L. Borsten, S. Nagy
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.
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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.
Limits of Symmetry in Schwarzschild: CKVs and BRST Triviality in the Kerr-Schild Double Copy
针对施瓦西解的Kerr-Schild double copy剩余对称性问题，拓展分析至共形基灵矢量发现结构不匹配，通过构建外尔补偿BRST复形证明无穷维模式非物理，验证了其量子自洽性。
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 redefinitio…
The Becchi-Rouet-Stora-Tyutin (BRST) ghost field is a key element in constructing Witten's cubic open string field theory. However, to date, the ghost sector of the string field theory has not received a great deal of attention. In this study, we address the BRST ghost on multiple $Dp$-branes, which carries non-Abelian indices and couples to a non-Ablelian gauge field. We found that the massless components of the BRST ghost field can play the role of the Faddeev-Popov ghost in the non-Alelian gauge field, such that the string field theory maintains the local non-Abelian gauge invariance.
Using BRST-BV formulation of relativistic dynamics, we study arbitrary spin massive and massless fields propagating in flat space. Generating functions of gauge invariant off-shell cubic interaction vertices for mixed-symmetry and totally symmetric fields are obtained. For the case of totally symmetric fields, we derive restrictions on the allowed values of spins and the number of derivatives, which provide a classification of cubic interaction vertices for such fields. As by product, we present simple expressions for the Yang-Mills and gravitational interactions of massive totally symmetric a…
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.
We develop an approach to constructing the manifestly Lorentz covariant cubic interaction vertices for the four-dimensional massless higher spin bosonic fields with two-component dotted and undotted spinor indices. Such fields automatically satisfy the traceless conditions what simplify form of the equations determining the irreducible massless representation of the Poincar'e group with given helicity. The cubic vertex is formulated in the framework of the BRST approach to higher spin field theory. Use of the above spin-tensor fields allows to simplify a form of the BRST-charge and hence to fi…
Residual Symmetries and BRST Cohomology of Schwarzschild in the Kerr-Schild Double Copy
本文研究Kerr-Schild双拷贝中Schwarzschild解的剩余对称性，发现规范侧无限维代数在引力侧仅存等距子群，并通过BRST算符平凡化验证了结构不匹配。
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 construct a class of nilpotent operators using the BRST current and ghost fields in superstring theory. The operator can be realized in cubic superstring field theory as a kinetic operator in the background of an identity-based solution. For a particular type of the deformed BRST operators, we find a homotopy operator and discuss its relationship to the cohomology in a similar way to the bosonic case, which has been elaborated by the authors.
We investigate the Lagrangian formulation of the double-copy correspondence between gauge theories and gravity, up to the cubic order. Building on the definition of the double-copy field as a convolution of two vectors, we obtain free gravitational Lagrangians as products of two Yang-Mills Lagrangians, in a form amenable to be easily extended to the massive case. We discuss the origin of these results from tensionless strings and show the existence of gauge fixings that mix the two spin-one sectors and lead to an alternative, especially simple, version of the free Lagrangian. We then construct…
The double copy relates scattering amplitudes in gauge and gravity theories. It has also been extended to classical solutions, and a number of approaches have been developed for doing so. One of these involves expressing fields in a variety of (super-)gravity theories in terms of convolutions of gauge fields, including also BRST ghost degrees of freedom that map neatly to their corresponding counterparts in gravity. In this paper, we spell out how to use the convolutional double copy to map gauge and gravity solutions in the manifest Lorenz and de Donder gauges respectively. We then apply this…
Towards the Double Copy Formulation for the Abelian Sector of Heterotic Double Field Theory
本文通过带电标量场的杨-米尔斯理论的双拷贝，构造了异质双场论阿贝尔扇区直至三阶的作用量，并证明其精确匹配。
BRST-BV approach for interacting higher spin fields
本文发展了BRST-BV方法，通过在耦合常数各阶保持主方程有效性，构造了d维Minkowski空间上高自旋场的离壳Lorentz协变相互作用顶点，并基于完整BRST算子显式求得了部分场的三次相互作用作用量。
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.
