Extended Supersymmetric BMS${}_3$ algebras and Their Free Field Realisations

Abstract

We study $N=(2,4,8)$ supersymmetric extensions of the three dimensional BMS algebra (BMS${}_3$) with most generic possible central extensions. We find that $N$-extended supersymmetric BMS${}_3$ algebras can be derived by a suitable contraction of two copies of the extended superconformal algebras. Extended algebras from all the consistent contractions are obtained by scaling left-moving and right-moving supersymmetry generators symmetrically, while Virasoro and R-symmetry generators are scaled asymmetrically. On the way, we find that the BMS/GCA correspondence does not in general hold for supersymmetric systems. Using the $\beta$-$\gamma$ and the $\mathfrak{b}$-$\mathfrak{c}$ systems, we construct free field realisations of all the extended super-BMS${}_3$ algebras.

arXiv comment25 pages, 1 table

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Cited by in corpus (9)

• Soft hairy horizons in three spacetime dimensions
• Black Hole Horizon Fluffs: Near Horizon Soft Hairs as Microstates of Three Dimensional Black Holes
• Geometric actions and flat space holography
• N=4 Supersymmetric BMS3 algebras from asymptotic symmetry analysis
• Celestial Holography: Lectures on Asymptotic Symmetries
• Maximally $\mathcal{N}$-extended super-BMS${}_3$ algebras and Generalized 3D Gravity Solutions
• The (super)conformal BMS${}_3$ algebra
• Semi-simple enlargement of the ${\mathfrak{bms}}_3$ algebra from a $\mathfrak{so}(2,2)\oplus \mathfrak{so}(2,1)$ Chern-Simons theory
• Equivalent Dual Theories for 3D N=2 Supergravity