Abstract
We explore the supersymmetry invariance of a supergravity theory in the presence of a non-trivial boundary. The explicit construction of a bulk Lagrangian based on an enlarged superalgebra, known as $AdS$-Lorentz, is presented. Using a geometric approach we show that the supersymmetric extension of a Gauss-Bonnet like gravity is required in order to restore the supersymmetry invariance of the theory.
Highlights
JHEP09(2016)007 using a geometrical approach, we explore the boundary terms needed in order to restore a particular enlarged supersymmetry known as AdS-Lorentz
We explore the supersymmetry invariance of a supergravity theory in the presence of a non-trivial boundary
Using a geometric approach we show that the supersymmetric extension of a Gauss-Bonnet like gravity is required in order to restore the supersymmetry invariance of the theory
Summary
In the geometric framework the variational field equations obtained from the Lagrangian are written in terms of exterior differential forms, excluding the Hodge duality operator They can be implemented either on the x-space manifold, or on any larger manifold containing the x-space. If they are implemented on the full superspace, one obtains algebraic relations between curvature components in x-space and curvature components in directions orthogonal to x-space When it happens, the former completely determines the latter, and a solution of the field equations on the x-space submanifold can be uniquely extended to a solution of the whole group manifold. 4) define the supervielbein basis in superspace [33] In this framework, the supersymmetry invariance is satisfied requiring that the Lie derivative of the Lagrangian vanishes for diffeomorphisms in the fermionic directions of superspace, δǫL = lǫL = ıǫdL + d (ıǫL) = 0.
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