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Toward A Supersymmetric $w_{1+\infty}$ Symmetry in the Celestial Conformal Field Theory
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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.
Forward citations
Cited by 3 Pith papers
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Symmetries of the Celestial Supersphere
The celestial sphere is extended to a supermanifold C^{1|N}, yielding universal supersymmetric extensions of the BMS and w_{1+8} symmetry algebras of flat-space quantum gravity.
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Multi-Particle Contributions to the Celestial Algebra in the ${\cal N}=8$ Supergravity
Multi-particle OPEs of single-particle celestial operators with two-particle operators in N=8 supergravity yield ninety-five (anti)commutators of the soft current algebra plus amplitude relations.
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A Supersymmetric $w_{1+\infty}$ Symmetry, the Extended Supergravity and the Celestial Holography
An N=4 supersymmetric w_{1+∞} algebra at λ=1/4 is proposed as the celestial soft current algebra of N=4 SO(4) supergravity, with truncations covering N=2,3 and matter-coupled cases.
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