Covariant Lagrangian Cubic Interaction Vertices For Irreducible Higher Spin Fields in Minkowski Backgrounds
本文利用 BRST 与 BRST-BV 方法构造闵可夫斯基空间中不可约高自旋场的协变三次相互作用顶点，并证明完整与不完全 BRST 算子所得拉格朗日动力学的等价性可提升，同时给出 Q_c 方法下约束需构成阿贝尔超代数的条件。
We find double copy relations between classical radiating solutions in Yang-Mills theory coupled to dynamical color charges and their counterparts in a cubic bi-adjoint scalar field theory which interacts linearly with particles carrying bi-adjoint charge. The particular color-to-kinematics replacements we employ are motivated by the BCJ double copy correspondence for on-shell amplitudes in gauge and gravity theories. They are identical to those recently used to establish relations between classical radiating solutions in gauge theory and in dilaton gravity. Our explicit bi-adjoint solutions a…
The structure of a cubic Lagrangian vertex is clarified for irreducible fields of helicities $s_1, s_2, s_3$ in a $d$-dimensional Minkowski space. An explicit form of the operator $\mathcal{Z}_j$ entering the vertex in a non-multiplicative way (examined in arXiv:2105.12030[hep-th] for $j=1$) is obtained. The solution is found within the BRST approach with complete BRST operators, which contain all constraints corresponding to the conditions that extract the irreducible fields, including trace operators.
One loop analysis of the cubic action for gravity
本文分析Cheung和Remmen提出的引力三次一阶作用量，讨论其BRST不变性、计算平直空间单圈量子涨落贡献并验证Slavnov-Taylor恒等式，还与二阶作用量结果对比。
We describe the ghost sector of cubic string field theory in terms of degrees of freedom on the two halves of a split string. In particular, we represent a class of pure ghost BRST operators as operators on the space of half-string functionals. These BRST operators were postulated by Rastelli, Sen, and Zwiebach to give a description of cubic string field theory in the closed string vacuum arising from condensation of a D25-brane in the original tachyonic theory. We find a class of solutions for the ghost equations of motion using the pure ghost BRST operators. We find a vanishing action for th…
We consider a massless higher spin field theory within the BRST approach and construct a general off-shell cubic vertex corresponding to irreducible higher spin fields of helicities $s_1, s_2, s_3$. Unlike the previous works on cubic vertices, which do not take into account of the trace constraints, we use the complete BRST operator, including the trace constraints that describe an irreducible representation with definite integer helicity. As a result, we generalize the cubic vertex found in [arXiv:1205.3131 [hep-th]] and calculate the new contributions to the vertex, which contain additional …
In this paper, we outline a method to compute supersymmetric one-loop integrands in ten-dimensional SYM theory. It relies on the constructive interplay between their cubic-graph organization and BRST invariance of the underlying pure spinor superstring description. The five- and six-point amplitudes are presented in a manifestly local form where the kinematic dependence is furnished by BRST-covariant expressions in pure spinor superspace. At five points, the local kinematic numerators are shown to satisfy the BCJ duality between color and kinematics leading to supergravity amplitudes as a bypr…
We examine interacting bosonic higher spin gauge fields in the BRST-antifield formalism. Assuming that an interacting action $S$ is a deformation of the free action with a deformation parameter $g$, we solve the master equation $(S,S)=0$ from the lower orders in $g$. It is shown that choosing a certain cubic interaction as the first order deformation, we can solve the master equation and obtain an action containing all orders in $g$. The anti-ghost number of the obtained action is less than or equal to two. Furthermore we show that the obtained action is lifted to that of interacting bosonic h…
We explore extensions of the double copy to massive theories and find a new cubic theory with a local double copy. We consider the nonlinear sigma model and the special galileon theory, massless versions of which are known to be related through the double copy. We show that by performing a Kaluza-Klein reduction of these theories from five dimensions down to four, a double copy relation exists between the resulting massive four-dimensional scalar field theories. This requires the vanishing contribution of new galileon terms arising in high dimensions. We further explore if other interactions t…
From noncommutative Yang-Mills to noncommutative gravity through a classical double copy map
本文通过经典双拷贝映射，从非对易杨-米尔斯理论出发构造非对易引力，计算了三次双重场论作用量的θ²修正，并在D=4横向无迹规范下分析了纯引力极限。
Towards Lagrangian dynamics for constrained mixed-symmetric interacting higher-spin fields
本文针对d维闵可夫斯基空间的不可约相互作用无质量高自旋场，在不完备BRST算子框架下推导其自洽拉格朗日构造的充要条件，明确顶点约束要求并得到相互作用顶点的显式形式。
Towards a unified viewpoint of Gribov--Zwanziger and Serreau--Tissier gauge fixing
本文提出了一种统一的规范固定框架，结合ST复制平均和RGZ地平线抑制，通过BRST不变动作研究红外行为，并提供可调参数进行格点验证。
We investigate the existence of double copy structure, or the lack thereof, in higher derivative operators for Nambu-Goldstone bosons. At the leading ${\cal O}(p^2)$, tree amplitudes of Nambu-Goldstone bosons in the adjoint representation can be (trivially) expressed as the double copy of itself and the cubic bi-adjoint scalar theory, through the Kawai-Lewellen-Tye bilinear kernel. At the next-to-leading ${\cal O}(p^4)$ there exist four operators in general, among which we identify one operator whose amplitudes exhibit the flavor-kinematics duality and can be written as the double copy of ${\c…
