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International Conference "Fields & Strings 2024"
February 8, 2024 15:30–16:25, Moscow, Steklov Mathematical Institute
 


Chern-Simons theory: duality, integrability and topology

A. V. Sleptsovabc

a Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
b Institute for Theoretical and Experimental Physics named by A.I. Alikhanov of National Research Centre «Kurchatov Institute»
c Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
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Abstract: I will talk about what interesting directions there are for research related to the Chern-Simons theory. First, Chern-Simons theory is one of the simplest three-dimensional quantum field theories that we can solve exactly using quantum algebra and the R-matrix. The question of searching for integrable structures in other gauge theories seems promising. Second, vacuum expectation values in Chern-Simons theory are invariants of knots (or links) in a given 3-dimensional manifold. Since the theory of knots and their invariants is far from its complete description, this question is of great interest. Third, there are two dualities with the Chern-Simons theory. One holographic duality between 3D Chern-Simons theory and 2D conformal WZW theory. The second duality arises from string theory and is a mirror symmetry between the A-model (Chern-Simons theory) and the B-model (Gromov-Witten theory). Due to the progress in the Chern-Simons theory, it is possible to investigate this duality in explicit terms.

Language: English
 
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