BIMSA > SIMIS String Math Seminar A quantum deformation of the N=2 superconformal algebra
A quantum deformation of the N=2 superconformal algebra
Organizer
Veronica Pasquarella
Speaker
Junichi Shiraishi
Time
Wednesday, November 27, 2024 4:00 PM - 5:00 PM
Venue
SIMIS-1610
Abstract
We introduce a unital associative algebra, (1) having two complex parameters ($q$ and $k$), (2) generated by a certain set of generators ($K^\pm_m$ ($\pm m\geq 0$), $T_m$ ($m\in \mathbb{Z}$), and $G^\pm_m$ ($m\in \mathbb{Z}+{1\over 2}$ in the Neveu-Schwarz sector, $m\in \mathbb{Z}$ in the Ramond sector), and (3) satisfying relations which are at most quartic. Brute force calculations of some low-lying Kac determinants are made, providing us with a conjecture for the factorization property of the Kac determinants in general. It is shown that by taking the conformal limit ($q\rightarrow 1$) we recover the ordinary N=2 superconformal algebra. We also give a Heisenberg representation of the algebra, making a twist of the $U(1)$ boson in the Wakimoto representation of the quantum affine algebra $U_q(\widehat{sl}_2)$. (Based on a collaboration with H. Awata, K. Harada and H. Kanno.)