Gravity as the Square of Gauge Theory

By Z. Bern, Tristan Dennen, Yu-tin Huang, Michael Kiermaier. 2010

469 citations recorded by the source corpus.

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 frommore » the duality between color and kinematics.« less

Subfields: History and Philosophy of Science, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c1fd97f605cae8c7316b16f3b66cccc60e69dc26

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In History and Philosophy of Science

1. D. O’Connell
2. Chris D. White
3. R. Monteiro

In Nuclear and High Energy Physics

1. Alexander Ochirov
2. C. Cheung
3. D. O’Connell
4. R. Monteiro
5. A. Luna
6. Chris D. White
7. H. Johansson
8. Song He

In Statistical and Nonlinear Physics

1. R. Monteiro
2. Alexander Ochirov
3. D. O’Connell
4. C. Cheung
5. Song He
6. F. Cachazo
7. A. Luna
8. Chris D. White

Citations in the corpus

• Scattering of massless particles: scalars, gluons and gravitons (2013, background): “[17]) is not unique and not very useful for practical computations as it is tautological in nature.”
• Explicit BCJ numerators from pure spinors (2011, unknown): “There exist Kawai-Lewellen-Tye (KLT) inspired expressions for ni in terms of color ordered gauge theory amplitudes [37, 38] which do not exhibit manifest locality.”
• The double copy: Bremsstrahlung and accelerating black holes (2016, background): “More recently, the perturbative relationship between gauge and gravity theories has been formulated in a particularly suggestive manner by Bern, Carrasco and Johansson (BCJ) [3–5].”
• Color-kinematic duality for form factors (2012, methodology): “Color-dual numerators have been constructed explicitly at tree level for all multiplicities through a variety of methods [6–8], and at loop level in specific examples in N = 4 SYM for five points up to two loops [9] and for four points up to four loops [10].”
• Closed string amplitudes as single-valued open string amplitudes (2014, background): “There an apparent similarity between perturbative gauge– and gravity–theories is established through the double copy construction [4,5].”
• Perturbative spacetimes from Yang-Mills theory (2016, methodology): “[3, 87], and can be carried out to arbitrary perturbative order.”