The Bootstrap Program for Quantum Field Theory

Projektinformationen

QFTinAdS

ID Finanzhilfevereinbarung: 101087025

DOI

10.3030/101087025

EK-Unterschriftsdatum 23 Mai 2023

Startdatum 1 September 2023

Enddatum 31 August 2028

Finanziert unter

• European Research Council (ERC)

Gesamtkosten

€ 1 930 051,25

EU-Beitrag

€ 1 930 051,00

Koordiniert durch

ECOLE POLYTECHNIQUE
France

Periodic Reporting for period 1 - QFTinAdS (The Bootstrap Program for Quantum Field Theory)

Berichtszeitraum: 2023-09-01 bis 2026-02-28

Zusammenfassung vom Kontext und den Gesamtzielen des Projekts

This project studies the general mathematical properties of certain observables in quantum field theories. The general philosophy is that of the "bootstrap" and proceeds in two steps. First, rigorous properties are established that should hold universally for these observables, irrespective of the specific quantum field theory under consideration. This is a formal and mathematical exercise, where one tries to understand the structure by starting from some completely general axioms. One derives for example analyticity, crossing symmetry, and other properties. Second, these rigorous and sometimes rather abstract properties are translated into concrete predictions for experiment, or more precisely constraints for the range of possible experimental values for these observables. These predictions can be completely general, so valid for every quantum field theory under the sun, or more specific by supplementing the universal properties with specific information about the quantum field theory under consideration. This second stage often uses advanced numerical methods.

What this project specifically focuses on is the derivation of mathematical properties of so-called scattering amplitudes, and the observable consequences that follow from them. Its approach to doing so is distinguished by a new method, called QFT in AdS, which uses curved-space quantum field theory. This change of perspective allows one to start from well-understood mathematical structures and leverage existing numerical methods to derive new properties about the relatively poorly understood scattering amplitudes.

Arbeit, die ab Beginn des Projekts bis zum Ende des durch den Bericht erfassten Berichtszeitraums geleistet wurde, und die wichtigsten bis dahin erzielten Ergebnisse

In the first two years of the grant we made progress on various fronts. First, we rigorously proved a property of conformal correlation functions which provides an important first step in rigorously deriving results on scattering amplitudes using QFT in AdS. In fact, our result applies much more generally and the new methodology can also be used to study the asymptotic structure of other observables like partition functions in two-dimensional conformal quantum field theories.

We also made some progress in the numerical component of the research. One important exploration studies the specific quantum field theory that governs the strong interactions in the standard model of particle physics. We found constraints on some observables that might be difficult to measure experimentally but should be computable in simulations in the near future. This study also gave us an insight into the capabilities of the current numerical methods and promising avenues for future research.

In the next three years we plan to combine various ingredients, strengthen the mathematical rigor of existing derivations, and arrive at a novel way to describe the fundamental structure of scattering amplitudes.

Fortschritte, die über den aktuellen Stand der Technik hinausgehen und voraussichtliche potenzielle Auswirkungen (einschließlich der bis dato erzielten sozioökonomischen Auswirkungen und weiter gefassten gesellschaftlichen Auswirkungen des Projekts)

This is theoretical work and as such the impact will mostly be restricted to the theoretical physics community. That said, it is part of an important line of research to rigorously define (aspects of) quantum field theory. Indeed, even though quantum field theory is essential to describe physics ranging from elementary particles to boiling water at high temperatures and pressures, its status as a mathematical structure remains deeply unsatisfactory. Making some progress in this direction is an important subject in the mathematical physics field.

Our numerical problems can often be formulated as semidefinite programs or as an infinite-dimensional variation of linear programs. These kind of programs are used more widely, both in academia and in the professional world, so the algorithms we develop may also be useful to others.