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Vertex operator algebras from supersymmetric quantum field theories - dualities, new structures and relations

Project description

Advancing our understanding of twist vertex operator algebras

Progress in theoretical physics has deepened our understanding of the foundational structures of quantum field theories, particularly their algebraic and categorical frameworks. Many breakthroughs are closely tied to developments in the study of vertex operator algebras (VOAs). However, twist VOAs associated with general three-dimensional supersymmetric gauge theories remain largely unexplored. With support from the Marie Skłodowska-Curie Actions programme, the QFT2VOA-DuStRel project aims to change that by pioneering a novel approach to constructing twist VOAs. This method interprets them as chiralisations of the moduli spaces of vacua associated with these gauge theories. This framework will enable the systematic collection and interpretation of data, opening up exciting possibilities for mathematics and theoretical physics.

Objective

A main goal in theoretical physics is to understand foundational aspects of quantum field theories, such as their algebraic or categorical structures, and much of the recent progress in this direction has been deeply linked to advances in mathematics, notably vertex operators algebras (VOA).

This interplay has generated surprising insights in both directions, particularly through relations between three-dimensional supersymmetric quantum field theories and certain distinguished VOAs. The latter capture special algebras of local operators, which can be defined from the boundary sector of the parent three-dimensional theories though a twisting procedure, and they are expected to provide meaningful classification invariants for these by encoding fundamental algebraic data.

Nevertheless, the twist VOAs related to general three-dimensional supersymmetric gauge theories remain largely mysterious, with physical analyses usually limited to simple examples. To overcome this impasse, an innovative approach developed by the applicant constructs twist VOAs for large classes of theories as chiralizations of corresponding moduli spaces of vacua. This is a rigorous, systematic procedure which lifts the classical functions on these associated geometries to generating currents of the VOAs, and provides powerful insights into hidden VOA structures. Supported by preliminary data, this breakthrough enables: 1) a systematic analysis of physical symmetries and relations - such as 3d mirror symmetry - from a VOA perspective, as well as 2) concrete realizations of new and intriguing logarithmic VOAs through the lens of supersymmetric quantum field theories - which will be the main objectives of this action.

The proposed research projects tackle fundamental and technically challenging long-standing questions in quantum field theory by creatively using the newly developed technology of chiralization, and they are expected to make an impact by establishing new exact methods of analysis.

Fields of science (EuroSciVoc)

Keywords

Programme(s)

Topic(s)

Funding Scheme

HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships

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Call for proposal

(opens in new window) HORIZON-MSCA-2024-PF-01

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Coordinator

THE UNIVERSITY OF EDINBURGH
Net EU contribution
€ 276 187,92
Address
OLD COLLEGE, SOUTH BRIDGE
EH8 9YL Edinburgh
United Kingdom
Region
Scotland Eastern Scotland Edinburgh
Activity type
Higher or Secondary Education Establishments
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Total cost
No data