In this paper, we present a candidate for $$\mathcal {N}=(1,1)$$ N = ( 1 , 1 ) extended higher-spin $$AdS_3$$ A d S 3 supergravity with the most general boundary conditions discussed by Grumiller and Riegler recently. We show that the asymptotic symmetry algebra consists of two copies of the $$\mathfrak {osp}(3|2)_k$$ osp ( 3 | 2 ) k affine algebra in the presence of the most general boundary conditions. Furthermore, we impose some certain restrictions on gauge fields on the most general boundary conditions and that leads us to the supersymmetric extension of the Brown–Henneaux boundary conditions. We eventually see that the asymptotic symmetry algebra reduces to two copies of the $$\mathcal {SW}(\frac{3}{2},2)$$ SW ( 3 2 , 2 ) algebra for $$\mathcal {N}=(1,1)$$ N = ( 1 , 1 ) extended higher-spin supergravity.
In this paper, we explicitly construct an asymptotic W5 symmetry algebra of the three-dimensional anti-de Sitter (AdS3) higher spin gravity. We use an sl(5,R)⊕sl(5,R) Lie algebra valued Chern-Simons gauge theory with a negative cosmological constant, and its asymptotic symmetry algebra is explicitly calculated as two copies of the classical W5 algebra with central charge c. Our results can be interpreted as a spin 5 extension of AdS3 gravity and a proof of how the higher spin Ward identities and the asymptotic W5 symmetry algebra is derived from the higher spin bulk field equations of motion. This higher spin asymptotic W5 symmetry algebra contains a finite number of conformal primary spin s: s = 2, 3, 4, 5. We also indicated how to introduce chemical potentials and holonomy conditions associated with these higher spin charges in AdS3 higher spin gravity in a manner that it preserves the asymptotic symmetry algebra.
We present the first example of $${\mathcal {N}}=(2,2)$$ N = ( 2 , 2 ) formulation for the extended higher-spin $$AdS_3$$ A d S 3 supergravity with the most general boundary conditions as an extension of the $${\mathcal {N}}=(1,1)$$ N = ( 1 , 1 ) work, discovered recently by us (Özer and Filiz in Eur Phys J C 80(11):1072, 2020). Using the method proposed by Grumiller and Riegler, we restrict a consistent class of the most general boundary conditions to extend it. An important consequence of our method is that, for the loosest set of boundary conditions it ensures that their asymptotic symmetry algebras consist of two copies of the $${\mathfrak {sl}}(3|2)_k$$ sl ( 3 | 2 ) k . Moreover, we impose some restrictions on the gauge fields for the most general boundary conditions, leading to the supersymmetric extensions of the Brown and Henneaux boundary conditions. Based on these results, we finally find out that the asymptotic symmetry algebras are two copies of the super $${\mathcal {W}}_3$$ W 3 algebra for $${\mathcal {N}}=(2,2)$$ N = ( 2 , 2 ) extended higher-spin supergravity theory in $$AdS_3$$ A d S 3 .
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.