[Paper Review] Strong-$CP$ with and without gravity

Gia Dvali|arXiv (Cornell University)|Sep 28, 2022

Dark Matter and Cosmic Phenomena4 citations

TL;DR

This paper proposes that the strong-CP problem is resolved not by an ad hoc global U(1)_{PQ} symmetry, but by a gauge-theoretic axion realized as a 2-form field $ B_{\mu\nu} $ that couples to QCD's Chern-Simons 3-form, inducing a Higgs-like mechanism that exactly cancels $ \bar{\vartheta} $ to all orders. Gravity enforces this mechanism via the S-matrix consistency, making the axion mechanism exact and protected from UV deformations.

ABSTRACT

Conventionally, the strong-$CP$ problem is assumed to be a naturalness puzzle, with the axion solution sometimes viewed as an ad hoc fix. Gravity is either ignored or taken as a threat for the global Peccei-Quinn symmetry. We explain that the situation is fundamentally different. In gravity, axion is a matter of consistency imposed by the $S$-matrix: Each gauge sector must include axion with exact relaxation of the corresponding $\barθ$. We show that this favors an alternative and remarkably simple formulation of the axion, fully fixed by the gauge redundancy of QCD, without involvement of a global symmetry. The axion mechanism is a Higgs effect for the QCD $3$-form, ensuring that physics is independent of $\barθ$ to all orders in operator expansion. A near-future experimental detection of the neutron EDM will be an unambiguous signal of $CP$-violating physics beyond the Standard Model. The axion coupling is tied to the scale of gravity.

Motivation & Objective

• To resolve the strong-CP problem not as a naturalness puzzle, but as a consistency requirement of quantum gravity.
• To show that the axion mechanism is not an ad hoc fix but a consequence of gauge redundancy in QCD.
• To demonstrate that the $ B_{\mu\nu} $-axion formulation, without global symmetries, ensures exact $ \bar{\vartheta} = 0 $ to all orders in operator expansion.
• To establish that gravity’s S-matrix formulation demands the absence of $ \vartheta $-vacua, necessitating axion relaxation.
• To show that the axion mechanism is stable against gravitational and UV-induced deformations due to gauge protection.

Proposed method

• Formulate the axion as a gauge 2-form $ B_{\mu\nu} $ with QCD gauge charge, replacing the global $ U(1)_{PQ} $ symmetry.
• Implement a Higgs-like mechanism where the QCD Chern-Simons 3-form becomes massive by absorbing the $ B_{\mu\nu} $-axion.
• Use the S-matrix formulation of quantum gravity to argue that non-degenerate $ \vartheta $-vacua are inconsistent, requiring exact $ \bar{\vartheta} $ relaxation.
• Show that gauge redundancy protects the axion mechanism from arbitrary local operators, including gravitational ones.
• Dualize the $ B_{\mu\nu} $-theory to a pseudo-scalar axion $ a $, but retain the integration constant that encodes gauge structure and ensures protection.
• Demonstrate that the topological susceptibility of the vacuum vanishes due to the Higgs effect, making $ \bar{\vartheta} $ unphysical.

Experimental results

Research questions

• RQ1 Why does gravity demand the existence of an axion per gauge sector, and how does this differ from the standard naturalness-based view?
• RQ2 How can the axion mechanism be exact and protected from UV and gravitational effects without relying on a global symmetry?
• RQ3 What is the role of the $ B_{\mu\nu} $ 2-form field in ensuring $ \bar{\vartheta} = 0 $ to all orders in the operator expansion?
• RQ4 How does the S-matrix formulation of gravity rule out $ \vartheta $-vacua and enforce axion relaxation?
• RQ5 Why is the $ B_{\mu\nu} $-axion formulation more predictive than the standard Peccei-Quinn model with a global $ U(1)_{PQ} $ symmetry?

Key findings

• The axion mechanism is not an ad hoc fix but a consistency requirement of quantum gravity, enforced by the S-matrix formulation.
• The $ B_{\mu\nu} $-axion formulation ensures exact $ \bar{\vartheta} = 0 $ to all orders in the operator expansion due to gauge redundancy.
• The topological susceptibility of the vacuum vanishes because the QCD Chern-Simons 3-form becomes massive via the Higgs-like mechanism with $ B_{\mu\nu} $.
• The axion mechanism is stable against gravitational effects, including virtual black holes, due to gauge protection.
• The theory predicts that the QCD contribution to the neutron EDM is exactly zero, making any future detection a signal of new physics beyond QCD and the weak interaction.
• The absence of $ \vartheta $-vacua in gravity implies that the gravitational topological susceptibility must also vanish, possibly requiring a second axion or chiral fermion for cancellation.