In this final part of a series of three papers, we will assemble supersymmetric expressions for one-loop correlators in pure-spinor superspace that are BRST invariant, local, and single valued. A key driving force in this construction is the generalization of a so far unnoticed property at tree level; the correlators have the symmetry structure akin to Lie polynomials. One-loop correlators up to seven points are presented in a variety of representations manifesting different subsets of their defining properties. These expressions are related via identities obeyed by the kinematic superfields a…
Residual Symmetries and Their Algebras in the Kerr-Schild Double Copy
本文研究 Kerr-Schild 双重复制中残余对称性与引力的代数关系，发现 gauge 理论中残余对称性形成无限维函数代数，而引力中残余微分同胚生成 conformal 代数，最终通过 BRST 复合体证明物理对称性还原为 Schwarzschild 的全局对称性。
We construct the homotopy operators for the BRST operator in the theory around the identity-based solutions, which are believed to represent the tachyon vacuum in cubic bosonic open string field theory. Using the homotopy operators, we find that the one-loop vacuum energy at the tachyon vacuum is independent of moduli such as interbrane distances, which are included in the BRST operator. We also revisit the cohomology problem, which was solved earlier without the homotopy operators.
We argue that the complex transformation relating the Schwarzschild to the Taub-NUT metric, introduced by Talbot, is in fact an electric-magnetic duality transformation. We show that at null infinity, the complex transformation is equivalent to a complexified BMS supertranslation, which rotates the supertranslation and the dual (magnetic) supertranslation charges. This can also be seen from the cubic coupling between the classical source and its background, which for Taub-NUT is given by a complex phase rotation acting on gravitational minimal couplings. The same phase rotation generates dyons…
A stringy massive double copy
本文在弦理论中利用开弦有质量矢量构造闭弦有质量自旋-2态，通过三点振幅揭示双重复制结构，并在平坦时空下重现无鬼影双度量理论的立方拉格朗日量。
A simple BRST-closed expression for the color-ordered super-Yang-Mills 5-point amplitude at tree-level is proposed in pure spinor superspace and shown to be BRST-equivalent to the field theory limit of the open superstring 5-pt amplitude. It is manifestly cyclic invariant and each one of its five terms can be associated to the five Feynman diagrams which use only cubic vertices. Its form also suggests an empirical method to find superspace expressions in the cohomology of the pure spinor BRST operator for higher-point amplitudes based on their kinematic pole structure. Using this method, Ansae…
Starting from a Lie algebroid ${\cal A}$ over a space V we lift its action to the canonical transformations on the principle affine bundle ${\cal R}$ over the cotangent bundle $T^*V$. Such lifts are classified by the first cohomology $H^1({\cal A})$. The resulting object is the Hamiltonian algebroid ${\cal A}^H$ over ${\cal R}$ with the anchor map from $\G({\cal A}^H)$ to Hamiltonians of canonical transformations. Hamiltonian algebroids generalize the Lie algebras of canonical transformations. We prove that the BRST operator for ${\cal A}^H$ is cubic in the ghost fields as in the Lie algebra c…
Higher-Derivative Corrections via the Double Copy Procedure
本文通过双复制过程将高阶导数规范理论扩展为高阶导数双理论，揭示其与DFT+的关联，为构造α'修正拉格朗日量提供了新途径。
Constructing Conformal Double Field Theory through a Double Copy Map
本文将经典 Double Copy 程序应用于四阶导数规范理论，构建了包含 Weyl 引力的共形双场论，揭示了规范理论与 T-duality 不变模型间的深刻联系。
We examine, in a quantum mechanical setting, the Hilbert space representation of the BRST symmetry associated with Schwinger-Keldysh path integrals. This structure had been postulated to encode important constraints on influence functionals in coarse-grained systems with dissipation, or in open quantum systems. Operationally, this entails uplifting the standard Schwinger-Keldysh two-copy formalism into superspace by appending BRST ghost degrees of freedom. These statements were previously argued at the level of the correlation functions. We provide herein a complementary perspective by working…
The Double Copy of Maximal Supersymmetry in $D=10$
本文将同伦代数方法应用于 $D=10$ 的 $N=1$ 超杨-米尔斯理论，在场三次阶上推导出 IIA/IIB 型超引力，并证明全局超对称超李代数经双重复制可得到超引力的极大超对称。
We apply a recently presented BRST procedure to construct the Largangian cubic vertex of higher-spin gauge field triplets interacting with massive free scalars. In flat space, the spin-s triplet propagates the series of irreducible spin-s, s-2,..,0/1 modes which couple independently to corresponding conserved currents constructed from the scalars. The simple covariantization of the flat space result is not enough in AdS, as new interaction vertices appear. We present in detail the cases of spin-2 and spin-3 triplets coupled to scalars. Restricting to a single irreducible spin-s mode we uncover…
In this note, we construct a BRST invariant cubic vertex for massless fields of arbitrary mixed symmetry in flat space-time. The construction is based on the vertex given in bosonic Open String Field Theory. The algebra of gauge transformations is closed without any additional, higher than cubic, couplings due to the presence of an infinite tower of massless fields. We briefly discuss the generalization of this result to a curved space-time and other possible implications.
