Vertex operator algebras of Argyres-Douglas theories from M5-branes

Song, Jaewon; Xie, Dan; Yan, Wenbin

doi:10.1007/jhep12(2017)123

Vertex operator algebras of Argyres-Douglas theories from M5-branes

Journal Article · Thu Dec 21 00:00:00 EST 2017 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep12(2017)123· OSTI ID:1505129

Song, Jaewon ^[1]; Xie, Dan ^[2]; Yan, Wenbin ^[3]

Univ. of California, San Diego, CA (United States). Dept. of Physics; Korea Inst. for Advanced Study, Seoul (Korea, Republic of). School of Physics; Univ. of California, San Diego, CA (United States)
Harvard Univ., Cambridge, MA (United States). Center of Mathematical Sciences and Applications. Jefferson Physical Lab.
Harvard Univ., Cambridge, MA (United States). Center of Mathematical Sciences and Applications. Jefferson Physical Lab.; Tsinghua Univ., Beijing (China). Yau Mathematical Sciences Center

We study aspects of the vertex operator algebra (VOA) corresponding to Argyres-Douglas (AD) theories engineered using the 6d

N = (2, 0)

theory of type J on a punctured sphere. We denote the AD theories as (J ^b [k], Y), where J ^b [k] and Y represent an irregular and a regular singularity respectively. We restrict to the ‘minimal’ case where J ^b [k] has no associated mass parameters, and the theory does not admit any exactly marginal deformations. The VOA corresponding to the AD theory is conjectured to be the W-algebra

W^{k_{2 d}} (J, Y)

, where

k_{2 d} = - h + \frac{b}{b + k}

with h being the dual Coxeter number of J. We verify this conjecture by showing that the Schur index of the AD theory is identical to the vacuum character of the corresponding VOA, and the Hall-Littlewood index computes the Hilbert series of the Higgs branch. We also find that the Schur and Hall-Littlewood index for the AD theory can be written in a simple closed form for b = h. We also test the conjecture that the associated variety of such VOA is identical to the Higgs branch. The M5-brane construction of these theories and the corresponding TQFT structure of the index play a crucial role in our computations.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of California, San Diego, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

Grant/Contract Number:: SC0009919

OSTI ID:: 1505129

Alternate ID(s):: OSTI ID: 22712789

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 12 Vol. 2017; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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