scholarly journals The slˆ(n)k-WZNW fusion ring: A combinatorial construction and a realisation as quotient of quantum cohomology

2010 ◽  
Vol 225 (1) ◽  
pp. 200-268 ◽  
Author(s):  
Christian Korff ◽  
Catharina Stroppel
Keyword(s):  
Quantum Cohomology ◽  
Fusion Ring ◽  
Combinatorial Construction

scholarly journals Wilson loop algebras and quantum K-theory for Grassmannians

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Hans Jockers ◽  
Peter Mayr ◽  
Urmi Ninad ◽  
Alexander Tabler
Keyword(s):  
Wilson Loop ◽  
Gauge Theories ◽  
Wilson Line ◽  
Quantum Cohomology ◽  
Three Dimensional ◽  
Loop Algebra ◽  
Loop Algebras ◽  
Verlinde Algebra ◽  
K Theory ◽  
Chern Simons

Abstract We study the algebra of Wilson line operators in three-dimensional $$ \mathcal{N} $$ N = 2 supersymmetric U(M ) gauge theories with a Higgs phase related to a complex Grassmannian Gr(M, N ), and its connection to K-theoretic Gromov-Witten invariants for Gr(M, N ). For different Chern-Simons levels, the Wilson loop algebra realizes either the quantum cohomology of Gr(M, N ), isomorphic to the Verlinde algebra for U(M ), or the quantum K-theoretic ring of Schubert structure sheaves studied by mathematicians, or closely related algebras.

scholarly journals The center of the extended Haagerup subfactor has 22 simple objects

2017 ◽  
Vol 28 (01) ◽  
pp. 1750009 ◽  
Author(s):  
Scott Morrison ◽  
Kevin Walker
Keyword(s):  
Fusion Category ◽  
Dimension Function ◽  
Fusion Ring ◽  
Fusion Categories ◽  
Modular Data ◽  
Grothendieck Rings ◽  
Combinatorial Data

We explain a technique for discovering the number of simple objects in [Formula: see text], the center of a fusion category [Formula: see text], as well as the combinatorial data of the induction and restriction functors at the level of Grothendieck rings. The only input is the fusion ring [Formula: see text] and the dimension function [Formula: see text]. In particular, we apply this to deduce that the center of the extended Haagerup subfactor has 22 simple objects, along with their decompositions as objects in either of the fusion categories associated to the subfactor. This information has been used subsequently in [T. Gannon and S. Morrison, Modular data for the extended Haagerup subfactor (2016), arXiv:1606.07165 .] to compute the full modular data. This is the published version of arXiv:1404.3955 .

scholarly journals COMPLETION OF THE CONJECTURE: QUANTUM COHOMOLOGY OF FANO HYPERSURFACES

2000 ◽  
Vol 15 (02) ◽  
pp. 101-120 ◽  
Author(s):  
MASAO JINZENJI
Keyword(s):  
Quantum Cohomology

In this letter, we propose the formulas that compute all the rational structural constants of the quantum Kähler subring of Fano hypersurfaces.

scholarly journals Virasoro constraints for quantum cohomology

1998 ◽  
Vol 50 (3) ◽  
pp. 537-590 ◽  
Author(s):  
Xiaobo Liu ◽  
Gang Tian
Keyword(s):  
Quantum Cohomology ◽  
Virasoro Constraints
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