Universal bounds on CFT Distance Conjecture

Creators: Ooguri, Hirosi^{1, 2}; Wang, Yifan³

1. California Institute of Technology
2. Kavli Institute for the Physics and Mathematics of the Universe
3. New York University

Abstract

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.

Copyright and License

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Article funded by SCOAP3.

Acknowledgement

We thank Ofer Aharony, Bruno Balthazar, Nathan Benjamin, José Calderón-Infante, Sergio Cecotti, Thomas Hartman, Zohar Komargodski, Ying-Hsuan Lin, Juan Maldacena, Sridip Pal, Julio Parra-Martinez, Eric Perlmutter, Massimo Porrati, Daniel Roggenkamp, Thomas Rudelius, Shu-Heng Shao, Eva Silverstein, David Simmons-Duffin, Yan Soibelman, Cumrun Vafa, Irene Valenzuela, Katrin Wendland, Edward Witten, and Xi Yin for discussions. The work of HO is supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632, JSPS Grants-in-Aid for Scientific Research 23K03379, the Bershadsky Fellowship, the Guggenheim Fellowship, and the Simons Investigator Award (MPS-SIP-00005259). The work of YW is supported in part by the NSF grant PHY-2210420 and by the Simons Junior Faculty Fellows program. HO thanks the hospitalities of the Center for Cosmology and Particle Physics at New York University, where this work was initiated, and of the Center for the Fundamental Laws of Nature at Harvard University, where this work was completed. His work was also performed in part at the Kavli Institute for the Physics and Mathematics of the Universe at the University of Tokyo, which is supported by the World Premier International Research Center Initiative, MEXT, Japan, and at the Kavli Institute for Theoretical Physics (KITP) at the University of California, Santa Barbara, which is supported by NSF grant PHY-2309135.

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