RNS derivation of N-point disk amplitudes from the revisited S-matrix approach

Abstract

In the past year, in arXiv:1208.6066 we proposed a revisited S-matrix approach to efficiently find the bosonic terms of the open superstring low energy effective lagrangian (OSLEEL). This approach allows to compute the ${{\alpha }^{\prime }}^N$ terms of the OSLEEL using open superstring $n$-point amplitudes in which $n$ is very much lower than $(N+2)$ (which is the order of the required amplitude to obtain those ${{\alpha }^{\prime }}^N$ terms by means of the conventional S-matrix approach). In this work we use our revisited S-matrix approach to examine the structure of the scattering amplitudes, arriving at a closed form for them. This is a RNS derivation of the formula first found by Mafra, Schlotterer and Stieberger in arXiv:1106.2645, using the Pure Spinor formalism. We have succeeded doing this for the 5, 6 and 7-point amplitudes. In order to achieve these results we have done a careful analysis of the kinematical structure of the amplitudes, finding as a by-product a purely kinematical derivation of the BCJ relations (for N=4, 5, 6 and 7). Also, following the spirit of the revisited S-matrix approach, we have found the ${\alpha }^{\prime }$ expansions for these amplitudes up to ${{\alpha }^{\prime }}^6$ order in some cases, by only using the well known open superstring 4-point amplitude, cyclic symmetry and tree level unitarity: we have not needed to compute any numerical series or any integral involving polylogarithms, at any moment.

77 pages, 3 figures

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• Tree-level amplitudes from the pure spinor superstring
• On the soft limit of closed string amplitudes with massive states
• On the soft limit of open string disk amplitudes with massive states
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• Constraining Higher Derivative Supergravity with Scattering Amplitudes
• Composing Effective Prediction at Five Points
• New Formulas for Amplitudes from Higher-Dimensional Operators
• Berends-Giele currents in Bern-Carrasco-Johansson gauge for $F^3$- and $F^4$-deformed Yang-Mills amplitudes
• Uniqueness from gauge invariance and the Adler zero
• Graviton and gluon scattering from first principles
• String-motivated one-loop amplitudes in gauge theories with half-maximal supersymmetry
• Expansion of Einstein-Yang-Mills theory by Differential Operators
• Differential Equations, Associators, and Recurrences for Amplitudes
• A minimal approach to the scattering of physical massless bosons
• Simplifying one-loop amplitudes in superstring theory
• The analytic structure of amplitudes on backgrounds from gauge invariance and the infra-red
• A graphic approach to gauge invariance induced identity
• Remarks on the mixed Ramond -Ramond, open string scattering amplitudes of BPS, non-BPS and brane-anti brane
• On D-brane-Anti D-brane Effective actions and their all order Bulk Singularity Structures
• On Bulk Singularity Structures and all order ${\alpha }^{\prime }$ Contact Terms of BPS String Amplitudes
• Gauge invariance induced relations and the equivalence between distinct approaches to NLSM amplitudes
• One-loop superstring six-point amplitudes and anomalies in pure spinor superspace
• Expansion of EYM Amplitudes in Gauge Invariant Vector Space
• Highly Symmetric D-brane-Anti-D-brane Effective Actions
• On SYM theory and all order Bulk Singularity Structures of BPS Strings in type II theory
• Remarks on Non-BPS String Amplitudes and Their All Order ${\alpha }^{\prime }$ Contact Interactions in IIB, IIA
• On WZ and RR Couplings of BPS Branes and their all order ${\alpha }^{\prime }$ Corrections in IIB, IIA
• On All-Order Higher-Point $\text{D}p$-$\overline{\text{D}p}$ Effective Actions
• The origin of the KLT relations and nonlinear relations for Yang-Mills amplitudes
• All-Order Quartic Couplings in Highly Symmetric D-brane-Anti-D-brane Systems
• On Non-BPS Effective Actions of String Theory
• On New Bulk Singularity Structures, RR Couplings in Asymmetric Picture and Their All Order ${\alpha }^{\prime }$ Corrections
• All Order ${\alpha }^{\prime }$ Corrections to Fermionic Couplings of D-brane-Anti-D-brane Effective Actions
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• On BPS World Volume, RR Couplings and their ${\alpha }^{\prime }$ Corrections in type IIB