Three-dimensional topologically gauged N=6 ABJM type theories

Abstract

In this paper we construct the $\mathcal{N}=6$ conformal supergravity in three dimensions from a set of Chern-Simons-like terms one for each of the graviton, gravitino, and R-symmetry gauge field and then couple this theory to the $\mathcal{N}=6$ superconformal ABJM theory. In a first step part of the coupled Lagrangian for this topologically gauged ABJM theory is derived by demanding that all terms of third and second order in covariant derivatives cancel in the supersymmtry variation of the Lagrangian. To achieve this the transformation rules of the two separate sectors must be augmented by new terms. In a second step we analyze all terms in $\delta L$ that are of first order in covariant derivatives. The cancelation of these terms require additional terms in the transformation rules as well as a number of new terms in the Lagrangian. As a final step we check that all remaining terms in $\delta L$ which are bilinear in fermions cancel which means that the presented Lagrangian and transformation rules constitute the complete answer. In particular we find in the last step new terms in the scalar potential containing either one or no structure constant. The non-derivative higher fermion terms in $\delta L$ that have not yet been completely analyzed are briefly discussed.

26 pages, v.2 minor corrections, comment on relation to chiral gravity added.

References in corpus (11)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• M2 to D2
• Measurement of the charm fragmentation function in D* photoproduction at HERA
• AdS_4/CFT_3 -- Squashed, Stretched and Warped
• The Superconformal Gaugings in Three Dimensions
• Three-algebras, triple systems and 3-graded Lie superalgebras
• Three-dimensional N=8 conformal supergravity and its coupling to BLG M2-branes
• Superconformal M2-branes and generalized Jordan triple systems

Cited by in corpus (23)

• Off-shell supergravity-matter couplings in three dimensions
• Multiple Membranes in M-theory
• Holographic applications of logarithmic conformal field theories
• Conformal Chern-Simons holography - lock, stock and barrel
• N=6 superconformal gravity in three dimensions from superspace
• N=6 conformal supergravity in three dimensions
• Topologically gauged superconformal Chern-Simons matter theories
• Higgsing M2 to D2 with gravity: N=6 chiral supergravity from topologically gauged ABJM theory
• Higher Derivative Supergravities in Diverse Dimensions
• Gravity/CFT correspondence for three dimensional Einstein gravity with a conformal scalar field
• Topologically massive higher spin gauge theories
• The non-linear coupled spin 2 - spin 3 Cotton equation in three dimensions
• D=3, N=8 conformal supergravity and the Dragon window
• Critical solutions in topologically gauged N=8 CFTs in three dimensions
• On the conformal higher spin unfolded equation for a three-dimensional self-interacting scalar field
• Saturating the unitarity bound in AdS/CFT_(AdS)
• Aspects of topologically gauged M2-branes with six supersymmetries: towards a "sequential AdS/CFT"?
• Coupling of the BLG theory to a conformal supergravity background
• Minimal $\mathcal{N}=4$ topologically massive supergravity
• On Topologically Massive Gravity with Extended Supersymmetry
• Towards an exact frame formulation of conformal higher spins in three dimensions
• Complete superspace classification of three-dimensional Chern-Simons-matter theories coupled to supergravity
• A twistor string for the ABJ(M) theory