The renormalization of sine-Gordon type models, which have relevance both in high-energy and low-temperature physics represents a challenge in quantum field theory. We use the Wegner-Houghton renormalization group method, in the local potential approximation to determine the phase strusture and the infrared scaling laws of the two diemnsional sine-Gordon (SG) and the massive sine-Gordon (MSG) models. The phase structure of the SG model is reconstructed by studying the sensitivity of the dynamics on microscopic parameters. The global features of the RG flow of the MSG model are also discussed and it is shown that the model possesses two phases, (i) one containing no condensate, where the IR physics can be parametrized with the fundamental mode of the potential and (ii) the other with a condensate for weak enough mass in the remnant of the molecular phase of the SG model. Based on our RG analysis one can recover the well-known phase structure of the bosonized version of QED$_2$ in the LPA. We made calculations beyond the LPA by using the internal space RG method and found that the phase structure qualitatively remains unchanged when one considers the wave function renormalization.
We propose a quantum field theoretical approach to the vortex dynamics of magnetically coupled layered superconductors by constructing a two-dimensional multi-layer sine-Gordon type model which we map onto a gas of topological excitations. The known interaction potentials of magnetically coupled vortices are consistently obtained from our field-theoretical analysis. Originally, this layered sine-Gordon model has been introduced as the bosonized version of the multi-flavor Schwinger model, and, consequently, it has been used to study quark confinement. The number of flavors of the bosonized multi-flavor Schwinger model is equal to the number of layers of the superconducting layered system. We analyze the phase structure of the multi-flavor, i.e. multi-layer sine-Gordon model by functional renormalization group (RG) methods.
In the limit of small fermion mass, i.e. for small fugacity, the linearized RG flow is sufficient to determine the low-energy behavior of the N-flavor model, which undergoes a KTB-type phase transition. The dependence of the transition temperature on the number of layers is found to be in agreement with known results based on other methods. For large fermion mass, the exact RG flow has been solved numerically. The low-energy behavior of the multi-flavor model is rather different depending on whether N=1 or N>1, where N is the number of flavors. For N>1 the reflection symmetry always suffers breakdown in both the weak and strong coupling regimes, in contrary to the N=1 case, where it remains unbroken in the strong coupling phase.
Georgi-Glashow model based on SU(5) has some shortcomings which we can overcome by minimally extending the content of the SU(5), either in Higgs or matter sector. One such extension with an adjoint fermionic representation turns out to be very predictive. If some states coming from this representation are light, they can correct for the unification of gauge couplings. This indeed happens, but it turns out that some states have to be light in order to achieve unification at a scale which prevents proton from decaying. I will show how one calculates the beta coefficients and running of gauge coupling constants and briefly comment on phenomenology of such a model.