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We study relativistic fermions in three euclidean dimensions with four- and six-fermion interactions of the Gross-Neveu type. In the limit of many fermion flavors, and besides the isolated free fixed point, the theory displays a line of…
We study the generation of fermion mass in a context where interactions break a discrete chiral symmetry. Then, fermion mass is not protected by a symmetry, no symmetry is broken by the generation of mass, and a vanishing mass no longer…
Taking inspiration from lattice QCD results, we argue that a non-perturbative mass term for fermions can be generated as a consequence of the dynamical phenomenon of spontaneous chiral symmetry breaking, in turn triggered by the explicitly…
Taking inspiration from lattice QCD data, we argue that a finite non-perturbative contribution to the quark mass is generated as a consequence of the dynamical phenomenon of spontaneous chiral symmetry breaking, in turn triggered by the…
We consider a U(1) gauge theory, minimally coupled to a massless Dirac field, where a higher-derivative term is added to the pure gauge sector, as in the Lee-Wick models. We find that this term can trigger chiral symmetry breaking at low…
In this talk we present a numerical lattice study of an SU(3) gauge model where an SU(2) doublet of non-Abelian strongly interacting fermions is coupled to a complex scalar field doublet via a Yukawa and a Wilson-like term. The model enjoys…
We discuss models with a massless fermion and a self-interacting massive scalar field with the Yukawa interaction. The chiral condensate and the fermion mass are calculated analytically. It is shown that the models have a phase transition…
Massless 2+1D Dirac fermions arise in a variety of systems from graphene to the surfaces of topological insulators, where generating a mass is typically associated with breaking a symmetry. However, with strong interactions, a symmetric…
The canonical Gross-Neveu model for $N$ two-component Dirac fermions in $2+1$ dimensions suffers a continuous phase transition at a critical interaction $g_{c1} \sim 1/N$ at large $N$, at which its continuous symmetry $\text{SO}(2N)$ is…
We consider a field theoretical model where a SU(2) fermion doublet, subjected to non-Abelian gauge interactions, is also coupled to a complex scalar field doublet via a Yukawa and an irrelevant Wilson-like term. Despite the presence of…
A new formulation of perturbation theory for a description of the Dirac and scalar fields (the Yukawa model) is suggested. As the main approximation the self-consistent field model is chosen, which allows in a certain degree to account for…
The effective potential for a scalar theory with $\lambda\phi^4$ interaction, coupled to a massless fermion through Yukawa interaction is calculated by summing over infinite number of two particle irreducible (2PI) diagrams of two different…
Dynamical spontaneous breaking of some discrete symmetries including special parities and time reversal and their restoration at finite temperature T are researched in 3D Gross-Neveu model by means of Schwinger-Dyson equation in the…
We propose and investigate a Yukawa model featuring a dynamical scalar field coupled to relativistic Luttinger fermions. Using the functional renormalization group (RG) as well as large-$N_{\text{f}}$ or perturbative expansions, we observe…
We propose a model of dynamical symmetry breaking, in which a new type of fundamental scalar fields of zero mass-dimension mediate the couplings of fermions to the gravitational field, represented here as a tetrad field in the same manner…
We describe dynamical symmetry breaking in a system of massless Dirac fermions with both electromagnetic and four-fermion interactions in (2+1) dimensions. The former is described by the Pseudo Quantum Electrodynamics (PQED) and the latter…
It was recently established that the paradigmatic Gross--Neveu model with $N$ copies of two-dimensional Dirac fermions features an $\mathrm{SO}(2N)$ symmetry if certain interactions are suppressed. This becomes evident when the theory is…
Dynamical symmetry breaking in three-dimensional QED with N fermion flavours is considered at finite temperature, in the large $N$ approximation. Using an approximate treatment of the Schwinger-Dyson equation for the fermion self-energy, we…
Emergent symmetry in Dirac system means that the system acquires an enlargement of two basic symmetries at some special critical point. The continuous quantum criticality between the two symmetry broken phases can be described within the…
We study numerically on the lattice the 2D Yukawa model with the U(1) chiral symmetry and $N_F$ = 16 at infinite scalar field self-coupling. The scaling behaviour of the fermion mass, as the Yukawa coupling approaches zero, is analysed…