A CFT Distance Conjecture

Abstract: 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. This is sustained by known data collected from the landscape of SCFTs, and yet it suggests a number of intriguing new properties. 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. This relates to recent developments of the Distance Conjecture in N=1 4d supergravity theories, where higher spin fields also play an essential role as the conjecture seems to follow from the universal presence of an axionic BPS string at every infinite field distance limit.

HEP - theory

Audience: researchers in the topic

SISSA HEP seminars

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