Скачать или смотреть Anirudh Deb - The Nilpotency Index for 4d N=2 SCFTs

23.05.2025 at Quiver Meeting

Anirudh Deb (Stony Brook University) - The Nilpotency Index for 4d N=2 SCFTs

To a four-dimensional N=2 superconformal field theory (SCFT), one can associate a two-dimensional vertex operator algebra (VOA). In this talk, I will discuss a quantity called the "nilpotency index'', which is the smallest integer "n" such that T^n = 0 in the C_2 algebra, where T is the VOA stress tensor. As an alternative to the classification of theories based on Coulomb branch geometry, which arranges theories by increasing rank, the nilpotency index provides a natural way to arrange theories from the VOA perspective. Extrapolating from several examples, it is conjectured that the nilpotency index is an RG monotone and further, it satisfies the inequality rank$\leq n-1$. I will discuss these conjectures and various methods used to determine the nilpotency index. I will also discuss the classification of theories with n = 1, 2.