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Five-point Type IIB String Amplitudes at One Loop

Emiel Claasen, Mehregan Doroudiani

Abstract

Massless type IIB superstring amplitudes are organized according to the number of external states and their ${\mathrm U}(1)$ charge under the R-symmetry of type IIB supergravity. In this work, we analyze the low-energy expansion of one-loop five-point amplitudes in all charge sectors, focusing on the representative processes involving five gravitons and four gravitons with one dilaton. We compute the one-loop contributions to the moduli-dependent couplings in the type IIB effective action up to the $D^{12}R^5$ and $D^{14}φR^4$ interactions. The results are consistent with $S$-duality constraints in every charge sector and exhibit rich arithmetic structure, including single-valued multiple zeta values, affine linear combinations of logarithmic derivatives of the Riemann zeta function at odd integers, and a new constant of currently unknown nature.

Five-point Type IIB String Amplitudes at One Loop

Abstract

Massless type IIB superstring amplitudes are organized according to the number of external states and their charge under the R-symmetry of type IIB supergravity. In this work, we analyze the low-energy expansion of one-loop five-point amplitudes in all charge sectors, focusing on the representative processes involving five gravitons and four gravitons with one dilaton. We compute the one-loop contributions to the moduli-dependent couplings in the type IIB effective action up to the and interactions. The results are consistent with -duality constraints in every charge sector and exhibit rich arithmetic structure, including single-valued multiple zeta values, affine linear combinations of logarithmic derivatives of the Riemann zeta function at odd integers, and a new constant of currently unknown nature.
Paper Structure (19 sections, 94 equations, 4 tables)

This paper contains 19 sections, 94 equations, 4 tables.

Table of Contents

  1. Introduction
  2. Overview
  3. Review of genus-zero and genus-one string amplitudes
  4. $S$-duality and R-symmetry in type IIB
  5. Massless genus-zero superstring amplitudes
  6. Four- and five-point examples
  7. Massless genus-one closed-superstring amplitudes
  8. Conversion algorithm
  9. Massless genus-one five-point amplitudes
  10. Four-graviton warm-up
  11. The general five-point amplitude
  12. The U(1)-conserving sector
  13. The U(1)-violating sector
  14. Connecting sectors through $S$-duality
  15. Comments on transcendentality patterns
  16. ...and 4 more sections