Eur. Phys. J. C (2022) 82: 630
https://doi.org/10.1140/epjc/s10052-022-10582-9

Regular Article - Theoretical Physics

A deformed supersymmetric $w_{1+\infty }$ symmetry in the celestial conformal field theory

Department of Physics, Kyungpook National University, 41566, Taegu, Korea

^a ahn@knu.ac.kr

Received: 28 March 2022
Accepted: 4 July 2022
Published online: 22 July 2022

Abstract

By using the K-free complex bosons and the K-free complex fermions, we construct the $\mathcal{N}=2$ supersymmetric $W_{\infty }^{K,K}$ algebra which is the matrix generalization of previous $\mathcal{N}=2$ supersymmetric $W_{\infty }$ algebra. By twisting this $\mathcal{N}=2$ supersymmetric $W_{\infty }^{K,K}$ algebra, we obtain the $\mathcal{N}=1$ supersymmetric $W_{\infty }^K$ algebra which is the matrix generalization of known $\mathcal{N}=1$ supersymmetric topological $W_{\infty }$ algebra. From this two-dimensional symmetry algebra, we propose the operator product expansion (OPE) between the soft graviton and gravitino (as a first example), at nonzero deformation parameter, in the supersymmetric Einstein–Yang–Mills theory explicitly. Other six OPEs between the graviton, gravitino, gluon and gluino can be determined completely. At vanishing deformation parameter, we reproduce the known result of Fotopoulos, Stieberger, Taylor and Zhu on the above OPEs via celestial holography.