Exact Renormalization Group and Sine Gordon Theory

Abstract

The exact renormalization group is used to study the RG flow of quantities in field theories. The basic idea is to write an evolution operator for the flow and evaluate it in perturbation theory. This is easier than directly solving the differential equation. This is illustrated by reproducing known results in four dimensional ${\varphi }^4$ field theory and the two dimensional Sine-Gordon theory. It is shown that the calculation of beta function is somewhat simplified. The technique is also used to calculate the c-function in two dimensional Sine-Gordon theory. This agrees with other prescriptions for calculating c-functions in the literature. If one extrapolates the connection between central charge of a CFT and entanglement entropy in two dimensions, to the c-function of the perturbed CFT, then one gets a value for the entanglement entropy in Sine-Gordon theory that is in exact agreement with earlier calculations (including one using holography) in arXiv:1610.04233.

References in corpus (7)

• Exact evolution equation for the effective potential
• Comparison of renormalization group schemes for sine-Gordon type models
• Renormalization-group flow and asymptotic behaviors at the Berezinskii-Kosterlitz-Thouless transitions
• Quantum Master Equation for QED in Exact Renormalization Group
• Asymptotic safety in the sine-Gordon model
• Sine-Gordon Theory : Entanglement entropy and holography
• On the renormalization of the sine-Gordon model

Cited by in corpus (7)

• The nonperturbative functional renormalization group and its applications
• A Holographic form for Wilson's RG
• Wilson Action for the $O(N)$ Model
• Sine-Gordon Theory : Entanglement entropy and holography
• Holographic Beta functions for the Generalized Sine Gordon Theory
• Renormalization of the bilocal sine-Gordon model
• One-dimensional extended Hubbard model with soft-core potential