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Projekt Druckansicht

Integrabilität und Konforme Symmetrie in vier Dimensionen

Fachliche Zuordnung Kern- und Elementarteilchenphysik, Quantenmechanik, Relativitätstheorie, Felder
Förderung Förderung von 2017 bis 2024
Projektkennung Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 363895012
 
Erstellungsjahr 2023

Zusammenfassung der Projektergebnisse

Symmetries are of crucial importance in all areas of physics and greatly simplify involved calculations. In particular, integrable structures play a distinguished role since they allow to solve whole models or to facilitate computations which are unaccessible by standard techniques. In the context of theoretical high energy physics, integrable structures entered the scene via the celebrated gauge/gravity duality, which relates a gauge quantum field theory to a theory of gravity. For the first time a quantum field theory in four spacetime dimensions was found to be integrable, which furnishes a crucial step beyond the paradigm of two-dimensional integrable models studied in the past. In this context, however, the integrability of the four dimensional quantum field theory model relies on its special supersymmetric nature. The main outcome of the present project was to lift the above integrable structures to individual Feynman integrals and to develop a bootstrap approach for their computation. Moreover, integrability alias Yangian symmetry of these integrals was generalized to cases including massive particles, which furnishes a surprising new step that was not to be expected from the point of view of the gauge/gravity duality. Extending the class of considered Feynman graphs beyond the realm of the so-called dual conformal symmetry (and integrability), this also led to the finding of a new massive generalization of momentum space conformal symmetry for an infinite class of integrals. Since the evaluation of Feynman integrals represents one of the major bottle necks for precision calculations in particle and gravitational wave physics, the finding of new symmetries is of great value and emphasizes the use of integrability beyond toy models. The above insights were extended in a couple of further directions, i.e. to integrals with Minkowski signature, to divergent integrals treated in dimensional regularization and relevant for gravitational physics, or to particular coincidence limits leading to the class of the so-called Basso-Dixon family of integrals. Finally, a curious outcome of this project was the interpretation of certain Feynman integrals as volumes of Calabi–Yau geometries and the identification of the Yangian constraints with the so-called Picard–Fuchs differential equations which characaterize the latter. This new relation between integrability and geometry also promises further connections in the context of pure mathematics. In conclusion, the research performed during the funding period has led to new insights on integrable systems, the mathematical structure of Feynman integrals as well as to relations to geometry and gravity. The obtained results were published in recognized scientific journals and presented at various international conferences and workshops.

Projektbezogene Publikationen (Auswahl)

 
 

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