Non-analytic terms of string amplitudes from partial waves

Abstract

We describe a general formalism based on the partial-wave decomposition to compute the iterative $s$-channel discontinuity of four-point amplitudes at any loop order. As an application, we focus on the low-energy expansions of type I and II superstring amplitudes. Besides providing new results for their leading and sub-leading logarithmic contributions beyond genus one, our approach elucidates the general structure of non-analytic threshold terms. In the case of open strings, the use of orthogonal colour projectors allows us to efficiently compute all contributions from different worldsheet topologies at a given loop order.

36 pages and 1 ancillary file; v2: minor improvements, typos fixed; v3: minor changes, published version

References in corpus (28)

• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Three-Loop Superfiniteness of N=8 Supergravity
• Duality and higher derivative terms in M theory
• Two-Loop Superstrings VI: Non-Renormalization Theorems and the 4-Point Function
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the Superstring
• The low energy expansion of the one-loop type II superstring amplitude
• Low energy expansion of the four-particle genus-one amplitude in type II superstring theory
• All Tree-Level Correlators in AdS${}_5\times$S${}_5$ Supergravity: Hidden Ten-Dimensional Conformal Symmetry
• Equivalence of Two-Loop Superstring Amplitudes in the Pure Spinor and RNS Formalisms
• Two-loop superstrings and S-duality
• On the modular structure of the genus-one Type II superstring low energy expansion
• The closed-string 3-loop amplitude and S-duality
• Super-Poincare Covariant Two-Loop Superstring Amplitudes
• New Higher-Derivative $R^4$ Theorems
• 5 loops in 24/5 dimensions
• Genus-One String Amplitudes from Conformal Field Theory
• Matching the $D^6{\mathcal{R}}^4$ interaction at two-loops
• Two-Loop Superstrings V: Gauge Slice Independence of the N-Point Function
• Non-renormalization conditions for four-gluon scattering in supersymmetric string and field theory
• Graviton partial waves and causality in higher dimensions
• Exploring transcendentality in superstring amplitudes
• Superstring loop amplitudes from the field theory limit
• All loop structures in Supergravity Amplitudes on $Ad{S}_5\times S^5$ from CFT
• Leading Infrared Logarithms from Unitarity, Analyticity and Crossing
• The vanishing of two-point functions for three-loop superstring scattering amplitudes
• Superstring measure and non-renormalization of the three-point amplitude
• Unitarity Cuts of the Worldsheet

Cited by in corpus (2)

• Type II superstring amplitude at one-loop and transcendentality
• One-loop four-graviton string amplitude at finite ${\alpha }^{\prime }$