Abstract
Abstract Using the attractor mechanism for extremal solutions in $$ \mathcal{N}=2 $$ N = 2 gauged supergravity, we construct a c-function that interpolates between the central charges of theories at ultraviolet and infrared conformal fixed points corresponding to anti-de Sitter geometries. The c-function we obtain is couched purely in terms of bulk quantities and connects two different dimensional CFTs at the stable conformal fixed points under the RG flow.
Highlights
JHEP11(2014)138 whose value does not increase along the trajectory
We are referring to a function that interpolates between central charges of fixed point conformal field theories (CFT) in a strictly monotonic manner
The gauge/gravity duality allows us to equate the c-theorem in the boundary field theory to a statement about the holographically dual gravitational background [10,11,12,13,14,15,16]
Summary
In holographic RG, the radial direction in AdS is a proxy for the scale of the Wilsonian flow in the dual field theory [27,28,29,30]. We need to demand only that at the endpoints of the RG flow, the function takes values corresponding to the central charges at the fixed points, where the theory is exactly conformal. These central charges are related to the radius of the AdS geometry dual to the fixed point. AdS boundary to the near-horizon AdS factor is holographically dual to the Wilsonian flow of the effective field theory action that encodes the dynamics of the field theory operators dual to the scalar fields in the specified black background. Infrared fixed points of the form of AdS2 × X have been studied extensively especially in the context of stability under perturbations and the interested reader is referred to [32,33,34,35,36] for further details
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