9/13/2023 0 Comments Christopher beem cv![]() ![]() ![]() We wish to thank Chris Beem, Jan de Boer, Sergio Cecotti, Tristan Collins, Daniel Jafferis, Received: Accepted: SeptemPublished: October 8, 2021. 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. We discuss further implications for conformal manifolds of superconformal field theories in three and four dimensions. Interpreted gravitationally, they imply that approaching infinite distance in moduli space at fixed AdS radius, a tower of higher-spin fields becomes massless at an exponential rate that is bounded from below in Planck units. In the holographic context our conjectures are related to the Distance Conjecture in the swampland program. Stated geometrically, the diameter of a non-compact conformal manifold must diverge logarithmically in the higher-spin gap. Our central conjecture is that all theories at infinite distance possess an emergent higher-spin symmetry, generated by an infinite tower of currents whose anomalous dimensions vanish exponentially in the distance. We focus on conformal manifolds with limiting points at infinite distance with respect to the Zamolodchikov metric. We formulate a series of conjectures relating the geometry of conformal manifolds to the spectrum of local operators in conformal field theories in d > 2 spacetime dimensions. ![]()
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