Ising-like and Fibonacci anyons from KZ-equations

Journal of High Energy Physics

Regular Article - Theoretical Physics

Babak Haghighat¹  Xia Gu¹  Yihua Liu¹ 

[1] Yau Mathematical Sciences Center, Tsinghua University, 100084, Beijing, China;

关键词: Anyons;    Topological States of Matter;    Topological Field Theories;    Field Theories in Lower Dimensions;   

DOI  :  10.1007/JHEP09(2022)015

 received in 2022-01-04, accepted in 2022-08-15,  发布年份 2022

来源: Springer

【 摘 要 】

In this work we present solutions to Knizhnik-Zamolodchikov (KZ) equations corresponding to conformal block wavefunctions of non-Abelian Ising-like and Fibonacci Anyons. We solve these equations around regular singular points in configuration space in terms of hypergeometric functions and derive explicit monodromy representations of the braid group action. This confirms the correct non-Abelian statistics of the solutions. One novelty of our approach is that we explicitly keep track of spin basis states and identify conformal blocks uniquely with such states at relevant points in moduli space.

【 授权许可】

Unknown   
© The Author(s) 2022