Gravity as the square of gauge theory

Journal Article · Wed Sep 15 04:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.82.065003· OSTI ID:21421186

Bern, Zvi; Dennen, Tristan; Yutin, Huang ^[1]; Kiermaier, Michael ^[2]

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1. Department of Physics and Astronomy, UCLA, Los Angeles, California 90095-1547 (United States)
2. Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08544 (United States)

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.

• OSTI ID: 21421186
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 6 Vol. 82; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
COLOR MODEL
COMPOSITE MODELS
DUALITY
EXPANSION
FIELD THEORIES
FUNCTIONS
GAUGE INVARIANCE
GRAVITATION
INVARIANCE PRINCIPLES
LAGRANGIAN FUNCTION
MATHEMATICAL MODELS
PARTICLE MODELS
QUARK MODEL
RECURSION RELATIONS
UNITARITY
YANG-MILLS THEORY