Three particle superstring amplitudes with massive legs

On-shell superspaces and associated spinor helicity techniques give an efficient formulation of the Ward identities of on-shell supersymmetry for scattering amplitudes and supply tools to construct their solutions. Based on these techniques in this paper the general solutions of the Ward identities are presented for three particle scattering amplitudes with one, two or three massive legs for simple supersymmetry in ten and eight dimensions. It is shown in examples how these solutions may be used to obtain concrete amplitudes for the closed (IIB) and open superstring in a flat background. Explicit results include all three point amplitudes with one massive leg whose functional form is shown to be dictated completely by super-Poincare symmetry. The resulting surprisingly simple series only involves massive superfields labelled by completely symmetric little group representations. The extension to more general explicit three and higher point amplitudes in string theory is initiated. In appendices the field content of the fundamental massive superfields of the open and closed superstring are listed in terms of the Dynkin labels of a variety of groups which may be of independent interest.Comment: 45 pages. v2: typos corrected, references adde

On correlation functions of Wilson loops, local and non-local operators

We discuss and extend recent conjectures relating partial null limits of correlation functions of local gauge invariant operators and the expectation value of null polygonal Wilson loops and local gauge invariant operators. We point out that a particular partial null limit provides a strategy for the calculation of the anomalous dimension of short twist-two operators at weak and strong coupling.Comment: 29 pages, 8 figure

On BCFW shifts of integrands and integrals

In this article a first step is made towards the extension of Britto-Cachazo-Feng-Witten (BCFW) tree level on-shell recursion relations to integrands and integrals of scattering amplitudes to arbitrary loop order. Surprisingly, it is shown that the large BCFW shift limit of the integrands has the same structure as the corresponding tree level amplitude in any minimally coupled Yang-Mills theory in four or more dimensions. This implies that these integrands can be reconstructed from a subset of their `single cuts'. The main tool is powercounting Feynman graphs in a special lightcone gauge choice employed earlier at tree level by Arkani-Hamed and Kaplan. The relation between shifts of integrands and shifts of its integrals is investigated explicitly at one loop. Two particular sources of discrepancy between the integral and integrand are identified related to UV and IR divergences. This is cross-checked with known results for helicity equal amplitudes at one loop. The nature of the on-shell residue at each of the single-cut singularities of the integrand is commented upon. Several natural conjectures and opportunities for further research present themselves.Comment: 43 pages, 6 figures, v2: minor improvement in exposition, typos fixed, bibliography update

Simple superamplitudes in higher dimensions

We provide simple superspaces based on a formulation of spinor helicity in general even dimensions. As a distinguishing feature these spaces admit a fermionic super-momentum conserving delta function solution to the on-shell supersymmetry Ward identities. Using these solutions, we present beautifully simple formulae for the complete three, four and five point superamplitudes in maximal super Yang-Mills theory in eight dimensions, and for the three and four point superamplitudes in ten dimensional type IIB supergravity. In addition, we discuss the exceptional kinematics of the three point amplitude, and the supersymmetric spinorial BCFW recursion, in general dimensions.Comment: 34 page

On tree amplitudes with gluons coupled to gravitons

In this paper, we study the tree amplitudes with gluons coupled to gravitons. We first study the relations among the mixed amplitudes. With BCFW on-shell recursion relation, we will show the color-order reversed relation, $U(1)$-decoupling relation and KK relation hold for tree amplitudes with gluons coupled to gravitons. We then study the disk relation which expresses mixed amplitudes by pure gluon amplitudes. More specifically we will prove the disk relation for mixed amplitudes with gluons coupled to one graviton. Using the disk relation and the properties of pure gluon amplitudes, the color-order reversed relation, $U(1)$-decoupling relation and KK relation for mixed amplitudes can also be proved. Finally, we give some brief discussions on BCJ-like relation for mixed amplitudes.Comment: 33pages,no figur

Yang-Mills amplitude relations at loop level from non-adjacent BCFW shifts

This article studies methods to obtain relations for scattering amplitudes at the loop level, with concrete examples at one loop. These methods originate in the analysis of large so-called Britto-Cachazo-Feng-Witten shifts of tree level amplitudes and loop level integrands. In particular BCFW shifts for particles which are not color adjacent and some particular generalizations of this situation are analyzed in some detail in four and higher dimensions. For generic non-adjacent shifts our results are independent of loop order for integrands and hold for generic minimally coupled gauge theories with possible scalar potential and Yukawa terms. By a standard argument this result indicates a generalization of the Bern-Carrasco-Johansson relations for tree level amplitudes exists to the integrand at all loop levels. A concrete relation is presented at one loop. Furthermore, inspired by results in QED it is shown that the results on generalized BCFW shifts of tree level amplitudes imply relations for the so-called rational, bubble and triangle terms of one loop amplitudes in pure Yang-Mills theory. Bubble and triangle terms for instance are shown to obey a five photon decoupling identity, while a three photon decoupling identity is demonstrated for the rational terms. Along the same lines recently conjectured relations for helicity equal amplitudes at one loop are shown to generalize to helicity independent relations for the massive box coefficient of the rational terms.Comment: 69 pages, 27 figure

Massive amplitudes on the Coulomb branch of N=4 SYM

We initiate a systematic study of amplitudes with massive external particles on the Coulomb-branch of N=4 super Yang Mills theory: 1) We propose that (multi-)soft-scalar limits of massless amplitudes at the origin of moduli space can be used to determine Coulomb-branch amplitudes to leading order in the mass. This is demonstrated in numerous examples. 2) We find compact explicit expressions for several towers of tree-level amplitudes, including scattering of two massive W-bosons with any number of positive helicity gluons, valid for all values of the mass. 3) We present the general structure of superamplitudes on the Coulomb branch. For example, the n-point "MHV-band" superamplitude is proportional to a Grassmann polynomial of mixed degree 4 to 12, which is uniquely determined by supersymmetry. We find explicit tree-level superamplitudes for this MHV band and for other simple sectors of the theory. 4) Dual conformal generators are constructed, and we explore the dual conformal properties of the simplest massive amplitudes. Our compact expressions for amplitudes and superamplitudes should be of both theoretical and phenomenological interest; in particular the tree-level results carry over to truncations of the theory with less supersymmetry.Comment: 29 pages, 1 figur

On-shell Recursion in String Theory

We prove that all open string theory disc amplitudes in a flat background obey Britto-Cachazo-Feng-Witten (BCFW) on-shell recursion relations, up to a possible reality condition on a kinematic invariant. Arguments that the same holds for tree level closed string amplitudes are given as well. Non-adjacent BCFW-shifts are related to adjacent shifts through monodromy relations for which we provide a novel CFT based derivation. All possible recursion relations are related by old-fashioned string duality. The field theory limit of the analysis for amplitudes involving gluons is explicitly shown to be smooth for both the bosonic string as well as the superstring. In addition to a proof a less rigorous but more powerful argument based on the underlying CFT is presented which suggests that the technique may extend to a much more general setting in string theory. This is illustrated by a discussion of the open string in a constant B-field background and the closed string on the level of the sphere.Comment: 36 + 9 pages text, one figure, v3: added discussion on relation to old-fashioned factorization, typos corrected, published versio