For 2<d<4, 2D massless fermions coupled to a d-dimensional Maxwell field are exactly described by a scalar whose scaling dimension runs from 0 in the UV to (4-d)/2 in the IR.
Double-trace operators and one-loop vacuum energy in AdS/CFT
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We perform a one-loop calculation of the vacuum energy of a tachyon field in anti de-Sitter space with boundary conditions corresponding to the presence of a double-trace operator in the dual field theory. Such an operator can lead to a renormalization group flow between two different conformal field theories related to each other by a Legengre transformation in the large N limit. The calculation of the one-loop vacuum energy enables us to verify the holographic c-theorem one step beyond the classical supergravity approximation.
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A Nonlocal Schwinger Model
For 2<d<4, 2D massless fermions coupled to a d-dimensional Maxwell field are exactly described by a scalar whose scaling dimension runs from 0 in the UV to (4-d)/2 in the IR.