Proof of the graviton MHV formula using Plebanski's second heavenly equation
| Autor: | Miller, Noah |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Self-dual spacetimes can be thought of as spacetimes containing only positive helicity gravitons. In this work we present a new perturbiner expansion for self-dual spacetimes based on Plebanski's second heavenly equation. Our expansion is naturally organized as a sum over ``marked tree graphs'' where each node corresponds to a positive helicity graviton and can have an arbitrary number of edges. Negative helicity gravitons must be added in by hand. We then use this perturbiner expansion to give a first principles derivation of the NSVW tree formula for the MHV amplitude in Einstein gravity. A unique feature of this proof is that it does not use BCFW recursion or twistor theory. It works by plugging the spacetime with arbitrarily many $+$ gravitons and two $-$ gravitons into the on-shell gravitational action and evaluating it. The action we use is the self-dual Plebanski action plus an additional boundary term. Interestingly, the amplitude comes entirely from the boundary term. In the appendix we give another way to express our perturbiner expansion using binary tree graphs instead of marked tree graphs, and prove the equivalence of these two expansions diagrammatically. We also provide an introduction to self-dual gravity aimed at non-experts, as well as a proof of the Parke-Taylor formula in Yang Mills theory analogous to our proof of the NSVW formula in gravity. Comment: 38 pages + 3 appendices |
| Databáze: | arXiv |
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