Perturbative path-integral of string fields and the A.sub.∞./sub. structure of the BV master equation

0568016 - FZÚ 2023 RIV US eng J - Journal Article
Masuda, Toru - Matsunaga, Hiroaki
Perturbative path-integral of string fields and the A_∞ structure of the BV master equation.
Progress of Theoretical and Experimental Physics. Roč. 2022, č. 11 (2022), č. článku 113B04. ISSN 2050-3911
R&D Projects: GA ČR(CZ) GX20-25775X
Institutional support: RVO:68378271
Keywords : perturbation theory * field theory: string * master equation: Batalin-Vilkovisky
OECD category: Particles and field physics
Impact factor: 8.3, year: 2022
Method of publishing: Open access

The perturbative path-integral gives a morphism of the (quantum) A∞ structure intrinsic to each quantum field theory, which we show explicitly on the basis of the homological perturbation. As is known, in the Batalin–Vilkovisky (BV) formalism, any effective action also solves the BV master equation, which implies that the path-integral can be understood as a morphism of the BV differential. Since each solution of the BV master equation is in one-to-one correspondence with a quantum A∞ structure, the path-integral preserves this intrinsic A∞ structure of quantum field theory, where A∞ reduces to L∞ whenever multiplications of space-time fields are graded commutative. We apply these ideas to string-field theory and (re-)derive some quantities based on the perturbative path-integral, such as effective theories with finite α′, reduction of gauge and unphysical degrees, the S-matrix, and gauge-invariant observables.
Permanent Link: https://hdl.handle.net/11104/0339349