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Clearing up the Strong $CP$ problem

Joshua N. Benabou, Anson Hook, Claudio Andrea Manzari, Hitoshi Murayama, Benjamin R. Safdi

TL;DR

The paper argues that the Strong CP problem is a genuine issue despite recent claims to the contrary. It shows that gauged discrete symmetries, particularly gauged $P$ or $CP$ in UV completions, can enforce a CP-preserving vacuum with $\theta+\bar{\theta}=0$ or $\pi$ and yield calculable neutron EDMs after spontaneous breaking. The authors provide concrete UV realizations in higher-dimensional theories and string theory, including a simple 5D model and string constructions, and they defend the physical relevance of $\bar{\theta}$ through standard QCD dynamics such as the topological susceptibility and the Witten–Veneziano relation. They also critique alternative EFT approaches and discuss the swampland perspective, arguing that discrete gauged symmetries in quantum gravity remain viable routes to solve or mitigate the Strong CP problem.

Abstract

The absence of a neutron electric dipole moment (EDM) constrains the quantum chromodynamics (QCD) theta angle to be less than one part in ten billion, posing the Strong $CP$ problem. We revisit two classes of proposed solutions. First, we show that when $P$ or $CP$ is realized as a gauged discrete symmetry - as can arise in quantum gravity - the vacuum necessarily preserves $CP$, contrary to recent claims that discrete-symmetry solutions fail. Gauged discrete models face model-building challenges, such as avoiding contributions to the neutron EDM after spontaneous $P$ or $CP$ breaking, but in principle have no fundamental obstructions. Second, we critically examine recent arguments that the Strong $CP$ problem is illusory, demonstrating that a nonzero neutron EDM at finite $\barθ$ follows directly from well-understood QCD dynamics. Taken together, our results reinforce the reality of the Strong $CP$ problem and highlight gauged discrete-symmetry realizations of $P$ or $CP$ as plausible solutions.

Clearing up the Strong $CP$ problem

TL;DR

The paper argues that the Strong CP problem is a genuine issue despite recent claims to the contrary. It shows that gauged discrete symmetries, particularly gauged or in UV completions, can enforce a CP-preserving vacuum with or and yield calculable neutron EDMs after spontaneous breaking. The authors provide concrete UV realizations in higher-dimensional theories and string theory, including a simple 5D model and string constructions, and they defend the physical relevance of through standard QCD dynamics such as the topological susceptibility and the Witten–Veneziano relation. They also critique alternative EFT approaches and discuss the swampland perspective, arguing that discrete gauged symmetries in quantum gravity remain viable routes to solve or mitigate the Strong CP problem.

Abstract

The absence of a neutron electric dipole moment (EDM) constrains the quantum chromodynamics (QCD) theta angle to be less than one part in ten billion, posing the Strong problem. We revisit two classes of proposed solutions. First, we show that when or is realized as a gauged discrete symmetry - as can arise in quantum gravity - the vacuum necessarily preserves , contrary to recent claims that discrete-symmetry solutions fail. Gauged discrete models face model-building challenges, such as avoiding contributions to the neutron EDM after spontaneous or breaking, but in principle have no fundamental obstructions. Second, we critically examine recent arguments that the Strong problem is illusory, demonstrating that a nonzero neutron EDM at finite follows directly from well-understood QCD dynamics. Taken together, our results reinforce the reality of the Strong problem and highlight gauged discrete-symmetry realizations of or as plausible solutions.
Paper Structure (19 sections, 117 equations, 1 figure)

This paper contains 19 sections, 117 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Definition of the problem
  3. Symmetry Solutions to the Strong $CP$ Problem
  4. Gauged $P$ from quantum gravity in higher dimensions
  5. Gauging $P$: a simple 5D example
  6. Gauging $P$ and $CP$ in string theory
  7. There is a Strong $CP$ problem
  8. Order of limits in QCD partition function
  9. $\bar{\theta}$ in the Chiral Lagrangian
  10. Discussion
  11. QED in 1+1D
  12. Perspectives on theta vacua
  13. Canonical and Path Integral Formulation of QED in 1+1D
  14. An analogy to the Strong $CP$ Problem
  15. Gauging parity in 1+1D QED
  16. ...and 4 more sections

Figures (1)

  • Figure 1: The eigenvalues of the Hamiltonian of 1+1D QED on $S^{1}$ as a function of the angle $\theta - \theta_0$ (black) with the ground state indicated in red.