Holography and the Swampland: Constraints on Quantum Gravity from Holographic Principles

Abstract: The Swampland Program aims to delineate the space of consistent low-energy effective field theories (EFTs) that admit a UV completion in quantum gravity from those that do not. In parallel, holography, and particularly the AdS/CFT correspondence, offers a non-perturbative definition of quantum gravity in asymptotically anti-de Sitter (AdS) spacetimes. In this paper, we explore the Swampland Conjectures through the lens of holography, focusing on how holographic consistency conditions, such as the convexity of the conformal field theory (CFT) spectrum, the averaged null energy condition (ANEC), and the modular bootstrap, map onto Swampland constraints in the bulk. We argue that the holographic principle provides a geometric realization of Swampland bounds, particularly on scalar field potentials and the absence of long-lived de Sitter vacua. Finally, we discuss how the emergent bulk locality in AdS/CFT provides evidence that the Swampland conjectures may themselves be manifestations of deeper holographic consistency conditions.