 at 10:10
• Also, I think it's incorrect to characterize the BV (or BV-BRST) formalism as a generalization intended for "supersymmetric gauge theories". The BV formalism applies quite happily to field theories with or without any kind of symmetries (gauge-, super- or otherwise). What BV can do that simple BRST cannot is to allow certain symmetry-related identities to hold only modulo the equations of motion. The Barnich-Brandt-Henneaux review you linked to in fact already covers the BV (aka "field-antifield") formalism, with evidently copious applications of methods of homological algebra. Commented Feb 10, 2015 at 10:15