Year: 2024
Type: article
Abstract: A bstract For any unitary conformal field theory in two dimensions with the central charge c , we prove that, if there is a nontrivial primary operator whose conformal dimension ∆ vanishes in some limit on the conformal manifold, the Zamolodchikov distance t to the limit is infinite, the approach to this limit is exponential ∆ = exp(− αt + O (1)), and the decay rate obeys the universal bounds c −1 / 2 ≤ α ≤ 1. In the limit, we also find that an infinite tower of primary operators emerges without a gap above the vacuum and that the conformal field theory becomes locally a tensor product of a sigma-model in the large radius limit and a compact theory. As a corollary, we establish a part of the Distance Conjecture about gravitational theories in three-dimensional anti-de Sitter space. In particular, our bounds on α indicate that the emergence of exponentially light states is inevitable as the moduli field corresponding to t rolls beyond the Planck scale along the steepest path and that this phenomenon can begin already at the curvature scale of the bulk geometry. We also comment on implications of our bounds for gravity in asymptotically flat spacetime by taking the flat space limit and compare with the Sharpened Distance Conjecture.
Source: Journal of High Energy Physics
Authors: Hirosi Ooguri, Yifan Wang
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Funders: National Science Foundation, U.S. Department of Energy, Harvard University, York University, Ministry of Education, Culture, Sports, Science and Technology, University of Tokyo, Office of Science, University of California, Santa Barbara, Japan Society for the Promotion of Science, Kavli Institute for Theoretical Physics, University of California, Santa Barbara, High Energy Physics
Awards: G1099677550, Distance Conjecture in Quantum Gravity, G3398237449, G4689434848, Defects and Extended Objects in Quantum Field Theory and Quantum Gravity, RESEARCH ACCOMPLISHMENTS AND GOALS OF THE THEORETICAL HIGH ENERGY PHYSICS GROUP, Kavli Institute for Theoretical Physics, RESEARCH ACCOMPLISHMENTS AND GOALS OF THE THEORETICAL HIGH ENERGY PHYSICS GROUP
OpenAlex ID: W4405984444