Related papers: Ward Identity Implies Recursion Relation at Tree a…

We show that tree-level form factors with length-two operators in Yang-Mills-scalar (YMS) theory exhibit structures very similar to scattering amplitudes of gluons and scalars, which leads to new relations between them. Just like…

We present a general algorithm to compute off-shell, one-loop multigluon Green functions using bosonic string amplitudes. We identify and parametrize the regions in the space of moduli of one-loop Riemann surfaces that contribute to the…

In unitarity cut method, compact input of on-shell tree level amplitudes is crucial to simplify calculations. Although BCFW on-shell recursion relation gives very compact tree level amplitudes, they usually contain spurious poles. In this…

Using the double-copy construction of Yang-Mills-Einstein theories formulated in our earlier work, we obtain compact presentations for single-trace Yang-Mills-Einstein tree amplitudes with up to five external gravitons and an arbitrary…

We calculate form factors of half-BPS operators in N=4 super Yang-Mills theory at tree level and one loop using novel applications of recursion relations and unitarity. In particular, we determine the expression of the one-loop form factors…

M\"obius invariance is used to construct gluon tree amplitudes in the Cachazo, He, and Yuan (CHY) formalism. If it is equally effective in steering the construction of off-shell tree amplitudes, then the S-matrix CHY theory can be used to…

We present a method to compute the integrands of one-loop Einstein-Yang-Mills amplitudes for any number of external gauge and gravity multiplets. Our construction relies on the double-copy structure of Einstein-Yang-Mills as…

Starting from two-loops, there are Feynman integrals with higher powers of the propagators. They arise from self-energy insertions on internal lines. Within the loop-tree duality approach or within methods based on numerical unitarity one…

We establish a set of new on-shell recursion relations for amplitudes satisfying soft theorems. The recursion relations can apply to those amplitudes whose additional physical inputs from soft theorems are enough to overcome the bad large-z…

Supersymmetry and R-symmetry Ward identities relate on-shell amplitudes in a supersymmetric field theory. We solve these Ward identities for (Next-to)^K MHV amplitudes of the maximally supersymmetric N=4 and N=8 theories. The resulting…

One loop corrections to the helicity amplitudes of all 2 -> 2 subprocesses are calculated in QCD and in N=1 supersymmetric Yang-Mills theory using two versions of dimensional regularization: the `t~Hooft-Veltman scheme and dimensional…

We derive stringy Ward identities from the decoupling of two types of zero-norm states in the old covariant first quantized (OCFQ) spectrum of open bosonic string. These Ward identities are valid to all energy and all loop orders in string…

Attached to both Yang-Mills and General Relativity about Minkowski spacetime are distinguished gauge independent objects known as the on-shell tree scattering amplitudes. We reinterpret and rigorously construct them as $L_\infty$ minimal…

We construct a modified on-shell BCFW recursion relation to derive compact analytic representations of tree-level amplitudes in QED. As an application, we study the amplitudes of a fermion pair coupling to an arbitrary number of photons and…

We investigate the relation between 4d ambitwistor string theory and on-shell diagrams for planar N=4 super-Yang-Mills and N=8 supergravity, and deduce several new results about their scattering amplitudes at tree-level and 1-loop. In…

We derive and study Yangian Ward identities for the infinite class of four-point ladder integrals and their Basso-Dixon generalisations. These symmetry equations follow from interpreting the respective Feynman integrals as correlation…

We derive color decompositions of arbitrary tree and one-loop QCD amplitudes into color ordered objects called primitive amplitudes. Furthermore, we derive general fermion flip and reversion identities spanning the null space among the…

We verify the QED Ward identity for the two- and three -point functions at non-equilibrium in the HTL limit. We use the Keldysh formalism of real time finite temperature field theory. We obtain an identity of the same form as the Ward…

The one-loop corrections to the lattice supersymmetric Ward-Takahashi identity (WTi) are investigated in the off-shell regime. In the Wilson formulation of the N=1 supersymmetric Yang-Mills (SYM) theory, supersymmetry (SUSY) is broken by…

In this paper, we propose new understandings for recently discovered hidden zeros and novel splittings, by utilizing Feynman diagrams. The study focus on ordered tree level amplitudes of three theories, which are ${\rm Tr}(\phi^3)$,…