The Hamilton-Jacobi equation and holographic renormalization group flows on sphere

• Main Authors: Nakwoo Kim, Se-Jin Kim
• Format: Article
• Language: English
• Published: SpringerOpen 2020-10-01
• Series: Journal of High Energy Physics
• Subjects: AdS-CFT Correspondence; Gauge-gravity correspondence; Supersymmetric Gauge Theory
• Online Access: http://link.springer.com/article/10.1007/JHEP10(2020)068

Abstract We study the Hamilton-Jacobi formulation of effective mechanical actions associated with holographic renormalization group flows when the field theory is put on the sphere and mass terms are turned on. Although the system is supersymmetric and it is described by a superpotential, Hamilton’s characteristic function is not readily given by the superpotential when the boundary of AdS is curved. We propose a method to construct the solution as a series expansion in scalar field degrees of freedom. The coefficients are functions of the warp factor to be determined by a differential equation one obtains when the ansatz is substituted into the Hamilton-Jacobi equation. We also show how the solution can be derived from the BPS equations without having to solve differential equations. The characteristic function readily provides information on holographic counterterms which cancel divergences of the on-shell action near the boundary of AdS.