Inönü–Wigner contraction and \(D=2+1\) supergravity

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• 作者：P. K. Concha ; O. Fierro ; E. K. Rodríguez
• 刊名：The European Physical Journal C
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：77
• 期：1
• 全文大小：699KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Elementary Particles, Quantum Field Theory; Nuclear Physics, Heavy Ions, Hadrons; Quantum Field Theories, String Theory; Measurement Science and Instrumentation; Astronomy, Astrophysics and Cosmology;
• 出版者：Springer Berlin Heidelberg
• ISSN：1434-6052
• 卷排序：77

文摘

We present a generalization of the standard Inönü–Wigner contraction by rescaling not only the generators of a Lie superalgebra but also the arbitrary constants appearing in the components of the invariant tensor. The procedure presented here allows one to obtain explicitly the Chern–Simons supergravity action of a contracted superalgebra. In particular we show that the Poincaré limit can be performed to a \(D=2+1\)\(\left( p,q\right) \)AdS Chern–Simons supergravity in presence of the exotic form. We also construct a new three-dimensional \(\left( 2,0\right) \) Maxwell Chern–Simons supergravity theory as a particular limit of \(\left( 2,0\right) \)AdS–Lorentz supergravity theory. The generalization for \(\mathcal {N}=p+q\) gravitinos is also considered.