Inverse Symmetry Breaking with 4d Lattice Simulations

I review dynamical chiral symmetry breaking in four-fermi models, including results of Monte Carlo simulations with dynamical fermions. For 2<d<4, where the phase transition defines an ultraviolet fixed point of the renormalisation group, the continuum theory may either be describable using the large-N_f expansion, as in the case of the Gross-Neveu model, or be intrinsically non-perturbative, as in the case of the Thirring model. For d=4, the models are trivial and are descri...

This is a short review on the subject of symmetry nonrestoration at high temperature. Special emphasis is put on experimental discoveries and different theoretical mechanisms. At the end, possible cosmological applications are briefly mentioned.

Lattice gauge theories are considered with a partial axial gauge fixing along one direction only. This leaves a residual gauge symmetry that is still local in three directions but now global in one. It is found that this $N^{d-1}$ fold symmetry (on an $N^d$ lattice) breaks spontaneously at weak coupling with the gauge field elements on links averaged over 1-d chains along the gauge-fixing direction as order parameters. This phase transition is observed with Monte-Carlo simula...

Spontaneous symmetry breaking in quantum field theories at non-zero temperature still holds fundamental open questions, in particular what happens to vacuum Goldstone bosons when the temperature is increased. By investigating a complex scalar field theory on the lattice we demonstrate that Goldstone bosons at non-zero temperature behave like screened massless particle-like excitations, so-called thermoparticles, which continue to exist even in the symmetry-restored phase of t...

At high temperatures a four dimensional field theory is reduced to a three dimensional field theory. In this letter we consider the $\phi^4$ theory whose parameters are chosen so that a thermal phase transition occurs at a high temperature. Using the known properties of the three dimensional theory, we derive a non-trivial correction to the critical temperature.

Spontaneous symmetry breaking is studied in the ultralocal limit of a scalar quantum field theory, that is when $E\approx m$ (or infrared limit). In this limit we show that a $ \varphi^4$ theory in the euclidean space in four-dimensions describes naturally instantons. Furthermore, in the infrared limit we show that there is an exact map between $ \varphi^4$ with self-dual Yang-Mills theories. The spontaneous symmetry breaking in the infrared limit for a Higgs portal is also c...

Using a high-statistics lattice simulation of the Ising limit of $(\lambda \Phi^4)_4$ theory, we have measured the susceptibility and propagator in the broken phase. We confirm our earlier finding of a discrepancy between the field re-scaling implied by the propagator data and that implied by the susceptibility. The discrepancy becomes {\it worse} as one goes closer to the continuum limit; thus, it cannot be explained by residual perturbative effects. The data are consistent ...

The commonly assumed cosmological history of our universe is that at early-times and high-temperatures the universe went through an ElectroWeak Phase Transition (EWPT). Assuming an EWPT, and depending on its strength, there are many implications for baryogenesis, gravitational waves, and the evolution of the universe in general. However, it is not true that all spontaneously broken symmetries at zero-temperature are restored at high-temperature. In particular the idea of "inv...

In the Standard Model the Fermi constant is associated with the vacuum expectation value of the Higgs field, `the condensate', usually believed to be a cutoff-independent quantity. General arguments related to the `triviality' of $\Phi^4$ theory in 4 space-time dimensions suggest, however, a dramatic renormalization effect in the continuum limit that is clearly visible on the relatively large lattices available today. The result can be crucial for the Higgs phenomenology and ...

We study a $U(N)\times U(N)$ symmetric scalar field model in four and three dimensions. First, using our data in four dimensions in the weak coupling region, we demonstrate explicitly that the observed first order phase transition is induced by quantum fluctuations. Next, based on the renormalization group and our new simulation results in three dimensions we argue that even if the $U_A(1)$ symmetry is restored below the critical temperature the QCD finite temperature chiral ...