Periodic Reporting for period 4 - QUASIFT (Quantum Algebraic Structures In Field Theories)
Berichtszeitraum: 2021-03-01 bis 2021-08-31
The project "Quantum Algebraic Structures in Field Theories" aimed to
discover and study novel mathematical structures underlying the
physics of quantum field theories that is the current universal
framework to address quantum physical systems with infinitely many
interacting degrees of freedom. The traditional method of Feynman
diagrams or perturbation theory works well when the interaction is
weak, but breaks when the interaction is strong. Thus, the project
QUASIFT was devoted to developing new mathematical formalisms to address
the computations in Quantum Field Theories not achievable by the
traditional Feynman perturbation theory. One example where such
computations are possible are provided quantum field theory analogues
of dynamical integrable systems.
Quantum field theory is the current paradigm of the theoretical
physics that describes the space-time and matter at the most
fundamental level, for example, the current model of elementary
particles and subatomic physics called the Standard Model, is a
Quantum Field Theory. Besides nuclear physics, Quantum Field Theory
describes a range of phenomena in condensed matter physics such as
strongly correlated organic conductors, carbon nanotubes, high
temperature superconductors, quantum Hall systems, Josephson junction
arrays, superfluid helium, and many others. All these phenomena, at
the cutting edge of the research, might find groundbreaking
technological applications. Therefore, it is vital to develop strong
theoretical control of these phenomena and necessary mathematical
formalism.
discover and study novel mathematical structures underlying the
physics of quantum field theories that is the current universal
framework to address quantum physical systems with infinitely many
interacting degrees of freedom. The traditional method of Feynman
diagrams or perturbation theory works well when the interaction is
weak, but breaks when the interaction is strong. Thus, the project
QUASIFT was devoted to developing new mathematical formalisms to address
the computations in Quantum Field Theories not achievable by the
traditional Feynman perturbation theory. One example where such
computations are possible are provided quantum field theory analogues
of dynamical integrable systems.
Quantum field theory is the current paradigm of the theoretical
physics that describes the space-time and matter at the most
fundamental level, for example, the current model of elementary
particles and subatomic physics called the Standard Model, is a
Quantum Field Theory. Besides nuclear physics, Quantum Field Theory
describes a range of phenomena in condensed matter physics such as
strongly correlated organic conductors, carbon nanotubes, high
temperature superconductors, quantum Hall systems, Josephson junction
arrays, superfluid helium, and many others. All these phenomena, at
the cutting edge of the research, might find groundbreaking
technological applications. Therefore, it is vital to develop strong
theoretical control of these phenomena and necessary mathematical
formalism.
The research team in the project was directed by the Principal
Investigator Prof. Vasily Pestun. His team included a group at
Institut des Hautes Études Scientifiques, IHES (the Host Institution)
as well as renowned scientists from University of Zurich
(Switzerland), University of Glasgow (UK), University of Aberdeen
(UK), University of Arizona (USA), University of Kentucky (USA),
Caltech (USA), Simons Center for Geometry and Physics (USA), Keio
University (Japan), Center for Geometry and Physics (Korea).
The results of the project are presented in 53 journal publications
and/or preprints available in the open access on arXiv.
The multiple results are spanned across the topics of localisation in
supersymmetric gauge theories, BPS invariants and quiver varieties,
tau-functions of integrable hierarchies and matrix models and
intersection theory, multiplicative Higgs bundles and W-algebras,
representation theory of quantum groups, quantum information
categories, holomorphic quantum field theories and factorization
algebras.
Among other outcomes, an important impact was an organization of major
a week-long workshop "Higher Structures in Holomorphic and Topological
Field Theory", January 14 - 19, IHES, France devoted to the topic of
the project. Renowned researchers, mathematicians and physicists,
participated in the workshop, presented their work and had multiple
discussions establishing direction for the future
collaboration and research.
Investigator Prof. Vasily Pestun. His team included a group at
Institut des Hautes Études Scientifiques, IHES (the Host Institution)
as well as renowned scientists from University of Zurich
(Switzerland), University of Glasgow (UK), University of Aberdeen
(UK), University of Arizona (USA), University of Kentucky (USA),
Caltech (USA), Simons Center for Geometry and Physics (USA), Keio
University (Japan), Center for Geometry and Physics (Korea).
The results of the project are presented in 53 journal publications
and/or preprints available in the open access on arXiv.
The multiple results are spanned across the topics of localisation in
supersymmetric gauge theories, BPS invariants and quiver varieties,
tau-functions of integrable hierarchies and matrix models and
intersection theory, multiplicative Higgs bundles and W-algebras,
representation theory of quantum groups, quantum information
categories, holomorphic quantum field theories and factorization
algebras.
Among other outcomes, an important impact was an organization of major
a week-long workshop "Higher Structures in Holomorphic and Topological
Field Theory", January 14 - 19, IHES, France devoted to the topic of
the project. Renowned researchers, mathematicians and physicists,
participated in the workshop, presented their work and had multiple
discussions establishing direction for the future
collaboration and research.
We conclude that the project was very successful in terms of new
research results as well as establishing a network of international
collaborations across the world with a strong impact in the domain of
the theoretical physics and mathematics.
research results as well as establishing a network of international
collaborations across the world with a strong impact in the domain of
the theoretical physics and mathematics.