Renormalization group flow, Entropy and Eigenvalues

Abstract

The irreversibility of the renormalization group flow is conjectured to be closely related to the concept of entropy. In this paper, the variation of eigenvalues of the Laplacian in the Polyakov action under the renormalization group flow will be studied. Based on the one-loop approximation to the effective field theory, we will use the heat kernel method and zeta function regularization. In even dimensions, the variation of eigenvalues is given by the top heat kernel coefficient, and the conformal anomaly is relevant. In odd dimensions, we will conjecture a formula for the variation of eigenvalues through the holographic renormalization in the setting of geometric AdS/CFT correspondence.

29 pages

References in corpus (6)

• Towards a derivation of holographic entanglement entropy
• On Renormalization Group Flows in Four Dimensions
• Ricci Flow and the Poincare Conjecture
• A refinement of entanglement entropy and the number of degrees of freedom
• Eigenvalues of the Laplacian under the Ricci Flow
• From the Boltzmann $H$-theorem to Perelman's $W$-entropy formula for the Ricci flow