Riccati equations for holographic 2-point functions

Progress on Holographic Three-Point Functions

The gauge/gravity correspondence provides an excellent tool for obtaining relevant information about supersymmetric Yang-Mills (SYM) theories from the study of their dual supergravity backgrounds, which are generated by stacks of D-branes. The most celebrated duality—known as the AdS/CFT correspondence— relates the superconformalN = 4 SYM theory in four dimensions (in the planar limit and at la...

Algebraic Riccati equations

Holographic three-point functions: one step beyond the tradition

Within the program of holographic renormalization, we discuss the computation of three-point correlation functions along RG flows. We illustrate the procedure in two simple cases. In an RG flow to the Coulomb branch of N = 4 SYM theory we derive a compact and finite expression for the three-point function of lowest CPO’s dual to inert scalars. In the GPPZ flow, that captures some features of N ...

GIP integrators for Matrix Riccati Differential Equations

Matrix Riccati Differential Equations (MRDEs) are initial value problems of the form: X 0 1⁄4 A21 XA11 þ A22X XA12X; Xð0Þ 1⁄4 X0: These equations arise frequently throughout applied mathematics, science, and engineering. It can happen that even when the Aij are smooth functions of t or constant, the solution X may have a singularity or even infinitely many singularities. This paper shows severa...

Inexact Kleinman-Newton Method for Riccati Equations

In this paper we consider the numerical solution of the algebraic Riccati equation using Newton's method. We propose an inexact variant which allows one control the number of the inner iterates used in an iterative solver for each Newton step. Conditions are given under which the monotonicity and global convergence result of Kleinman also hold for the inexact Newton iterates. Numerical results ...