## Project Details

### Description

My research strategy, as a theoretical physicist, is to leverage the insights I develop, through explicit prediction, to not only realize advances in technical facility but—crucially—to understand their underlying, potentially novel, physical ideas and principles. Below I describe one of my most important discoveries, and highlight two on-going lines of research I plan to pursue. Double Copy: “Gravity = (Gauge theory)2.” I, along with core collaborators, discovered an amazing truth: gravitational quantum scattering amplitudes—the invariant quantum evolution of what distance means in space and time, consistent in the classical limit with Einstein’s General Relativity—are much simpler than expected. This

simplicity can be traced to the fact that their perturbative dynamics are completely encoded in the amplitudes of much simpler gluonic or gauge theories. Surprisingly, these gauge theory predictions are spectacularly constrained by a structure entirely hidden in any standard ways of writing their actions. Specifically we found that perturbative dynamics, in predictions for gauge theories (like Yang-Mills), obey the same algebraic constraints as their color-weights (or charges). This makes such dynamics and charges interchangeable

and indeed realizes graviton (spin-2) scattering, in asymptotically flat space, as gluonic (spin-1) predictions whose charges are—operationally—the kinematics of gluons (spin-1). While the conceptual impact has yet to be fully realized, this discovery has already trivialized previously intractable analysis. One recent example is our explicit

calculation of the high-energy (UV) behavior of maximally supersymmetric supergravity at the five-loop order.

This analysis allowed, in turn, our discovery of a new recursive structure, solely observable in the UV, suggesting that even eight-loops may be within reach. Beyond calculation, this double-copy organization identifies a unified set of constructive elements in a wide swath of theories: from the completely formal—both open and closed string theory scattering admit field theoretic double-copy descriptions—to our most phenomenological field theories like

quantum chromodynamics, and even more effective, spontaneously broken chiral pions.

Immediate plans:

1. Counterterms as Tinker-Toys. Adding increasingly higher dimension counterterms to encode novel UV physics traditionally means working with increasingly more finicky and difficult operators. Can this be drastically simplified? I believe so. Consider as a warm-up, one of the simplest lowest-order gauge-theory operators, dabcd(F4). This does not naively manifest adjoint2 double-copy structure—at least not when looking only at the kinematics—

yet, amusingly, it clearly demonstrates a completely-symmetric charge/kinematics relationship and a consequent kinematic double-copy to the gravitational counterterm R4 = (F4)(F4). Do these operators also admit an adjointlike double-copy representation? Yes! The higher-derivative aspects of gauge and gravity operators can be pulled into higher- derivative scalar operators. This means that higher-order corrections can be achieved at the multi-loop level by taking known Yang-Mills results and double-copying with easy to construct scalar loop-integrands. To realize such a decomposition for arbitrary operators, we must introduce division between QFT predictions, i.e. taking a “single-copy” along a given algebraic structure. This will yield notions of prime (irreducible) building

blocks—atoms, if you like—of prediction.

2. The Root of Equivalence. Classical black hole space-t

simplicity can be traced to the fact that their perturbative dynamics are completely encoded in the amplitudes of much simpler gluonic or gauge theories. Surprisingly, these gauge theory predictions are spectacularly constrained by a structure entirely hidden in any standard ways of writing their actions. Specifically we found that perturbative dynamics, in predictions for gauge theories (like Yang-Mills), obey the same algebraic constraints as their color-weights (or charges). This makes such dynamics and charges interchangeable

and indeed realizes graviton (spin-2) scattering, in asymptotically flat space, as gluonic (spin-1) predictions whose charges are—operationally—the kinematics of gluons (spin-1). While the conceptual impact has yet to be fully realized, this discovery has already trivialized previously intractable analysis. One recent example is our explicit

calculation of the high-energy (UV) behavior of maximally supersymmetric supergravity at the five-loop order.

This analysis allowed, in turn, our discovery of a new recursive structure, solely observable in the UV, suggesting that even eight-loops may be within reach. Beyond calculation, this double-copy organization identifies a unified set of constructive elements in a wide swath of theories: from the completely formal—both open and closed string theory scattering admit field theoretic double-copy descriptions—to our most phenomenological field theories like

quantum chromodynamics, and even more effective, spontaneously broken chiral pions.

Immediate plans:

1. Counterterms as Tinker-Toys. Adding increasingly higher dimension counterterms to encode novel UV physics traditionally means working with increasingly more finicky and difficult operators. Can this be drastically simplified? I believe so. Consider as a warm-up, one of the simplest lowest-order gauge-theory operators, dabcd(F4). This does not naively manifest adjoint2 double-copy structure—at least not when looking only at the kinematics—

yet, amusingly, it clearly demonstrates a completely-symmetric charge/kinematics relationship and a consequent kinematic double-copy to the gravitational counterterm R4 = (F4)(F4). Do these operators also admit an adjointlike double-copy representation? Yes! The higher-derivative aspects of gauge and gravity operators can be pulled into higher- derivative scalar operators. This means that higher-order corrections can be achieved at the multi-loop level by taking known Yang-Mills results and double-copying with easy to construct scalar loop-integrands. To realize such a decomposition for arbitrary operators, we must introduce division between QFT predictions, i.e. taking a “single-copy” along a given algebraic structure. This will yield notions of prime (irreducible) building

blocks—atoms, if you like—of prediction.

2. The Root of Equivalence. Classical black hole space-t

Status | Active |
---|---|

Effective start/end date | 9/15/20 → 9/14/22 |

### Funding

- Alfred P. Sloan Foundation (FG-2020-13728)

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