Testing Macdonald index as a refined character of chiral algebra

Journal of High Energy Physics

Akimi Watanabe¹  Rui-Dong Zhu² 

[1] Department of Physics, The University of Tokyo, Bunkyo-ku, 113-8654, Tokyo, Japan;School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin, Ireland;

关键词: Conformal and W Symmetry;    Supersymmetry and Duality;    Conformal Field Theory;    Supersymmetric Gauge Theory;   

DOI  :  10.1007/JHEP02(2020)004

来源: Springer

【 摘 要 】

We test in (An−1, Am−1) Argyres-Douglas theories with gcd(n, m) = 1 the proposal of Song’s in [1] that the Macdonald index gives a refined character of the dual chiral algebra. In particular, we extend the analysis to higher rank theories and Macdonald indices with surface operator, via the TQFT picture and Gaiotto-Rastelli-Razamat’s Higgsing method. We establish the prescription for refined characters in higher rank minimal models from the dual (An−1, Am−1) theories in the large m limit, and then provide evidence for Song’s proposal to hold (at least) in some simple modules (including the vacuum module) at finite m. We also discuss some observed mismatch in our approach for surface operators with large vortex number.

【 授权许可】

CC BY