Perturbative Gravity and Gauge Theory Relations -- A Review

TL;DR

This review surveys how perturbative gravity amplitudes relate to gauge-theory amplitudes via KLT relations, rooted in closed-string–open-string factorization and explored through the field-theory limit. It develops a field-theoretic derivation of the n-point KLT relations, leveraging BCJ relations, regularized kernels, and BCFW recursion to avoid string-theory constructs. It then outlines the BCJ color-kinematic duality and the double-copy construction, showing how gravity amplitudes can be obtained by squaring gauge-theory numerators, with extensions to loops. The discussion highlights the structural unity of gravitational and gauge dynamics and outlines implications for multi-loop computations and amplitude methods.

Abstract

This review is dedicated to the amazing Kawai-Lewellen-Tye relations, connecting perturbative gravity and gauge theories at tree level. The main focus is on n-point derivations and general properties both from a string theory and pure field theory point of view. In particular the field theory part is based on some very recent developments.

Figures (5)

• Figure 1: The nested structure of the contours of integration for the $v^-_i$ variables corresponding to the ordering $0<v^+_2<v^+_3<\cdots<v^+_{n-2}<1$ of the $v_i^+$ variables.
• Figure 2: The three different ways of flipping contours in the five-point case.
• Figure 3: Diagrammatic representation of the KLT relation with $j=n-1$.
• Figure 4: Schematic outline of field theory proof.
• Figure 5: Diagrammatic representation of the Jacobi identity. The $c_i$'s can be obtained by dressing the vertices with structure constants $\tilde{f}^{abc}$, but the diagrams can also be thought of as representing the kinematic numerators $n_i$.