Noncommutative supergravity in D=3 and D=4

Abstract

We present a noncommutative D=3, N=1 supergravity, invariant under diffeomorphisms, local U(1,1) noncommutative \star-gauge transformations and local \star-supersymmetry. Its commutative limit is the usual D=3 pure supergravity, without extra fields. A noncommutative deformation of D=4, N=1 supergravity is also obtained, reducing to the usual simple supergravity in the commutative limit. Its action is invariant under diffeomorphisms and local GL(2,C) \star-gauge symmetry. The supersymmetry of the commutative action is broken by noncommutativity. Local \star-supersymmetry invariance can be implemented in a noncommutative D=4, N=1 supergravity with chiral gravitino and complex vierbein.

22 pages, LaTeX. We discuss in more depth the noncommutative deformation of D=4 simple supergravity, and how noncommutativity breaks the supersymmetry of the commutative action

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• Noncommutative scalar field in the non-extremal Reissner-Nordström background: QNM spectrum
• Noncommutative SO(2,3) gauge theory and noncommutative gravity
• AdS-inspired noncommutative gravity on the Moyal plane
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• Boundary Effects in the BLG Theory
• Four-Dimensional Gravity on a Covariant Noncommutative Space (II)
• Noncommutative gauge fields coupled to noncommutative gravity
• Field Theory on Curved Noncommutative Spacetimes
• Noncommutative Gauge Theory and Gravity in Three Dimensions
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• Classical phase space and Hadamard states in the BRST formalism for gauge field theories on curved spacetime
• Noncommutative Gravity and Quantum Field Theory on Noncommutative Curved Spacetimes
• Noncommutative Electrodynamics from $SO(2,3{)}_{\star }$ Model of Noncommutative Gravity
• Gravity as a Gauge Theory on Three-Dimensional Noncommutative spaces
• Dirac field and gravity in NC $SO(2,3{)}_{\star }$ model
• Intertwining noncommutativity with gravity and particle physics
• Noncommutative Solitons of Gravity
• Particle Classification and Dynamics in GL(2,C) Gravity
• Noncommutative $SO(2,3{)}_{\star }$ Gauge Theory of Gravity
• Canonical Deformation of $N=2$ $Ad{S}_4$ SUGRA
• Symmetry Reduction and Exact Solutions in Twisted Noncommutative Gravity
• Noncommutative hamiltonian formalism for noncommutative gravity
• Fermionic instantons
• Chern-Simons supergravities, with a twist
• Gauge Theories on Fuzzy Spaces and Gravity