Exploring new boundary conditions for $$\mathcal {N}=(1,1)$$ N = (
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Regular Article - Theoretical Physics
Exploring new boundary conditions for N = (1, 1) extended higher-spin Ad S3 supergravity H. T. Özera , Aytül Filizb Faculty of Science and Letters, Physics Department, Istanbul Technical University, 34469 Maslak, Istanbul, Turkey
Received: 28 July 2020 / Accepted: 28 October 2020 © The Author(s) 2020
Abstract In this paper, we present a candidate for N = (1, 1) extended higher-spin Ad S3 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 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 SW( 23 , 2) algebra for N = (1, 1) extended higher-spin supergravity.
Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . 2 Supergravity in three-dimensions, a review . . . . . . 2.1 Connection to Chern–Simons theory . . . . . . . 2.2 osp(1|2) ⊕ osp(1|2) Chern–Simons N = (1, 1) supergravity for affine boundary . . . . . . . . . 2.3 osp(1|2) ⊕ osp(1|2) Chern–Simons N = (1, 1) supergravity for superconformal boundary . . . . 3 N = (1, 1) osp(3|2) ⊕ osp(3|2) higher-spin Chern– Simons supergravity . . . . . . . . . . . . . . . . . . 3.1 For affine boundary . . . . . . . . . . . . . . . . 3.2 For superconformal boundary . . . . . . . . . . . 4 Other extended (super)gravity checks in the most general boundary conditions . . . . . . . . . . . . . . 4.1 Avery–Poojary–Suryanarayana for sl(2, R) ⊕ sl(2) 4.2 Avery–Poojary–Suryanarayana N = 1 supergravity for osp(1|2) ⊕ sl(2) . . . . . . . . . . . . 4.3 The on-shell action and the variational principle . 4.4 osp(1|2)-case . . . . . . . . . . . . . . . . . . . 4.5 osp(3|2)-case . . . . . . . . . . . . . . . . . . . a e-mail:
[email protected] (corresponding author)
b e-mail:
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5 Summary and comments . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . .
1 Introduction The most common asymptotic symmetries of Ad S3 gravity with a negative cosmological constant in 3D are known as two copies of the Virasoro algebras and this has been written first by Brown and Henneaux in their seminal paper [1]. So this work is well known as both a pioneer of Ad S3 /C F T2 correspondence [2,3] and also a realization of the Holographic Principle [4]. One of the biggest breakthroughs in theoretical physics in the past few decades is undoubtedly the discovery of the Ad S/C F T correspondence describing an equivalence between the Einstein gravity and a large N gauge field theory. The pure Einstein gravity in this context is simply a Chern– Simons gauge theory, that is, it is rewritten as a gauge field theory, in such a way that the structure simpli
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