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Holographic Renormalization of general dilaton-axion gravity

Ioannis Papadimitriou

TL;DR

The paper develops a general holographic renormalization framework for a dilaton-axion gravity system in arbitrary dimensions up to five, using a systematic radial Hamilton-Jacobi derivative-expansion to construct a universal boundary term that makes the variational problem well-posed. It then applies this boundary structure to Improved Holographic QCD, deriving generalized Fefferman-Graham expansions and exact renormalized one-point functions, and proving holographic Ward identities, with the dilaton acting as a scale compensator and the trace anomaly absent in IHQCD. The results extend holographic dictionary techniques to non-AdS backgrounds, including non-conformal branes, and provide a concrete method to study operators with running dimensions in holographic duals. Overall, the work delivers a practical, covariant renormalization scheme and explicit correlator expressions for IHQCD, enabling robust holographic analyses of YM-like and QCD-like theories in contexts beyond strict AdS asymptotics.

Abstract

We consider a very general dilaton-axion system coupled to Einstein-Hilbert gravity in arbitrary dimension and we carry out holographic renormalization for any dimension up to and including five dimensions. This is achieved by developing a new systematic algorithm for iteratively solving the radial Hamilton-Jacobi equation in a derivative expansion. The boundary term derived is valid not only for asymptotically AdS backgrounds, but also for more general asymptotics, including non-conformal branes and Improved Holographic QCD. In the second half of the paper, we apply the general result to Improved Holographic QCD with arbitrary dilaton potential. In particular, we derive the generalized Fefferman-Graham asymptotic expansions and provide a proof of the holographic Ward identities.

Holographic Renormalization of general dilaton-axion gravity

TL;DR

The paper develops a general holographic renormalization framework for a dilaton-axion gravity system in arbitrary dimensions up to five, using a systematic radial Hamilton-Jacobi derivative-expansion to construct a universal boundary term that makes the variational problem well-posed. It then applies this boundary structure to Improved Holographic QCD, deriving generalized Fefferman-Graham expansions and exact renormalized one-point functions, and proving holographic Ward identities, with the dilaton acting as a scale compensator and the trace anomaly absent in IHQCD. The results extend holographic dictionary techniques to non-AdS backgrounds, including non-conformal branes, and provide a concrete method to study operators with running dimensions in holographic duals. Overall, the work delivers a practical, covariant renormalization scheme and explicit correlator expressions for IHQCD, enabling robust holographic analyses of YM-like and QCD-like theories in contexts beyond strict AdS asymptotics.

Abstract

We consider a very general dilaton-axion system coupled to Einstein-Hilbert gravity in arbitrary dimension and we carry out holographic renormalization for any dimension up to and including five dimensions. This is achieved by developing a new systematic algorithm for iteratively solving the radial Hamilton-Jacobi equation in a derivative expansion. The boundary term derived is valid not only for asymptotically AdS backgrounds, but also for more general asymptotics, including non-conformal branes and Improved Holographic QCD. In the second half of the paper, we apply the general result to Improved Holographic QCD with arbitrary dilaton potential. In particular, we derive the generalized Fefferman-Graham asymptotic expansions and provide a proof of the holographic Ward identities.

Paper Structure

This paper contains 12 sections, 136 equations, 1 figure, 6 tables.

Table of Contents

  1. Introduction
  2. Boundary term for generic dilaton-axion gravity
  3. Hamiltonian formulation of the variational problem
  4. Recursive solution of the Hamilton-Jacobi equation
  5. Application to IHQCD
  6. Boundary term for IHQCD
  7. One-point functions and Fefferman-Graham expansions
  8. Asymptotic diffeomorphisms and Ward identities
  9. Concluding remarks
  10. Functional integration
  11. Dilaton-axion system with constant dilaton potential
  12. Asymptotic expansions

Figures (1)

  • Figure 1: A schematic illustration of the algorithm used to determine Hamilton's principal function iteratively. Here, the operators $\fint$ and $\delta$ stand respectively for the functional integration defined by the formula in (\ref{['integration-formula']}) and for functional differentiation with respect to the induced fields.