Related papers: Transmuting off-shell CHY integrals in the double-…
We show that the half-integrands in the CHY representation of tree amplitudes give rise to the definition of differential forms -- the scattering forms -- on the moduli space of a Riemann sphere with $n$ marked points. These differential…
Many gauge theories possess a hidden duality between color and kinematics in their on-shell scattering amplitudes. An open problem is to formulate an off-shell realization of the duality, thus manifesting a kinematic algebra. We show that…
In this letter we present a recursive method for computing one-loop off-shell amplitudes in colored quantum field theories. First, we generalize the perturbiner method by recasting the multiparticle currents as generators of off-shell tree…
We present a novel type of differential equations for on-shell loop integrals. The equations are second-order and importantly, they reduce the loop level by one, so that they can be solved iteratively in the loop order. We present several…
Evidence has recently emerged for a hidden symmetry of scattering amplitudes in N=4 super Yang-Mills theory called dual conformal symmetry. At weak coupling the presence of this symmetry has been observed through five loops, while at strong…
We give a simple prescription for computing, in the framework of the bosonic string theory, off-shell one-loop amplitudes with any number of external massless particles, both for the open and for the closed string. We discuss their…
This is the second one of a series of four papers devoted to a first calculation of the scalar and spinor QED four-photon amplitudes completely off-shell. We use the worldline formalism which provides a gauge-invariant decomposition for…
We give a careful definition of the open string propagator in Schnabl gauge and present its worldsheet interpretation. The propagator requires two Schwinger parameters and contains the BRST operator. It builds surfaces by gluing strips of…
A polynomial form is established for the off-shell CHY scattering equations proposed by Lam and Yao. Re-expressing this in terms of independent Mandelstam invariants provides a new expression for the polynomial scattering equations,…
The color structure of two-loop gluon amplitudes is examined both from a color trace basis expansion and an alternative based upon structure constants. We use use this as a vehicle for systemising relations between the partial amplitudes of…
In this paper, we investigate tree-level scattering amplitude relations in $U(N)$ non-linear sigma model. We use Cayley parametrization. As was shown in the recent works [23,24] both on-shell amplitudes and off-shell currents with odd…
We derive a vertex operator based expression for the kinematic numerators of Yang-Mills amplitudes by applying the momentum kernel formalism to open string amplitudes. The expression involves an $\alpha'$-weighted commutator induced by the…
In this note we present an explicit procedure for the regularization of tree level amplitudes involving discrete states, using open string field theory. We show that there is a natural correspondence between the discrete states and…
The transition amplitude of a kaon to a pion and two off-shell photons is studied. First, it is computed at leading order (one-loop level) of the Chiral Perturbation Theory expansion. Explicit analytical results for the leading-order…
The newly discovered splitting behavior of tree-level scattering amplitudes of particles and strings has been expressed in terms of currents containing one off-shell leg. In this work, we explain how to obtain on-shell representations of…
Form factors are quantities that involve both asymptotic on-shell states and gauge invariant operators. They provide a natural bridge between on-shell amplitudes and off-shell correlation functions of operators, thus allowing us to use…
The renormalization, finiteness and off-shellness of short distance power like singular interactions is discussed. We show analytically that the renormalizability of the off-shell scattering amplitude relies completely on the corresponding…
We derive a general expression for on-shell recursion relations of closed string tree-level amplitudes. Starting with the string amplitudes written in the form of the Koba-Nielsen integral, we apply the BCFW shift to deform them. In…
N=2 supersymmetric Yang--Mills theories coupled to matter are considered in the Wess--Zumino gauge. The supersymmetries are realized nonlinearly and the anticommutator between two susy charges gives, in addition to translations, gauge…
We initiate an exploration of on-shell functions in $\mathcal{N}=4$ SYM beyond the planar limit by providing compact, combinatorial expressions for all leading singularities of MHV amplitudes and showing that they can always be expressed as…