Perturbative path-integral of string fields and the A∞ structure of the BV master equation
Perturbative path-integral of string fields and the A∞ structure of the BV master equation
复制标题
弦场的微扰路径积分和 BV 主方程的 A∞ 场结构
DOI：
10.1093/ptep/ptac132
复制
发表时间：
2022
影响因子：
3.5
通讯作者：
Toru Masuda
中科院分区：
文献类型：
--
作者：
Hiroaki Matsunaga;Toru Masuda
微扰路径积分给出了每个量子场论固有的（量子）a∞结构的态射，我们在同调微扰的基础上显式地证明了这一点。众所周知，在Batalin-Vilkovisky （BV）形式主义中，任何有效作用也能解BV主方程，这意味着路径积分可以理解为BV微分的态射。由于BV主方程的每个解都与量子∞结构一一对应，因此路径积分保留了量子场论的这种本然∞结构，其中a∞在时空场的乘法是渐变可交换的情况下降低了toL∞。我们将这些思想应用于弦场理论，并（重新）推导出一些基于微扰路径积分的量，如有限α '的有效理论、规范度和非物理度的约化、s -矩阵和规范不变的可观测值。
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 quantumA∞structure, the path-integral preserves this intrinsicA∞structure of quantum field theory, whereA∞reduces toL∞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, theS-matrix, and gauge-invariant observables.