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(Non-)Conserved Currents and Cosmological Correlators

Charlotte Sleight, Massimo Taronna

TL;DR

The work investigates how global symmetries fail to persist at the late-time boundary of de Sitter space, showing that currents and the stress tensor generically acquire anomalous dimensions through shadow-based multiplet recombination. Using an EAdS reformulation of dS correlators, the authors interpret Dirichlet-boundary modes as Higgs-like states that mix with composites to gain small masses, while Neumann modes stay protected by gauge invariance. They explicitly verify the mechanism in scalar QED, Yang–Mills, and Einstein gravity, and argue for generalization to higher-spin and partially massless fields. The findings illuminate fundamental differences between AdS/CFT and dS holography, with implications for the fate of global symmetries in expanding spacetimes and for the structure of boundary correlators in cosmology.

Abstract

We study the fate of global symmetries at the late-time boundary of de Sitter space. In anti-de Sitter space, bulk gauge symmetries generally correspond to conserved global currents on the boundary. We show that in de Sitter space such currents tend to acquire anomalous dimensions due to multiplet recombination with composite operators, which is a consequence of the shadow structure of the boundary operator spectrum. As a result, global symmetries are generically (weakly) broken. This mechanism is transparent in the EAdS reformulation of dS late-time correlators given in arXiv:2007.09993 and arXiv:2109.02725, where Dirichlet modes mix with composites and acquire small masses, while Neumann modes remain protected by gauge invariance. We demonstrate this mechanism explicitly in scalar QED, Yang-Mills theory, and Einstein gravity, and argue that it extends to higher-spin and partially massless fields.

(Non-)Conserved Currents and Cosmological Correlators

TL;DR

The work investigates how global symmetries fail to persist at the late-time boundary of de Sitter space, showing that currents and the stress tensor generically acquire anomalous dimensions through shadow-based multiplet recombination. Using an EAdS reformulation of dS correlators, the authors interpret Dirichlet-boundary modes as Higgs-like states that mix with composites to gain small masses, while Neumann modes stay protected by gauge invariance. They explicitly verify the mechanism in scalar QED, Yang–Mills, and Einstein gravity, and argue for generalization to higher-spin and partially massless fields. The findings illuminate fundamental differences between AdS/CFT and dS holography, with implications for the fate of global symmetries in expanding spacetimes and for the structure of boundary correlators in cosmology.

Abstract

We study the fate of global symmetries at the late-time boundary of de Sitter space. In anti-de Sitter space, bulk gauge symmetries generally correspond to conserved global currents on the boundary. We show that in de Sitter space such currents tend to acquire anomalous dimensions due to multiplet recombination with composite operators, which is a consequence of the shadow structure of the boundary operator spectrum. As a result, global symmetries are generically (weakly) broken. This mechanism is transparent in the EAdS reformulation of dS late-time correlators given in arXiv:2007.09993 and arXiv:2109.02725, where Dirichlet modes mix with composites and acquire small masses, while Neumann modes remain protected by gauge invariance. We demonstrate this mechanism explicitly in scalar QED, Yang-Mills theory, and Einstein gravity, and argue that it extends to higher-spin and partially massless fields.

Paper Structure

This paper contains 14 sections, 85 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Notation and conventions
  3. Non-conservation of currents and the stress tensor
  4. Scalar QED
  5. Scalar field minimally coupled to gravity
  6. Pure Yang-Mills
  7. Einstein Gravity
  8. Anomalous dimensions
  9. Discussion and conclusion
  10. Gauge choice and locality.
  11. Gauge invariance.
  12. No Higgs mechanism for gravity in dS?
  13. Boundary correlators in Mellin space
  14. Partially-massless gauge fields

Figures (2)

  • Figure 1: Loop correction to gauge boson $A_{\Delta_J}$ and graviton $h_{\Delta_J}$ mass in EAdS induced by a the bound state of fields $\varphi_{\Delta_\pm}$.
  • Figure 2: Non-conserved three-point functions of $J_i$ or $T_{ij}$ with shadow operators ${\cal O}_{\Delta_\pm}$ on the future boundary of de Sitter space can be recast as EAdS Witten diagrams involving gauge bosons $A_{\Delta_J}$ or gravitons $h_{\Delta_T}$ and the fields $\varphi_{\Delta_\pm}$.