Triangle Seminars
Tuesday, 3 Mar 2020
W-algebras and Yangians
Tomas Prochazka
(LMU Munich)
Abstract:
I will discuss the connection between W-algebras, the higher spin generalizations of the Virasoro algebra which are the symmetry algebras in the 2-dimensional conformal field theory, and Tsymbaliuk's affine Yangian. The bridge between these two algebraic structures is the Miura operator which on one hand provides free field representations of W-algebras and on the other hand satisfies the RTT equations with Maulik-Okounkov R-matrix. The associated integrable structure allows one to easily reproduce many well-known results in conformal field theory.
I will discuss the connection between W-algebras, the higher spin generalizations of the Virasoro algebra which are the symmetry algebras in the 2-dimensional conformal field theory, and Tsymbaliuk's affine Yangian. The bridge between these two algebraic structures is the Miura operator which on one hand provides free field representations of W-algebras and on the other hand satisfies the RTT equations with Maulik-Okounkov R-matrix. The associated integrable structure allows one to easily reproduce many well-known results in conformal field theory.
Posted by: bogdan
Wednesday, 4 Mar 2020
Global symmetry and anomalies in (2+1)D topological quantum field theories
Maissam Barkeshli
(University of Maryland)
Abstract:
Topological quantum field theories, which can be used to model topologically ordered phases of matter in quantum many-body systems, exhibit rich behavior in the presence of global symmetries. In this talk I will present progress over the last few years in understanding (2+1)D TQFTs in the presence of a global symmetry group G. This leads to a new mathematical structure, G-crossed braided tensor categories, that characterizes different possible patterns of symmetry fractionalization for topologically non-trivial particles and the fusion and braiding properties of symmetry defects. Two types of anomalies arise in the discussion: (1) "symmetry localization anomalies," which can also be interpreted as the theory possessing a non-trivial 2-group symmetry, and (2) symmetry fractionalization anomalies, which are equivalent to 't Hooft anomalies of the TQFT. I will describe various methods that have been developed in the past few years to compute these anomalies from the algebraic data that defines the TQFT and the symmetry action.
Topological quantum field theories, which can be used to model topologically ordered phases of matter in quantum many-body systems, exhibit rich behavior in the presence of global symmetries. In this talk I will present progress over the last few years in understanding (2+1)D TQFTs in the presence of a global symmetry group G. This leads to a new mathematical structure, G-crossed braided tensor categories, that characterizes different possible patterns of symmetry fractionalization for topologically non-trivial particles and the fusion and braiding properties of symmetry defects. Two types of anomalies arise in the discussion: (1) "symmetry localization anomalies," which can also be interpreted as the theory possessing a non-trivial 2-group symmetry, and (2) symmetry fractionalization anomalies, which are equivalent to 't Hooft anomalies of the TQFT. I will describe various methods that have been developed in the past few years to compute these anomalies from the algebraic data that defines the TQFT and the symmetry action.
Posted by: QMW
Replica wormholes and the information paradox
Edgar Shaghoulian
(Cornell University)
Abstract:
The information paradox can be realized in two-dimensional models of gravity. In this setting, we show that the large discrepancy between the von Neumann entropy as calculated by Hawking and the requirement of unitarity is fixed by including new saddles in the gravitational path integral. These saddles arise in the replica method as wormholes connecting different copies of the black hole.
The information paradox can be realized in two-dimensional models of gravity. In this setting, we show that the large discrepancy between the von Neumann entropy as calculated by Hawking and the requirement of unitarity is fixed by including new saddles in the gravitational path integral. These saddles arise in the replica method as wormholes connecting different copies of the black hole.
Posted by: QMW