量子主方程与Hodge关联子
Quantum master equation and Hodge correlators
AI总结：
本研究推广了Goncharov的Hodge关联子扭子联络，得到取值于可含环的单-三价图DG李代数且满足Maurer–Cartan方程的联络1-形式，可分别对应非循环Chern–Simons微扰论中有效作用量与量子主方程的算术类比。
摘要：
我们对Goncharov的Hodge关联子扭子联络进行了推广。推广后的版本是取值于单-三价图DG李代数的联络1-形式，该图可含环且满足某种Maurer–Cartan方程。该联络与Maurer–Cartan方程可分别视为与平凡局部系统相关的非循环Chern–Simons微扰论中有效作用量与量子主方程的算术类比。
英文摘要：
We give a generalization of Goncharov's Hodge correlator twistor connection. Our generalized version is a connection 1-form with values in a DG Lie algebra of uni-trivalent graphs which may have loops and satisfies some Maurer--Cartan equation. This connection and the Maurer--Cartan equation can be viewed as an arithmetic analogue of effective action and quantum master equation respectively in non-acyclic Chern--Simons perturbation theory associated with the trivial local system.
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