AI 中文总结
该研究利用同伦代数的bar-cobar构造，将任意规范理论的运动方程转化为通用二次方程，证明其解与原理论解规范等价，还结合弦理论阐释了多局域场的物理意义。
AI 中文摘要
我们解释了同伦代数的“bar-cobar”构造如何将任意规范理论的运动方程重新表述为扩展场集合的规范协变二次方程。新方程的线性项编码了原理论的相互作用，而二次项是通用的。扩展场包括依赖一组坐标的I型多局域场，以及依赖多组坐标的II型多局域场。新的运动方程是微分分次结合代数或李代数的Maurer-Cartan方程。我们证明，新方程的每个解都规范等价于仅含I型场的解，该解对应原运动方程的解。在弦理论中，I型场是相关共形场论（CFT）的纠缠态，需插入黎曼面的多个刺点之间；一般II型态也可代表不连通的黎曼面。
英文摘要
We explain how the 'bar-cobar' construction for homotopy algebras reformulates the equations of motion of arbitrary gauge theories as gauge-covariant quadratic equations for an extended set of fields. The linear term of the new equations encodes the interactions of the original theory, while the quadratic term is universal. The extended fields include type-I multilocal fields, which depend on a set of coordinates and type-II multilocal fields, which depend on several sets of coordinates. The new equations of motion are the Maurer-Cartan equations of a differential graded associative algebra or Lie algebra. We show that every solution of the new equations is gauge equivalent to a solution with only type-I fields, that represents a solution of the original equations of motion. In string theory type-I fields are entangled states of the associated CFT, to be inserted across multiple punctures of a Riemann surface. General type-II states can also represent disconnected Riemann surfaces.
Comments70 pages plus 3 appendices
