# Gravity as the Square of Gauge Theory

1. Apr 7, 2010

### MTd2

http://arxiv.org/abs/1004.0693

Gravity as the Square of Gauge Theory

Zvi Bern, Tristan Dennen, Yu-tin Huang, Michael Kiermaier
(Submitted on 5 Apr 2010)
We explore consequences of the recently discovered duality between color and kinematics, which states that kinematic numerators in a diagrammatic expansion of gauge-theory amplitudes can be arranged to satisfy Jacobi-like identities in one-to-one correspondence to the associated color factors. Using on-shell recursion relations, we give a field-theory proof showing that the duality implies that diagrammatic numerators in gravity are just the product of two corresponding gauge-theory numerators, as previously conjectured. These squaring relations express gravity amplitudes in terms of gauge-theory ingredients, and are a recasting of the Kawai, Lewellen and Tye relations. Assuming that numerators of loop amplitudes can be arranged to satisfy the duality, our tree-level proof immediately carries over to loop level via the unitarity method. We then present a Yang-Mills Lagrangian whose diagrams through five points manifestly satisfy the duality between color and kinematics. The existence of such Lagrangians suggests that the duality also extends to loop amplitudes, as confirmed at two and three loops in a concurrent paper. By "squaring" the novel Yang-Mills Lagrangian we immediately obtain its gravity counterpart. We outline the general structure of these Lagrangians for higher points. We also write down various new representations of gauge-theory and gravity amplitudes that follow from the duality between color and kinematics.

2. Apr 7, 2010

### MTd2

I am trying to read this paper, but it seems that this duality gravity/duality is not restricted to the N=4 SUSY and N=8 SUGRA, but is generic to a large classe of different theories of gravity and gauge theories!

3. Apr 7, 2010

### MTd2

From the introduction of the paper:

"A natural question is: what Lagrangian generates diagrams that automatically satisfy the BCJ duality? We shall describe such a Lagrangian here, and present its explicit form up to five points, leaving the question of the more complicated explicit higher-point forms to the future. We have also worked out the six-point Lagrangian and outline its structure, and make comments about the all-orders form of the Lagrangian. We find that a covariant Lagrangian whose diagrams satisfy the duality is necessarily nonlocal.
We can make this Lagrangian local by introducing auxiliary fields. Remarkably we
find that, at least through six points, the Lagrangian differs from ordinary Feynman gauge
simply by the addition of an appropriate zero, namely terms that vanish by the color Jacobi identity. Although the additional terms vanish when summed, they appear in diagrams in just the right way so that the BCJ duality is satisfied. Based on the structures we find, it seems likely that any covariant Lagrangian where diagrams with an arbitrary number of external legs satisfy the duality must have an infinite number of interactions."

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For those who know a bit about asymptotic safetiy, why does that sound a bit to me like that? Maybe because we are relating an infinite complexity of interactions to a finite symmetry, BCJ, or in the case of the AS, to the safe point?