On Higher-Spin Points and Infinite Distances in Conformal Manifolds

Understand

Distances in the conformal manifold, the space of CFTs related by marginal deformations, can be measured in terms of the Zamolodchikov metric.

• Part of the CFT Distance Conjecture posits that points in this manifold where part of the spectrum becomes free, called higher-spin points, can only be at infinite distance from the interior.
• There, an infinite tower of operators become conserved currents, and the conformal symmetry is enhanced to a higher-spin algebra.
• This proposal was initially motivated by the Swampland Distance Conjecture, one of pillars of the Swampland Program.