Title: Locality and Unitarity of Scattering Amplitudes from Singularities and Gauge Invariance

Abstract

We conjecture that the leading two-derivative tree-level amplitudes for gluons and gravitons can be derived from gauge invariance together with mild assumptions on their singularity structure. Assuming locality (that the singularities are associated with the poles of cubic graphs), we prove that gauge invariance in just n-1 particles together with minimal power counting uniquely fixes the amplitude. Unitarity in the form of factorization then follows from locality and gauge invariance. We also give evidence for a stronger conjecture: assuming only that singularities occur when the sum of a subset of external momenta go on shell, we show in nontrivial examples that gauge invariance and power counting demand a graph structure for singularities. Thus, both locality and unitarity emerge from singularities and gauge invariance. Similar statements hold for theories of Goldstone bosons like the nonlinear sigma model and Dirac-Born-Infeld by replacing the condition of gauge invariance with an appropriate degree of vanishing in soft limits.

Authors:

Arkani-Hamed, Nima; Rodina, Laurentiu; Trnka, Jaroslav

Publication Date:

Fri Jun 08 00:00:00 EDT 2018

Research Org.:

Univ. of California, Davis, CA (United States). Inst. for Advanced Study

Sponsoring Org.:

USDOE

OSTI Identifier:

1441068

Alternate Identifier(s):

OSTI ID: 1498980

Grant/Contract Number:  

SC0009988; SC0009999

Resource Type:

Published Article

Journal Name:

Physical Review Letters

Additional Journal Information:

Journal Name: Physical Review Letters Journal Volume: 120 Journal Issue: 23; Journal ID: ISSN 0031-9007

Publisher:

American Physical Society

Country of Publication:

United States

Language:

English

Subject:

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS