论文标题
扭曲空间的运动学谎言代数
Kinematic Lie Algebras From Twistor Spaces
论文作者
论文摘要
我们从代数的角度分析了颜色界面二元性的理论，发现任何这样的理论都具有基本的bv $ {}^{\ color {灰色{灰色} \ blackSquare} $ - 代数结构，扩展了arxiv的思想：1912.03110。相反，我们表明，任何具有BV $ {}^{\ COLOR {灰色} \ BlackSquare} $的理论具有控制相互作用顶点的运动式代数。我们解释说，具有bv $ {}^{}^{\ color {灰色} \ blackSquare} $的理论的原型示例 - 代数是Chern-Simons理论，对于该理论而言，所得的Kinematic lie elgebra对多型schouten-nijenhuis algebra在多个场上对多态性。 bv $ {}^{\ color {灰色} \ blacksquare} $ - 代数意味着Chern-Simons理论的已知颜色界面二重性。 Similarly, we show that holomorphic and Cauchy-Riemann (CR) Chern-Simons theories come with BV${}^{\color{gray} \blacksquare}$-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 描述。我们表明，该结果在某些假设下扩展到循环级别。
We analyze theories with color-kinematics duality from an algebraic perspective and find that any such theory has an underlying BV${}^{\color{gray} \blacksquare}$-algebra structure, extending the ideas of arXiv:1912.03110. Conversely, we show that any theory with a BV${}^{\color{gray} \blacksquare}$-algebra features a kinematic Lie algebra that controls interaction vertices, both on- and off-shell. We explain that the archetypal example of a theory with BV${}^{\color{gray} \blacksquare}$-algebra is Chern-Simons theory, for which the resulting kinematic Lie algebra is isomorphic to the Schouten-Nijenhuis algebra on multivector fields. The BV${}^{\color{gray} \blacksquare}$-algebra implies the known color-kinematics duality of Chern-Simons theory. Similarly, we show that holomorphic and Cauchy-Riemann (CR) Chern-Simons theories come with BV${}^{\color{gray} \blacksquare}$-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.
