On Upper Bounds in Dimension Gaps of CFT's

TL;DR

This paper establishes universal upper bounds on the conformal dimension of the first non-trivial spin 2 operator and the minimal internal space diameter in holographic CFTs derived from branes probing singularities, applicable across various internal geometries.

Contribution

It introduces universal bounds on operator dimensions and internal space size in holographic CFTs, extending previous results to a broad class of internal manifolds including Sasaki-Einstein and sphere quotients.

Findings

Universal upper bound on the conformal dimension of the first spin 2 operator.

Minimal diameter bound for the internal space in holographic duals.

Conjecture that these bounds hold for all conformal field theories.

Abstract

We consider CFT's arising from branes probing singularities of internal manifolds. We focus on holographic models with internal space including arbtirary Sasaki-Einstein manifolds coming from CY as well as arbitrary sphere quotients. In all these cases we show that there is a universal upper bound (depending only on the spacetime dimension) for the conformal dimension of the first non-trivial spin 2 operator in the dual CFT and a minimal diameter (in AdS units) for the internal space of the holographic dual and conjecture it holds for all CFT's.