The Subleading Eikonal in Supergravity Theories

Abstract

In this paper we study the subleading contributions to eikonal scattering in (super)gravity theories with particular emphasis on the role of both elastic and inelastic scattering processes. For concreteness we focus on the scattering of various massless particles off a stack of D$p$-branes in type II supergravity in the limit of large impact parameter $b$. We analyse the relevant field theory Feynman diagrams which naturally give rise to both elastic and inelastic processes. We show that in the case analysed the leading and subleading eikonal only depend on elastic processes, while inelastic processes are captured by a pre-factor multiplying the exponentiated leading and subleading eikonal phase. In addition to the traditional Feynman diagram computations mentioned above, we also present a novel method for computing the amplitudes contributing to the leading and subleading eikonal phases, which, in the large $b$ limit, only involves knowledge of the onshell three and four-point vertices. The two methods are shown to give the same results. Furthermore we derive these results in yet another way, by computing various one-point amplitudes which allow us to extract the classical solution of the gravitational back reaction of the target D$p$-branes. Finally we show how our expressions for the leading and subleading eikonal agree with the calculation of the metric and corresponding deflection angle for massless states moving along geodesics in the relevant curved geometry.

40 pages, 5 figures

References in corpus (26)

• Effective one-body approach to general relativistic two-body dynamics
• String Solitons
• Causality Constraints on Corrections to the Graviton Three-Point Coupling
• The Pomeron and Gauge/String Duality
• Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory
• High-energy gravitational scattering and the general relativistic two-body problem
• General Relativity from Scattering Amplitudes
• Superstring Scattering from D-Branes
• Quantum Corrections to the Schwarzschild and Kerr Metrics
• Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings
• Essentials of Blackfold Dynamics
• Bending of Light in Quantum Gravity
• Scattering of Strings from D-branes
• The Size of p-Branes
• Light-like Scattering in Quantum Gravity
• Locality in quantum gravity and string theory
• High Energy Scattering in Perturbative Quantum Gravity at Next to Leading Power
• Gravitational spin-orbit coupling in binary systems, post-Minkowskian approximation and effective one-body theory
• Next-to-soft corrections to high energy scattering in QCD and gravity
• Wilson line approach to gravity in the high energy limit
• High energy scattering in gravity and supergravity
• High-energy string-brane scattering: leading eikonal and beyond
• Is a classical description of stable non-BPS D-branes possible?
• T-duality of the Riemann curvature corrections to supergravity
• Microscopic unitary description of tidal excitations in high-energy string-brane collisions
• Sphere-level Ramond-Ramond couplings in Ramond-Neveu-Schwarz formalism

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