Jefferson J250, 17 Oxford Street, Cambridge, Massachusetts 02138
Title: Universal Bounds on CFT Distance Conjecture
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 volume 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, the bounds on α indicate that the emergence of exponentially light particles 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.