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Double-soft behavior for scalars and gluons from string theory

Paolo Di Vecchia, Raffaele Marotta, Matin Mojaza

TL;DR

This paper derives the leading double-soft theorems for gluons and scalars in open-string amplitudes on a Dp-brane within the bosonic string. By evaluating the n+2 gluon, two-scalar + n-gluon, and n+2 scalar amplitudes, the authors obtain universal 1/(q1 q2) soft factors that multiply the corresponding nonsoft amplitudes, with explicit kernels depending on momenta and polarizations. In the α' → 0 limit these results reproduce the known field-theory double-soft theorems for Yang–Mills and scalar theories, while the full string-theoretic expressions reveal additional structure and pole features, including non-contiguous soft-gluon configurations. The analysis covers both contiguous and non-contiguous soft gluons and demonstrates the consistency of gauge invariance and factorization across dimensions, providing a string-theoretic derivation of double-soft behavior for gauge and scalar states. Overall, the work extends double-soft theorems to open-string amplitudes in arbitrary dimensions, connecting string theory with field-theoretic soft limits.

Abstract

We compute the leading double-soft behavior for gluons and for the scalars obtained by dimensional reduction of a higher dimensional pure gauge theory, from the scattering amplitudes of gluons and scalars living in the world-volume of a Dp-brane of the bosonic string. In the case of gluons, we compute both the double-soft behavior when the two soft gluons are contiguous as well as when they are not contiguous. From our results, that are valid in string theory, one can easily get the double-soft limit in gauge field theory by sending the string tension to infinity.

Double-soft behavior for scalars and gluons from string theory

TL;DR

This paper derives the leading double-soft theorems for gluons and scalars in open-string amplitudes on a Dp-brane within the bosonic string. By evaluating the n+2 gluon, two-scalar + n-gluon, and n+2 scalar amplitudes, the authors obtain universal 1/(q1 q2) soft factors that multiply the corresponding nonsoft amplitudes, with explicit kernels depending on momenta and polarizations. In the α' → 0 limit these results reproduce the known field-theory double-soft theorems for Yang–Mills and scalar theories, while the full string-theoretic expressions reveal additional structure and pole features, including non-contiguous soft-gluon configurations. The analysis covers both contiguous and non-contiguous soft gluons and demonstrates the consistency of gauge invariance and factorization across dimensions, providing a string-theoretic derivation of double-soft behavior for gauge and scalar states. Overall, the work extends double-soft theorems to open-string amplitudes in arbitrary dimensions, connecting string theory with field-theoretic soft limits.

Abstract

We compute the leading double-soft behavior for gluons and for the scalars obtained by dimensional reduction of a higher dimensional pure gauge theory, from the scattering amplitudes of gluons and scalars living in the world-volume of a Dp-brane of the bosonic string. In the case of gluons, we compute both the double-soft behavior when the two soft gluons are contiguous as well as when they are not contiguous. From our results, that are valid in string theory, one can easily get the double-soft limit in gauge field theory by sending the string tension to infinity.

Paper Structure

This paper contains 6 sections, 79 equations, 1 figure.

Table of Contents

  1. Introduction and results
  2. Double-soft behavior with $n+2$ gluons
  3. Double-soft behavior with $2$ scalars and $n$ gluons
  4. Double-soft behavior with $n+2$ scalars
  5. Conclusions
  6. Computation of various integrals to the leading order in the double-soft limit

Figures (1)

  • Figure 1: Sketchy diagrams of the color-ordered n+2 gluon amplitude, where solid lines are the hard gluons and dashed lines are the soft gluons. Each term in Eq. (\ref{['now12']}) corresponds to one of the diagrams, and shows that all poles allowed in the color-ordered amplitude contribute to the double-soft limit.