[Paper Review] Spontaneous Breaking of Space-Time Symmetries

Eliezer Rabinovici|arXiv (Cornell University)|Aug 14, 2007

Cosmology and Gravitation Theories8 references4 citations

TL;DR

This paper investigates kinematical and dynamical mechanisms for spontaneous breaking of space-time symmetries—translations, rotations, scale, and conformal invariance—through effective field theory and condensed matter analogies. It shows that spontaneous breaking of scale and conformal invariance in finite, stable theories leads to a vanishing vacuum energy across all phases, offering a new perspective on the cosmological constant problem.

ABSTRACT

Kinematical and dynamical mechanisms leading to the spontaneous breaking of space-time symmetries are described. The symmetries affected are space and time translations, space rotations, scale and conformal transformations. Applications are made to solidification, string theory compactifications, the analysis of stable theories with no ground states, supersymmetry breaking and the determination of the value of the vacuum energy.

Motivation & Objective

• To explore mechanisms for spontaneous breaking of space-time symmetries beyond standard Higgs-like mechanisms.
• To analyze how boundary conditions and effective potentials can kinematically break translational and rotational invariance.
• To investigate systems without ground states that spontaneously break time-translation invariance, relevant to cosmological dynamics.
• To examine the implications of scale and conformal invariance for vacuum energy, particularly in finite quantum field theories.
• To connect these mechanisms to unresolved problems in particle physics and cosmology, including the cosmological constant and dilaton phenomenology.

Proposed method

• Uses effective potential minimization to identify ground states with non-constant field expectation values, challenging the assumption of constant <φ(x)>.
• Applies Landau theory of phase transitions to model spontaneous breaking of space symmetries during solidification, extending it to compactification mechanisms.
• Analyzes systems with no ground state (e.g., conformal field theories) to demonstrate spontaneous breaking of time-translation invariance.
• Applies Kato’s approach to show that vacuum energy in scale-invariant theories is strictly zero, independent of phase or symmetry realization.
• Compares brane-world models (e.g., Randall-Sundrum) to φ⁶ theory in d=3, showing analogous behavior in vacuum energy and symmetry breaking.
• Considers the role of Goldstone modes (dilatons) in spontaneously broken scale symmetry and their potential detection via deviations from the equivalence principle.

Experimental results

Research questions

• RQ1 Can space-time symmetries be spontaneously broken via kinematical boundary conditions rather than dynamical mechanisms?
• RQ2 How does the absence of a ground state in conformal field theories lead to spontaneous breaking of time-translation invariance?
• RQ3 What constraints does scale invariance impose on vacuum energy, and why is it zero in all phases of a finite, stable theory?
• RQ4 Can the dilaton in spontaneously broken scale symmetry be detected through deviations from the equivalence principle?
• RQ5 To what extent do brane-world models with fine-tuned tensions mimic the behavior of φ⁶ theory in d=3 with spontaneous symmetry breaking?

Key findings

• Spontaneous breaking of space-time symmetries, including translations and rotations, can be induced via boundary conditions or dynamical mechanisms such as solidification.
• In systems without a ground state, time-translation invariance can be spontaneously broken, offering a new mechanism for non-equilibrium dynamics.
• Finite, scale-invariant quantum field theories exhibit zero vacuum energy in all phases, regardless of whether scale symmetry is broken or not.
• The vacuum energy in conformal/scale-invariant theories is strictly zero and does not depend on the presence of a dynamical scale or symmetry breaking.
• The Randall-Sundrum model with fine-tuned brane tensions exhibits behavior analogous to the φ⁶ theory in d=3, where the inter-brane distance acts as a Goldstone mode.
• Dilatons from spontaneously broken scale symmetry may lead to observable deviations from the equivalence principle at the 10⁻¹² level, potentially testable with current precision experiments.