Abstract
In this paper, we holographically study the renormalization group (RG) flow in a three-dimensional Einstein-dilaton gravity with a potential permitting several types of the RG flow with nontrivial beta-functions. By using the intrinsic parameter of the potential, we classify possible holographic RG flows and examine their physical features. Using the Ryu-Takayanagi formulation, furthermore, we investigate how the $c$-function of the entanglement entropy behaves along the RG flow numerically. We show that the entanglement $c$-function monotonically decreases even in the cases with a nontrivial beta-function. For checking the consistency, we also compare the result of the entanglement entropy with the $c$-function derived from the holographic renormalization procedure.
Highlights
Among contemporary theoretical physics, holography becomes one of the important research areas
We investigated several different types of renormalization group (RG) flow that can appear in a two-dimensional deformed conformal field theories (CFT)
Near this UV fixed point, if we restrict for the scalar field to have a mass only in the range of −1 < m2R2uv < 0, the local extremum at φ 1⁄4 0 becomes a local maximum or an unstable equilibrium point and, on the dual field theory side, the corresponding dual scalar operator becomes a relevant operator
Summary
Holography becomes one of the important research areas. The field-theoretic computation accompanies with a very complicated analysis In this circumstance, the holographic calculation [13,14] based on AdS=CFT correspondence [1,2,3,4,15,16] provides a more tractable tool because it enables us to interpret the entanglement entropy of strongly interacting systems as a geodesic in the dual Einstein gravity. One of the interesting and important tasks in physics may be counting the number of degrees of freedom of quantum field theories, which decreases monotonically along with the RG flow This feature called the c theorem is well expressed by a c function depending on the energy scale.
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