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On the new way of symmetry breaking in scalar QED and the one-loop renormalization

Lucas Ducastelo de C. C. Lima, Ilya L. Shapiro

TL;DR

This work reformulates scalar QED in terms of two real scalars to realize an explicit, non-Higgs type breaking of Abelian gauge symmetry in curved spacetime. Using the Schwinger-DeWitt method, it demonstrates one-loop renormalizability with counterterms that preserve the action's structure, including mass-splitting and nonminimal-curvature couplings. The authors derive complete RG equations showing standard gauge coupling running and reveal IR tendencies toward symmetry restoration when the symmetry-breaking parameters are perturbed, with preliminary considerations about higher-loop issues. They also argue that extending the Abelian framework to more real scalars is not feasible without entering non-Abelian territory, and discuss potential avenues for non-Abelian generalizations and applications to cosmology.

Abstract

It is well known that single real scalar field does not allow gauge coupling to the Abelian vector field. Using the complex scalar model as a starting point, we construct the Abelian gauge model with two real scalars. The gauge transformations for the scalars look different (albeit equivalent) from the conventional sQED. Spitting the masses of the scalars, or the scalar self-couplings, or the nonminimal parameters of scalar-curvature interaction, we arrive at a qualitatively new way of gauge symmetry breaking. Using the Schwinger-DeWitt technique, we explore the one-loop renormalization of this new model in curved spacetime.

On the new way of symmetry breaking in scalar QED and the one-loop renormalization

TL;DR

This work reformulates scalar QED in terms of two real scalars to realize an explicit, non-Higgs type breaking of Abelian gauge symmetry in curved spacetime. Using the Schwinger-DeWitt method, it demonstrates one-loop renormalizability with counterterms that preserve the action's structure, including mass-splitting and nonminimal-curvature couplings. The authors derive complete RG equations showing standard gauge coupling running and reveal IR tendencies toward symmetry restoration when the symmetry-breaking parameters are perturbed, with preliminary considerations about higher-loop issues. They also argue that extending the Abelian framework to more real scalars is not feasible without entering non-Abelian territory, and discuss potential avenues for non-Abelian generalizations and applications to cosmology.

Abstract

It is well known that single real scalar field does not allow gauge coupling to the Abelian vector field. Using the complex scalar model as a starting point, we construct the Abelian gauge model with two real scalars. The gauge transformations for the scalars look different (albeit equivalent) from the conventional sQED. Spitting the masses of the scalars, or the scalar self-couplings, or the nonminimal parameters of scalar-curvature interaction, we arrive at a qualitatively new way of gauge symmetry breaking. Using the Schwinger-DeWitt technique, we explore the one-loop renormalization of this new model in curved spacetime.
Paper Structure (6 sections, 52 equations, 3 figures)

This paper contains 6 sections, 52 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Classical action and gauge invariance
  3. More real scalars?
  4. One-loop divergences
  5. Renormalization group equations
  6. Conclusions and discussions

Figures (3)

  • Figure 1: Transformation of the vertices under splitting one complex scalar into two real scalars with different masses. Here and in what follows, the bold line indicates complex scalar.
  • Figure 2: Transformation of the snail and bubble one-loop diagrams under splitting a complex scalar into two real scalars with different masses.
  • Figure 3: Transformation of the two-loop diagrams under splitting a complex scalar into two real scalars with different masses. First line $D_{21}$ represents the snail-type diagrams; second line $D_{22}$ represents the first type two-loop bubble diagrams third line $D_{23}$ represents the second type two-loop bubble diagrams.