Abstract
In the context of the gauge/gravity duality, using the proposed candidate $c$-function, which is derived from the entanglement entropy of a strip-shaped region, we investigate the RG flow for $d+1$-dimensional quantum field theories with broken Lorentz and rotational symmetries in the IR, but preserved conformal invariance in the UV boundary. We examine conditions of monotonicity of the $c$-function for holographic anisotropic theories dual to the Einstein gravity via the constraints imposed by the null energy conditions. We consider near UV and IR behaviors and identify the sufficient conditions that guarantee the $c$ function decreases monotonically along the RG flows.
Highlights
A challenging question in the quantum field theory (QFT) is finding a proper quantity in order to probe the structure of parameter space of QFT
In the context of the gauge/gravity duality, using the proposed candidate c-function, which is derived from the entanglement entropy of a strip-shaped region, we investigate the renormalization group (RG) flow for d þ 1-dimensional quantum field theories with broken Lorentz and rotational symmetries in the IR, but preserved conformal invariance in the UV boundary
We examine conditions of monotonicity of the c-function for holographic anisotropic theories dual to the Einstein gravity via the constraints imposed by the null energy conditions
Summary
A challenging question in the quantum field theory (QFT) is finding a proper quantity in order to probe the structure of parameter space of QFT. On the other hand, [20] claimed that for Lorentzviolating strongly coupled field theories with holographic dual such a breakdown of the candidate c function can be seen They with respect to the asymptotic UV behavior of the geometry, identified sufficient conditions to have a monotonically decreasing c function along the RG flow. We raise the question that how the anisotropy affects the monotonicity of the RG flows, and in what conditions we can define the candidate c-function from holographic entanglement entropy for theories that exhibit Lorentz-violating as well as rotational symmetry breaking. We will construct a c-function that interpolates between a UV CFT and an IR anisotropic theory For this regarding, we consider the cases in which the Lorentz and rotational symmetries are broken only in the IR, while the UV boundary is still conformally invariant, and examine flowing from a fixed point and, in particular, a c-function of the RG flow. More details on deriving the RG-flow are provided in Appendix B
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