A supersymmetric symmetry, the extended supergravity and the celestial holography

Changhyun Ahn; Man Hea Kim

doi:10.1140/epjc/s10052-025-14479-1

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2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2025) 85: 834
https://doi.org/10.1140/epjc/s10052-025-14479-1

Regular Article - Theoretical Physics

A supersymmetric $w_{1 + \infty}$ $w_{1+\infty }$ symmetry, the extended supergravity and the celestial holography

Changhyun Ahn¹^a and Man Hea Kim²^,3

¹ Department of Physics, Kyungpook National University, 41566, Taegu, Korea
² Center for High Energy Physics, Kyungpook National University, 41566, Taegu, Korea
³ Department of Physics Education, Sunchon National University, 57922, Sunchon, Korea

^a ahn@knu.ac.kr

Received: 20 May 2025
Accepted: 1 July 2025
Published online: 4 August 2025

Abstract

We determine the $N = 4$ $\mathcal{N}=4$ supersymmetric $W_{1 + \infty}^{2, 2} [λ = \frac{1}{4}]$ $W_{1+\infty }^{2,2}[\lambda =\frac{1}{4}]$ algebra which is an extension of $N = 4$ $\mathcal{N}=4$ SO(4) superconformal algebra with vanishing central charge. We identify the soft current algebra between the graviton, the gravitinos, the vectors, the Majorana fermions, the scalar or the pseudoscalar, from the $N = 4$ $\mathcal{N}=4$ supersymmetric $w_{1 + \infty}^{2, 2} [λ = \frac{1}{4}]$ $w_{1+\infty }^{2,2}[\lambda =\frac{1}{4}]$ algebra, in two dimensions with the $N = 4$ $\mathcal{N}=4$ supergravity theory with SO(4) global symmetry in four dimensions found by Das (at Stony Brook in 1977), via celestial holography. Furthermore, the truncations of $N = 4$ $\mathcal{N}=4$ supersymmetric soft current algebra provide the soft current algebras for the $N = 2, 3$ $\mathcal{N}=2,3$ supergravity theories, the $N = 2$ $\mathcal{N}=2$ supergravity coupled to its Abelian vector multiplet and the $N = 1$ $\mathcal{N}=1$ supersymmetric Maxwell Einstein theory. For the $N = 2$ $\mathcal{N}=2$ supergravity theory, the soft current algebra can be also realized from the $N = 2$ $\mathcal{N}=2$ supersymmetric $w_{1 + \infty}^{K, K} [λ = 0]$ $w_{1+\infty }^{K,K}[\lambda =0]$ algebra.

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A supersymmetric w1+∞ symmetry, the extended supergravity and the celestial holography

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A supersymmetric $w_{1 + \infty}$ $w_{1+\infty }$ symmetry, the extended supergravity and the celestial holography