Objective
This project will contribute to our understanding of mathematical Quantum Field Theory (QFT) by formulating a discrete version of Factorisation Algebras (FAs). This will be used to solve an open conjecture about Topological QFT (TQFT), describe and establish dualities between QFTs, and form a bridge between discrete and category-theoretic techniques for Conformal Field Theory (CFT). FAs are among the most flexible approaches to mathematical QFT, but no description as FAs of discretised QFT is known. This project's combinatorial FAs (cFAs) fill this gap. They have many applications, three of which will be covered in this project.
The first is to prove that the discrete state-sum models for Topological QFT (TQFT) give rise to Functorial Field Theories by fitting state-sum models into the sFA formalism and establishing a continuum limit result for topological sFA. Functorial Field Theory (cf. Atiyah, Lurie and many others) is a formalism for QFT that is particularly popular for TQFT. While this conjecture has been around for over 20 years and is believed to be true no proof exists.
Secondly, I will use techniques from duality for sheaves and cosheaves on simplicial complexes to prove a duality result for sFA analogous to Poincar-Koszul-Verdier duality. Lattice models are a source of interesting dualities between QFTs, such as the Kramers-Wanier self-duality of the Ising model. These dualities will be shown to be an instance of sFA duality, and this description will be used to find new dualities for physically relevant QFTs. Associated to these dualities are defects which are intensively studied in theoretical physics.
Thirdly, cFAs will be used to give a FA description of the discrete QFT known as the Ising model. This will be linked with Discrete Holomorphicity techniques for CFT to find an FA description of the CFT in the continuum limit.
Fields of science (EuroSciVoc)
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CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques.
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Keywords
Programme(s)
- HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA) Main Programme
Funding Scheme
HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European FellowshipsCoordinator
02150 Espoo
Finland