Correlation functions in -deformed N=6 supergravity
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2015, The Author(s). Abstract: Gauged (Formula presented.) supergravity in four dimensions is now known to admit a deformation characterized by a real parameter lying in the interval 0 /8. We analyse the fluctuations about its anti-de Sitter vacuum, and show that the full (Formula presented.) supersymmetry can be maintained by the boundary conditions only for = 0. For non-vanishing , and requiring that there be no propagating spin s > 1 fields on the boundary, we show that (Formula presented.)is the maximum degree of supersymmetry that can be preserved by the boundary conditions. We then construct in detail the consistent truncation of the (Formula presented.) theory to give -deformed SO(6) gauged (Formula presented.) supergravity, again with in the range 0 /8. We show that this theory admits fully (Formula presented.) supersymmetry-preserving boundary conditions not only for = 0, but also for = /8. These two theories are related by a U(1) electric-magnetic duality. We observe that the only three-point functions that depend on involve the coupling of an SO(6) gauge field with the U(1) gauge field and a scalar or pseudo-scalar field. We compute these correlation functions and compare them with those of the undeformed (Formula presented.) theory. We find that the correlation functions in the =/8 theory holographically correspond to amplitudes in the U(N)k U(N)k ABJM model in which the U(1) Noether current is replaced by a dynamical U(1) gauge field. We also show that the -deformed (Formula presented.) gauged supergravities can be obtained via consistent reductions from the eleven-dimensional or ten-dimensional type IIA supergravities.
