Hidden Conformal Symmetry of the Discrete Series Scalars in dS$_2$

TL;DR

This paper reveals that in two-dimensional de Sitter space, scalar fields with special masses exhibit hidden conformal symmetry, which is confirmed through correlator analysis and duality with vector fields, expanding understanding of symmetries in curved spacetime.

Contribution

The paper demonstrates the presence of global conformal symmetry for discrete series scalar fields in D=2 de Sitter space and explores their duality with vector fields, revealing new symmetry structures.

Findings

Correlators of shift-invariant operators are conformally invariant.

Discrete series scalars in D=2 exhibit hidden conformal symmetry.

These scalar fields are dual to shift-invariant massive vector fields.

Abstract

In $D$ dimensional de Sitter space, a scalar field has an infinite tower of special tachyonic mass values at which enhanced shift symmetries appear. After modding out by these shift symmetries, these fields correspond to the unitary irreducible representations of the de Sitter group known as the discrete series. We show that in $D=2$ these theories have global conformal symmetry. In all but the massless case, these theories have no stress tensor and the conformal symmetry does not act in the usual way on the scalar field. We find the conformal symmetry by explicitly computing the correlators of the shift invariant local operators and showing that they take conformally invariant forms. We also demonstrate how these fields are self dual in $D=2$, and dual to the shift invariant massive vector fields, which are therefore also conformally invariant.