A CFT Distance Conjecture

by Irene Valenzuela (Harvard University)

Thursday 11 Feb 2021, 14:15 → 15:15 Europe/Berlin

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. Our central conjecture is that all theories at infinite distance in the Zamolodchikov metric possess an emergent higher-spin symmetry, generated by an infinite tower of currents whose anomalous dimensions vanish exponentially in the distance. In the holographic context our conjectures are related to the Distance Conjecture in the Swampland program. 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.