Toward A Supersymmetric $w_{1+\infty }$ Symmetry in the Celestial Conformal Field Theory

Abstract

The $w_{1+\infty }$ symmetry algebra appears in the Einstein--Yang--Mills theory, proposed recently by Strominger. In this paper, we derive the supersymmetric $w_{1+\infty }$ symmetry by using the known results on the operator product expansions (OPEs) between the graviton, gravitino, gluon, and gluino in the supersymmetric version of the above theory. We calculate the four additional commutator relations between the soft currents explicitly. In addition, we analyze the works of Odake et al. and Pope et al. and introduce the additional symmetry current that corresponds to the celestial gluino operator. Through this procedure, all seven commutator relations can be connected to the ones associated with the supersymmetric $w_{1+\infty }$ algebra with $SU(N)$ symmetry under the restrictions of wedge modes.

arXiv comment24 pages; Some of main texts are moved to the footnotes, some typos are corrected, the introduction is improved and to appear in PRD

References in corpus (15)

• Lectures on Celestial Amplitudes
• Holographic Symmetry Algebras for Gauge Theory and Gravity
• Celestial Operator Product Expansions and ${\mathrm{w}}_{1+\infty }$ Symmetry for All Spins
• Extended Super BMS Algebra of Celestial CFT
• Holographic Chiral Algebra: Supersymmetry, Infinite Ward Identities, and EFTs
• String Theory, Black Holes, and SL(2,R) Current Algebra
• Rectangular W-algebras, extended higher spin gravity and dual coset CFTs
• Higher Spin Currents in the N=1 Stringy Coset Minimal Model
• Rectangular W-(super)algebras and their representations
• Rectangular W-algebras of types $so(M)$ and $sp(2M)$ and dual coset CFTs
• The $\mathcal{N}=4$ Higher Spin Algebra for Generic $\mu$ Parameter
• The $\mathcal{N}=4$ Coset Model and the Higher Spin Algebra
• Spacetime Diffeomorphisms and Topological W-Infinity Symmetry in Two Dimensional Topological String Theory
• Adding Complex Fermions to the Grassmannian-like Coset Model
• The Grassmannian-like Coset Model and the Higher Spin Currents

Cited by in corpus (6)

• Celestial Supersymmetry
• Supersymmetric celestial OPEs and soft algebras from the ambitwistor string worldsheet
• The $\mathcal{N}=2$ Supersymmetric $w_{1+\infty }$ Symmetry in the Two-Dimensional SYK Models
• Deformed $w_{1+\infty }$ Algebras in the Celestial CFT
• Structure of deformed $w_{1+\infty }$ symmetry and topological generalization in Celestial CFT
• The Structure of the $\mathcal{N}=4$ Supersymmetric Linear $W_{\infty }[\lambda ]$ Algebra