Hidden conformal symmetry of the discrete series scalars in ${\mathrm{dS}}_2$

Journal Article · 05 May 2025 · Physical Review. D.

DOI: https://doi.org/10.1103/PhysRevD.111.105002 · OSTI ID:2564767

Farnsworth, Kara ; Hinterbichler, Kurt; Saha, Samanta

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. Published by the American Physical Society 2025

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0009946
• OSTI ID: 2564767
• Journal Information: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 10 Vol. 111; ISSN PRVDAQ; ISSN 2470-0010
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English