The supercooling window at weak and strong coupling

Abstract

Supercooled first order phase transitions are typical of theories where conformal symmetry is predominantly spontaneously broken. In these theories the fate of the flat scalar direction is highly sensitive to the size and the scaling dimension of the explicit breaking deformations. For a given deformation, the coupling must lie in a particular region to realize a supercooled first order phase transition. We identify the supercooling window in weakly coupled theories and derive a fully analytical understanding of its boundaries. Mapping these boundaries allows us to identify the deformations enlarging the supercooling window and to characterize their dynamics analytically. For completeness we also discuss strongly coupled conformal field theories with an holographic dual, where the complete characterization of the supercooling window is challenged by calculability issues.

Implication of nano-Hertz stochastic gravitational wave on dynamical dark matter through a dark first-order phase transition

“…The (classical) scale-invariance or conformal symmetry is realized by preventing any massive parameters in the Lagrangian. See [44,45] for details. Generally, the classically flat direction of the scalar field is lifted by radiative corrections, the conformal symmetry is therefore radiatively broken.…”

“…One important feature in this scenario is that the potential barrier exists even at zero temperature, so the phase transition strength or the vacuum expectation value over the temperature is usually large. In this work, we consider a dark phase transition model [45] where one introduces a complex scalar field Φ = (ϕ + iG)/ √ 2. ϕ is the order parameter of phase transition and G is the Goldstone boson. The conformal potential generally induces a flat direction, along which the leading-order effective potential consists of the Coleman-Weinberg zero-temperature and the thermal oneloop potential (The tree-level potential at zero temperature vanishes.).…”

“…The one-loop thermal corrections is g i and g j represent the dof for boson and fermion species respectively. In our case, we consider only gauge boson A with g A = 3 [9,45]. The complex scalar ϕ is charged under a U(1) gauge symmetry with coupling strength y A .…”

“…In this work, we focus on the parameter space y A ≳ 0.6 which can be seen in figure 1. The Daisy contributions become important for y A ≲ 0.53 [45], and hence be negligible for most of the parameter space considered in this work.…”

“…With the effective potential in hand, we can determine the nucleation rate by solving the bounce equation. The bounce action can be parameterized analytically as follows [45]: where…”