Loop Corrections to Soft Theorems in Gauge Theories and Gravity (1405.1410v2)

Abstract: In this paper, we study loop corrections to the recently proposed new soft theorem of Cachazo-Strominger, for both gravity and gauge theory amplitudes. We first review the proof of its tree-level validity based on BCFW recursion relations, which also establishes an infinite series of universals soft functions for MHV amplitudes, and a generalization to supersymmetric cases. For loop corrections, we focus on infrared finite, rational amplitudes at one loop, and apply recursion relations with boundary or double-pole contributions. For all-plus amplitudes, we prove that the subleading soft-theorems are exact to all multiplicities for both gauge and gravity amplitudes. For single-minus amplitudes, while the subleading soft-theorems are again exact for the minus-helicity soft leg, for plus-helicity loop corrections are required. Using recursion relations, we identify the source of such mismatch as stemming from the special contribution containing double poles, and obtain the all-multiplicity one-loop corrections to the subleading soft behavior in Yang-Mills theory. We also comment on the derivation of soft theorems using BCFW recursion in arbitrary dimensions.

Loop Corrections to Soft Theorems in Gauge Theories and Gravity: An Overview

This paper by He, Huang, and Wen meticulously investigates loop corrections to the soft theorems recently advanced by Cachazo and Strominger concerning gravity and gauge theory amplitudes. The authors begin by establishing the tree-level validity of these soft theorems through BCFW recursion relations. This elucidation leads to an infinite series of universal soft functions applicable to MHV amplitudes and presents a generalized approach for supersymmetric scenarios.

At the heart of the paper is the exploration of loop corrections within the domain of infrared finite, rational amplitudes at one loop level. The authors delve into gauge and gravity amplitudes, particularly focusing on scenarios involving all-plus and single-minus configurations. The examination hinges on using recursion relations, inclusive of boundary terms and double-pole contributions, to decode the exactitude and possible deviations at loop level.

One significant finding is the establishment that for all-plus amplitudes, the subleading soft theorems remain precise across all multiplicities, covering both gauge and gravity amplitudes. Conversely, for single-minus amplitudes, while subleading theorems hold exactly for the minus-helicity of the soft leg, discrepancies emerge when considering plus-helicity loop corrections. These deviations are traced back to particular contributions manifesting double poles, pinpointing the source of mismatch between expected and observed behaviors.

Numerically, the paper supports these assertions with robust formulas and systematically verifies the absence or presence of corrective factors at one loop. This pursuit not only highlights the nuances of soft theorems at loop levels but also suggests avenues for refining theoretical frameworks in gauge theories and gravity. It underscores the critical understanding necessary for advancing calculations related to these amplitudes.

The implications of this research are profound. Practically, these insights augment the precision of amplitude calculations required in quantum field theory applications. Theoretically, they invite further examination of symmetry principles, notably examining how loop corrections interweave with established symmetries like BMS and Yangian. Moreover, the exploration prompts speculation on future developments in AI concerning recursive methodologies utilized in amplitude computations, potentially enabling machine learning systems to predict loop effects efficiently.

In conclusion, He, Huang, and Wen's paper represents a rigorous examination of loop corrections to soft theorems. By leveraging previous foundational theories and extending them through meticulous recursion analysis, this work broadens understanding within particle physics, offering a detailed perspective on the symmetries and calculations at one-loop perturbative levels. Researchers engaged with amplitude studies and those exploring theoretical constructs in gauge and gravity frameworks will find this paper a valuable and insightful addition to ongoing efforts in the field.