Borsten Leron, Jurčo Branislav, Kim Hyungrok, Macrelli Tommaso, Saemann Christian, Wolf Martin
Department of Physics, Astronomy, and Mathematics, University of Hertfordshire, Hatfield AL10 9AB, United Kingdom.
Mathematical Institute, Faculty of Mathematics and Physics, Charles University Prague, Prague 186 75, Czech Republic.
Phys Rev Lett. 2023 Jul 28;131(4):041603. doi: 10.1103/PhysRevLett.131.041603.
We analyze theories with color-kinematics duality from an algebraic perspective and find that any such theory has an underlying BV^{▪}-algebra, extending the ideas of Reiterer [A homotopy BV algebra for Yang-Mills and color-kinematics, arXiv:1912.03110.]. Conversely, we show that any theory with a BV^{▪}-algebra features a kinematic Lie algebra that controls interaction vertices, both on shell and off shell. We explain that the archetypal example of a theory with a BV^{▪}-algebra is Chern-Simons theory, for which the resulting kinematic Lie algebra is isomorphic to the Schouten-Nijenhuis algebra on multivector fields. The BV^{▪}-algebra implies the known color-kinematics duality of Chern-Simons theory. Similarly, we show that holomorphic and Cauchy-Riemann Chern-Simons theories come with BV^{▪}-algebras and that, on the appropriate twistor spaces, these theories organize and identify kinematic Lie algebras for self-dual and full Yang-Mills theories, as well as the currents of any field theory with a twistorial description. We show that this result extends to the loop level under certain assumptions.
我们从代数角度分析具有色-运动学对偶性的理论，发现任何此类理论都有一个潜在的(BV^{▪})-代数，这扩展了赖特勒尔的观点[用于杨-米尔斯和色-运动学的同伦(BV)代数，arXiv:1912.03110。]。反之，我们证明任何具有(BV^{▪})-代数的理论都有一个运动学李代数，它控制壳上和壳外的相互作用顶点。我们解释说，具有(BV^{▪})-代数的理论的典型例子是陈-西蒙斯理论，其产生的运动学李代数与多向量场上的舒昂-尼延胡伊斯代数同构。(BV^{▪})-代数意味着陈-西蒙斯理论已知的色-运动学对偶性。类似地，我们证明全纯和柯西-黎曼陈-西蒙斯理论都带有(BV^{▪})-代数，并且在适当的扭量空间上，这些理论组织并识别自对偶和全杨-米尔斯理论的运动学李代数，以及任何具有扭量描述的场论的流。我们表明，在某些假设下，这个结果可以推广到圈级。
