## Periodic Reporting for period 4 - preQFT (Strategic Predictions for Quantum Field Theories)

Reporting period: 2019-12-01 to 2020-05-31

"This project aims to make it easy to extract meaningful predictions from some of our most important physical theories. We first encounter the so called strong force as it holds protons together at the center of atoms against all the electric repulsion struggling in vain to pull them apart. Whereas the electric field is transmitted by particles which classically ignore each other called photons, the strong force is transmitted by particles which even classically attract and repel each other called gluons. Much of the fascinating physics we learn from high energy particle colliders like the LHC at CERN is indeed from the scattering of gluons. The theory governing their scattering has special properties which makes it easier to predict the outcome as we scatter with higher energies, yet the calculations involved in making these predictions can still be incredibly laborious. Calculating predictions in gravity using traditional methods, such as how the orbits of spinning black holes decay by emitting gravitational waves, turns out to be even more horrendously complicated, not to mention the factorially more complicated quantum corrections.

Spectacularly we have found structure within all these predictions which may be exploited for tremendous simplicity. We call this structure a ""double-copy"" structure, metaphorically reminiscent of the double-helix of DNA. Instead of containing the information describing how varied life can be, this double-copy structure in theoretical predictions describes how varied different theories can be -- but also in terms of a small number of building blocks. Indeed this structure not only relates graviton predictions to much simpler gluon predictions, but finds a theoretical web weaving its way between many of our most important models for how nature behaves. With an improved ability to calculate we can answer questions in a few minutes by hand on a blackboard that took large supercomputers weeks and weeks to approach just a few years ago. We realize that we only need to calculate a few core predictions, and then we can combine them in various ways to accurately describe what would seem to be vastly different phenomena, exploiting this surprising universality. These methods suggest the possibility of insight across a huge range of scales: from the smallest interactions imaginable to the largest cosmological scales describing the formation of structure at the beginning of our universe.

Our field of scattering amplitudes bridges many communities allowing us to leverage ideas and insights for mutual benefit. Ultimately the most important achievement of this project will be seen as strengthening these connections in surprising new ways."

Spectacularly we have found structure within all these predictions which may be exploited for tremendous simplicity. We call this structure a ""double-copy"" structure, metaphorically reminiscent of the double-helix of DNA. Instead of containing the information describing how varied life can be, this double-copy structure in theoretical predictions describes how varied different theories can be -- but also in terms of a small number of building blocks. Indeed this structure not only relates graviton predictions to much simpler gluon predictions, but finds a theoretical web weaving its way between many of our most important models for how nature behaves. With an improved ability to calculate we can answer questions in a few minutes by hand on a blackboard that took large supercomputers weeks and weeks to approach just a few years ago. We realize that we only need to calculate a few core predictions, and then we can combine them in various ways to accurately describe what would seem to be vastly different phenomena, exploiting this surprising universality. These methods suggest the possibility of insight across a huge range of scales: from the smallest interactions imaginable to the largest cosmological scales describing the formation of structure at the beginning of our universe.

Our field of scattering amplitudes bridges many communities allowing us to leverage ideas and insights for mutual benefit. Ultimately the most important achievement of this project will be seen as strengthening these connections in surprising new ways."

We have found that even string theory predictions in the semi-classical (or Born) approximation can be understood in terms of this double-copy structure. Specifically we looked at the type of strings that are related to gluons called open-strings. Indeed these open-string predictions can be understood as a double-copy between gluonic predictive data and that of a theory we call Z theory. Z theory predictions satisfy simple particle-theory relations, which allows us to explore their properties from a particle perspective rather than a string perspective. This promises to open new ways of thinking about how string theory possesses the types of properties physicists have found enchanting for decades. Beyond this we have identified the type of building blocks that allow us to climb from pure color-factors all the way up to Z-theory predictions using simple composition rules---a structural new language for higher derivative prediction.

Previously the state of the art of exploiting double copy required us to manipulate theory predictions to make their double-copy structure manifest. This itself can be laborious for deep predictions. It is natural to wonder if it is possible to directly double-copy predictive data without performing such manipulation. Spectacularly the answer is yes and we have figured out how to generalize the double-copy procedure to work from generic representations.

We applied this new breakthrough to tackle a long-standing challenge, understanding the high-energy behavior of scattering two gravitons off of each other in the most symmetric gravitational theory when quantum corrections start to matter to the 5th order (a so-called 5-loop calculation )-- a calculation long through to be impossible, but brought into reach by these generalized double-copy advances. This data will allow us to test important questions about how robust particle descriptions can ever be for gravity.

Previously the state of the art of exploiting double copy required us to manipulate theory predictions to make their double-copy structure manifest. This itself can be laborious for deep predictions. It is natural to wonder if it is possible to directly double-copy predictive data without performing such manipulation. Spectacularly the answer is yes and we have figured out how to generalize the double-copy procedure to work from generic representations.

We applied this new breakthrough to tackle a long-standing challenge, understanding the high-energy behavior of scattering two gravitons off of each other in the most symmetric gravitational theory when quantum corrections start to matter to the 5th order (a so-called 5-loop calculation )-- a calculation long through to be impossible, but brought into reach by these generalized double-copy advances. This data will allow us to test important questions about how robust particle descriptions can ever be for gravity.

Our discovery of generalized double-copy of generic representations defines the new state of the art, as does the ability to perform higher-loop calculations in theories of gravity. With the advent of new next generation high-precision gravitational wave observation requiring unheard of perturbative precision in classical gravity this takes on much more pressing phenomenological urgency then we could have imagined at the beginning of this project. The field is now well leveraged to make contributions to both collider phenomenology as well as gravitational wave phenomenology.

The recognition that the open string can be thought of as a field theory double copy offers a completely new particle physics perspective on what string theories are, and promised to shed light on the inevitability (or freedom) in UV completions. This defines a drastically different way of thinking about higher-derivative operators in EFT -- applicable across many fields of physical inquiry, one that may lead to much easier higher-loop predictions. The long view is that having these types of structures manifest in our predictions could ultimately lead to new descriptions of our physical theories, placing these atoms of prediction front-and-center. We expect to see sharp progress on this later front --- making double-copy structure manifest at the level of the definition of physical theory --- based directly on what we have accomplished in this project.

The recognition that the open string can be thought of as a field theory double copy offers a completely new particle physics perspective on what string theories are, and promised to shed light on the inevitability (or freedom) in UV completions. This defines a drastically different way of thinking about higher-derivative operators in EFT -- applicable across many fields of physical inquiry, one that may lead to much easier higher-loop predictions. The long view is that having these types of structures manifest in our predictions could ultimately lead to new descriptions of our physical theories, placing these atoms of prediction front-and-center. We expect to see sharp progress on this later front --- making double-copy structure manifest at the level of the definition of physical theory --- based directly on what we have accomplished in this project.