Transcendentality and Crossing

TL;DR

This paper explores phase factors in the S-matrix of planar N=4 gauge theory, proposing modifications at four-loop order that could reconcile gauge and string theory discrepancies through a crossing-symmetric phase.

Contribution

It introduces a natural phase modification affecting odd zeta functions, potentially linking gauge theory results to a crossing-symmetric string theory phase.

Findings

Breakdown of perturbative BMN-scaling at four loops

Preservation of Kotikov-Lipatov transcendentality in the scaling function

Evidence for a non-perturbative relation to crossing-symmetric phase

Abstract

We discuss possible phase factors for the S-matrix of planar N=4 gauge theory, leading to modifications at four-loop order as compared to an earlier proposal. While these result in a four-loop breakdown of perturbative BMN-scaling, Kotikov-Lipatov transcendentality in the universal scaling function for large-spin twist operators may be preserved. One particularly natural choice, unique up to one constant, modifies the overall contribution of all terms containing odd zeta functions in the earlier proposed scaling function based on a trivial phase. Excitingly, we present evidence that this choice is non-perturbatively related to a recently conjectured crossing-symmetric phase factor for perturbative string theory on AdS_5xS^5 once the constant is fixed to a particular value. Our proposal, if true, might therefore resolve the long-standing AdS/CFT discrepancies between gauge and string theory.