Holographic Renormalization of String-Derived Lovelock--Horndeski Theory
Abstract
String-derived higher-curvature scalar--tensor gravities encode microscopic coupling data in boundary response, raising the question of whether holographic observables can reconstruct the underlying higher-dimensional parameters. We answer this question for the five-dimensional string-derived Lovelock--Horndeski (SDLH) theory on its exact linear-dilaton asymptotically locally AdS branch, constructing the renormalized generating functional for an arbitrary boundary metric and spacetime-dependent scalar source. A boundary-covariant radial hierarchy unifies the variational problem, local backreaction, logarithmic obstruction, finite one-point functions, and Ward identities. Two response determinants organize the recursion, resonant obstructions, and metric--scalar mixing. The Weyl anomaly condenses into an Euler density, a Weyl-squared density, and a single curvature--scalar square whose paired variations generate the metric and scalar obstructions. The resulting renormalized functional carries string-selected coupling data into boundary geometry, operator response, anomaly coefficients, and a calculable interface with gravitational observables. On the regular branch, four scalar-normalization-invariant holographic combinations admit a global rational inverse to the continuous reduced couplings. At fixed compactification dimension the map has maximal rank, while the curvature-anomaly sum reconstructs the higher-dimensional Gauss--Bonnet coefficient without sign ambiguity. Holographic response thus provides an explicit, overdetermined boundary fingerprint of the underlying string reduction.
Related
- 3d Lovelock gravity and the holographic c-theorem: Proof at all orders and resummation
- On the (In)equivalence of de Sitter and Holographic Entanglement Entropies in Lovelock Gravity
- Holographic s- and p-wave superconductors from the 4D regularization of Einstein-Lovelock theory
- Algebraic Tensor Network Renormalization and Holographic duality
- Thermodynamic scaling and string dynamics in rotating holographic QCD
BibTeX
@misc{wu2026holographic,
title = {{Holographic Renormalization of String-Derived Lovelock--Horndeski Theory}},
author = {Tianhao Wu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.13319},
eprint = {2608.13319},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.13319},
}
RIS
TY - UNPB
TI - Holographic Renormalization of String-Derived Lovelock--Horndeski Theory
AU - Tianhao Wu
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2608.13319
UR - https://arxiv.org/abs/2608.13319
AB - String-derived higher-curvature scalar--tensor gravities encode microscopic coupling data in boundary response, raising the question of whether holographic observables can reconstruct the underlying higher-dimensional parameters. We answer this question for the five-dimensional string-derived Lovelock--Horndeski (SDLH) theory on its exact linear-dilaton asymptotically locally AdS branch, constructing the renormalized generating functional for an arbitrary boundary metric and spacetime-dependent scalar source. A boundary-covariant radial hierarchy unifies the variational problem, local backreaction, logarithmic obstruction, finite one-point functions, and Ward identities. Two response determinants organize the recursion, resonant obstructions, and metric--scalar mixing. The Weyl anomaly condenses into an Euler density, a Weyl-squared density, and a single curvature--scalar square whose paired variations generate the metric and scalar obstructions. The resulting renormalized functional carries string-selected coupling data into boundary geometry, operator response, anomaly coefficients, and a calculable interface with gravitational observables. On the regular branch, four scalar-normalization-invariant holographic combinations admit a global rational inverse to the continuous reduced couplings. At fixed compactification dimension the map has maximal rank, while the curvature-anomaly sum reconstructs the higher-dimensional Gauss--Bonnet coefficient without sign ambiguity. Holographic response thus provides an explicit, overdetermined boundary fingerprint of the underlying string reduction.
ER -