Evaluating one-loop string amplitudes

Abstract

We evaluate one-loop open-string amplitudes at finite ${\alpha }^{\prime }$ for the first time. Our method involves a deformation of the integration contour over the modular parameter $\tau$ to a fractal contour introduced by Rademacher in the context of analytic number theory. This procedure leads to explicit and practical formulas for the one-loop four-point amplitudes in type-I superstring theory, amenable to numerical evaluation. We plot the amplitudes as a function of the Mandelstam invariants $s$ and $t$ and directly verify long-standing conjectures about their behaviour at high energies.

arXiv comment101 pages, many figures

References in corpus (23)

• Black Holes and Random Matrices
• Combinatorics of Boundaries in String Theory
• Split States, Entropy Enigmas, Holes and Halos
• Elliptic multiple zeta values and one-loop superstring amplitudes
• Explicit solutions of the multi-loop integral recurrence relations and its application
• Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the Superstring
• The Box Graph In Superstring Theory
• From elliptic multiple zeta values to modular graph functions: open and closed strings at one loop
• Chaotic scattering of highly excited strings
• Momentum Analyticity and Finiteness of the 1-Loop Superstring Amplitude
• Tree-level amplitudes from the pure spinor superstring
• Rademacher Expansions and the Spectrum of 2d CFT
• One-loop open-string integrals from differential equations: all-order alpha'-expansions at n points
• Rankin-Selberg methods for closed strings on orbifolds
• Dispersion Relations in String Theory
• All-order alpha'-expansion of one-loop open-string integrals
• Unitarity Cuts of the Worldsheet
• Renormalization and BRST symmetry in Donaldson-Witten theory
• On the Rankin-Selberg method for higher genus string amplitudes
• Snowmass White Paper: String Perturbation Theory
• Periods and Superstring Amplitudes
• The gravitational path integral for $N=4$ BPS black holes from black hole microstate counting
• Modular Graph Forms and Scattering Amplitudes in String Theory

Cited by in corpus (9)

• Renormalization and BRST symmetry in Donaldson-Witten theory
• Open String Amplitudes: Singularities, Asymptotics, and New Representations
• Lorentzian contours for tree-level string amplitudes
• Lectures in Quantum Gravity
• Chaotic and Thermal Aspects in the Highly Excited String S-Matrix
• Regge Limit of One-Loop String Amplitudes
• Tropological Sigma Models
• Rademacher expansion of modular integrals
• One-loop four-graviton string amplitude at finite ${\alpha }^{\prime }$