In 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 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 , and dual to the shift invariant massive vector fields, which are therefore also conformally invariant.
@article{osti_2564767,
author = {Farnsworth, Kara and Hinterbichler, Kurt and Saha, Samanta},
title = {Hidden conformal symmetry of the discrete series scalars in <math display='inline'> <mrow> <msub> <mrow> <mi>dS</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </math>},
annote = { 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 },
doi = {10.1103/PhysRevD.111.105002},
url = {https://www.osti.gov/biblio/2564767},
journal = {Physical Review. D.},
issn = {ISSN 2470-0010},
number = {10},
volume = {111},
place = {United States},
publisher = {American Physical Society},
year = {2025},
month = {05}}
Proceedings of Corfu Summer Institute 2021 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2021)https://doi.org/10.22323/1.406.0356