We show that the double copy of gauge theory amplitudes to $\mathcal{N}=0$ supergravity amplitudes extends from tree level to loop level. We first explain that color-kinematic duality is a condition for the Becchi-Rouet-Stora-Tyutin operator and the action of a field theory with cubic interaction terms to double copy to a consistent gauge theory. We then apply this argument to Yang-Mills theory, where color-kinematic duality is known to be satisfied onshell at tree level. Finally, we show that the latter restriction can only lead to terms that can be absorbed in a sequence of field redefinitions, rendering the double copied action equivalent to $\mathcal{N}=0$ supergravity.
We construct the pure gravity Becchi-Rouet-Stora-Tyutin (BRST) Einstein-Hilbert Lagrangian, to cubic order, using the BRST convolution product of two Yang-Mills theories, in conjunction with the Bern-Carrasco-Johansson (BCJ) double-copy.
Motivated by the results of Anastasiou et al., we consider the convolutional double copy for BRST and anti-BRST covariant formulations of gravitational and gauge theories in more detail. We give a general BRST and anti-BRST invariant formulation of linearised $\mathcal{N}=0$ supergravity using superspace methods and show how this may be obtained from the square of linearised Yang-Mills theories. We demonstrate this relation for the Schwarzschild black hole and the ten-dimensional black string solution as two concrete examples.
The BRST operator cohomology of $N=2$ $2d$ supergravity coupled to matter is presented. Descent equations for primary superfields of the matter sector are derived. We find one copy of the cohomology at ghost number one, two independent copies at ghost number two, and conjecture that there is a copy at ghost number three. The $N=2$ string has a twisted $N=4$ superconformal symmetry generated by the $N=2$ superstress tensor, the BRST supercurrent, the antighost superfield, and the ghost number supercurrent.
The entire geometric formulations of the BRST and the anti-BRST structures are worked out in presence of the Nakanishi-Lautrup field. It is shown that in the general form of gauge fixing mechanisms within the Faddeev-Popov quantization approach, the antiBRST invariance reflects thoroughly the classical symmetry of the Yang-Mills theories with respect to gauge fixing methods. The Nakanishi-Lautrup field is also defined and worked out as a geometric object. This formulation helps us to introduce two absolutely new topological invariants of quantized Yang-Mills theories, so called the Nakanishi-L…
BRST cohomology of Yang-Mills gauge fields in the presence of gravity in Ashtekar variables
利用所谓的Maurer-Cartan水平性条件，得到了Ashtekar变量描述的引力存在下Yang-Mills规范场的BRST变换.由Wess-Zumino一致性条件表示的BRST上同调群借助于S. P. Sorella引入的算子$δ$求解，在我们的例子中，该算子具有非常简单的形式，并与微分算子$d$和BRST算子$s$一起生成比纯Yang-Mills理论中更简单的代数。这样我们就可以找到杨-米尔斯拉格朗日量、陈-西蒙斯项和规范反常。
We develop the basic ideas and equations for the BRST quantization of Yang-Mills theories in an explicit Hamiltonian approach, without any reference to the Lagrangian approach at any stage of the development. We present a new representation of ghost fields that combines desirable self-adjointness properties with canonical anticommutation relations for ghost creation and annihilation operators, thus enabling us to characterize the physical states on a well-defined Fock space. The Hamiltonian is constructed by piecing together simple BRST invariant operators to obtain a minimal invariant extensi…
We extend previous work on antifield dependent local BRST cohomology for matter coupled gauge theories of Yang-Mills type to the case of gauge groups that involve free abelian factors. More precisely, we first investigate in a model independent way how the dynamics enters the computation of the cohomology for a general class of Lagrangians in general spacetime dimensions. We then discuss explicit solutions in the case of specific models. Our analysis has implications for the structure of characteristic cohomology and for consistent deformations of the classical models, as well as for divergenc…
We show that the BRST Lagrangian double copy construction of $\mathcal{N}=0$ supergravity as the `square' of Yang-Mills theory finds a natural interpretation in terms of homotopy algebras. We significantly expand on our previous work arguing the validity of the double copy at the loop level, and we give a detailed derivation of the double copied Lagrangian and BRST operator. Our constructions are very general and can be applied to a vast set of examples.
We study the BRST renormalization of an alternative formulation of the Yang-Mills theory, where the matrix-propagator of the gluon and the complementary fields is diagonal. This procedure involves scalings as well as non-linear mixings of the fields and sources. We show, in the Landau gauge, that the BRST identities implement a recursive proof of renormalizability to all orders.
We show that double field theory arises from the color-kinematic double copy of Yang-Mills theory. A precise double copy prescription for the Yang-Mills action at quadratic and cubic order is provided that yields the double field theory action in which the duality invariant dilaton has been integrated out. More precisely, at quadratic order this yields the gauge invariant double field theory, while at cubic order it yields the cubic double field theory action subject to a gauge condition that originates from Siegel gauge in string field theory.
