CFT dual to gravitational non-locality in string theory

Abstract

We investigate non-perturbative bulk corrections arising from instantons in string theory and M-theory. By deriving non-local curvature corrections of the form e-gamma RR mu nu R mu nu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ e<^>{-\gamma R} R_{\mu \nu } R<^>{\mu \nu } $$\end{document}, we demonstrate how these modifications emerge from wrapped brane instantons and their summation over multi-instanton configurations. Utilizing holographic techniques, we establish a direct connection between these non-perturbative effects and large-N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ N $$\end{document} gauge theories, identifying the appropriate holographic dual conformal field theory (CFT). We further analyze this connection through resummations in the large-N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ N $$\end{document} expansion. Additionally, we study black hole solutions in AdS backgrounds and show that these instanton-induced corrections significantly modify the near-horizon geometry. Finally, we explore the regularization of curvature singularities via these exponential damping terms, providing a natural resolution mechanism in quantum gravity. Our findings underscore the fundamental role of non-perturbative physics in shaping the structure of spacetime and its holographic duals.