Consistent Lagrangians for irreducible interacting higher-spin fields with holonomic constraints
本研究在BRST方法框架下，探讨了不可约高自旋场相互作用的拉格朗日量构建，明确了完整约束需与BRST算符及顶点算符构成阿贝尔（超）代数，以保证完全与不完全BRST公式等价并产生相同顶点。
The Double Copy of Maximal Supersymmetry in $D=4$
本文用同伦代数与费米子冗余表述证明，$N=4$ SYM 的双重复制可在三次阶构造离壳局域规范不变的 $N=8$ 超引力，并实现 $SU(8)$ 的 $R$ 对称增强。
Structure of Chern-Simons Graviton Scattering Amplitudes from Topological Graviton Equivalence Theorem and Double Copy
本文基于拓扑引力等价定理和双重复制方法，研究了Chern-Simons引力子散射幅度的结构，揭示了高能极限下引力子与稀释子散射幅度之间的等价关系，并证明了引力子散射幅度中能量抵消的规律。
Hidden Amplitude Zeros From Double Copy
本文通过双拷贝方法揭示了散射振幅中隐藏零点与颜色-运动学对偶的关联，并证明其可推广至伽利略子振幅。
The Geometry of Time in Topological Quantum Gravity of the Ricci Flow
本文证明Ricci流拓扑非相对论量子引力的超空间两步构造等价于对具有拓扑形变和超局域非相对论时空微分同胚对称性的理论进行一步BRST规范固定，并揭示其对偶解释。
We expose a double-copy structure in the scattering amplitudes of the generic Jordan family of N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity theories in four and five dimensions. The Maxwell-Einstein supergravity amplitudes are obtained through the color/kinematics duality as a product of two gauge-theory factors; one originating from pure N=2 super-Yang-Mills theory and the other from the dimensional reduction of a bosonic higher-dimensional pure Yang-Mills theory. We identify a specific symplectic frame in four dimensions for which the on-shell fields and amplitudes from the doub…
General Lagrangian formulations for mixed-antisymmetric tensor fields on flat backgrounds
通过BRST方法，首次给出了满足杨图Y[ŝ1,ŝ2,...,ŝk]的不可约整数高旋无质量和大质量庞加莱群表示的拉格朗日形式，并提出了约束与非约束两种等价动力学但不同构型空间的规范拉格朗日表述。
AdS$_4$ Boundary Wightman functions in Twistor Space: Factorization, Conformal blocks and a Double Copy
研究AdS$_4$边界Wightman函数的因子化、共形块及双重复制关系，通过扭矢空间方法推导出四点和五点函数的优美形式，并在Yang-Mills理论与广义相对论中建立简单双重复制关系。
Double Copy from Tensor Products of Metric BV${}^{\color{gray} \blacksquare}$-algebras
该研究揭示含运动学李代数的场论的BV^■-代数底层结构，证明两个度量BV^■-代数的张量积可生成包含经典double copy构造的新配合场论作用量，还给出色-味剥离同伦代数视角并证明任意场论都伴随运动学L_∞-代数。
Weakly Constrained Double Field Theory as the Double Copy of Yang-Mills Theory
本文在所有维度均为环面且加倍的条件下，构建了弱约束双场论的四阶相互作用，通过同伦转移和非局域移动在双拷贝张量积空间上建立其$L_{\infty}$代数，并验证雅可比恒等式确立了三括号的唯一性。
Supersymmetric Massive Gravity
本文利用在壳超空间构造至多 $\mathcal{N}=4$ 超对称的大质量自旋2引力子三次振幅，证明高扩展下相互作用归于 dRGT，并在最大超对称时唯一对应无渐近超光速结构。
Weakly constrained double field theory: the quartic theory
本文利用同伦代数与 Yang-Mills 运动学同伦代数的双副本，宣布并概述了将弱约束双场论从三次阶推广至四次阶的构造。
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