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Abelian and non-Abelian gauge theories are of central importance in many areas of physics. In condensed matter physics, Abelian U(1) lattice gauge theories arise in the description of certain quantum spin liquids. In quantum information…
The non-abelian generalization of the Holdom model --{\it i.e.} a theory with two gauge fields coupled to the kinetic mixing term $g {tr}(F_{\mu \nu} (A) F_{\mu \nu} (B))$-- is considered. Contrarily to the abelian case, the group structure…
A dual action is obtained for a general non-abelian and non-supersymmetric gauge theory at the classical level. The construction follows steps similar to those used in pure abelian gauge theory. As an example we study the spontaneously…
We study the effects of twisted boundary conditions on the quark fields in the epsilon regime of chiral perturbation theory. We consider the $SU(2)_L\times SU(2)_R$ chiral theory with non-degenerate quarks and the $SU(3)_L\times SU(3)_R$…
Noncommutative (NC) space-time leads to some strong constraints on the possible choices of gauge groups and allowed representations of matter and gauge fields. The standard model based on $U(3)\times U(2)\times U(1)$ can be transcribed to…
I point out that Gross-Neveu theory with SO(3) isospin in three spacetime dimensions -- proposed recently, for instance, as an effective description of the N\'eel transition in certain spin-orbital liquids -- also hosts quantum criticality…
By coupling {\cal N}=8 superconformal matter to {\cal N}=8 superconformal Chern-Simons gravity in three dimensions we obtain theories with novel terms in the scalar potential leading to AdS_3 solutions and superconformal symmetry breaking.…
In this article, we review gauge-Higgs unification models based on gauge theories defined on six-dimensional spacetime with $S^2/Z_2$ topology in the extra spatial dimensions. On the extra $S^2/Z_2$ space, non-trivial boundary conditions…
A tensor representation of the gluon propagator is found within covariant gauges for a non-Abelian theory after symmetry breaking due to $<A_0>\ne 0$ and the exact equations which determine the dispersion laws of plasma excitations are…
The idea of a spin-charge separation of the SU(2) gauge potential is extended to the SU(3) case. It is shown that in this case there exist different non-perturbative ground states characterized by different gauge condensate $A^B_\mu A^B_\mu…
We study the SU(3)-invariant relevant deformation of D=4 N=4 SU(N) gauge theory at large N using the AdS/CFT correspondence. At low energies, we obtain a nonsupersymmetric gauge theory with three left-handed quarks in the adjoint of SU(N).…
In a recent publication, we proposed two possible wave functions for the elementary excitations of the SU(3) Haldane--Shastry model (HSM), but argued on very general grounds that only one or the other can be a valid excitation. Here we…
The thesis is devoted to the problem of colour confinement in the non-Abelian Yang-Mills theory (gluon part of Quantum Chromodynamics). A generalisation of the 3-dimensional Fock-Schwinger gauge is proposed where the Gauss law constraint is…
The emergence of gauge particles (e.g., photons and gravitons) as Goldstone bosons arising from spontaneous symmetry breaking is an interesting hypothesis which would provide a dynamical setting for the gauge principle. We investigate this…
We introduce lattice gauge theories which describe three-dimensional, gapped quantum phases exhibiting the phenomenology of both conventional three-dimensional topological orders and fracton orders, starting from a finite group $G$, a…
Gauge theory is the foundation of the particle physics Standard Model (SM). Considering the multiple gauge sectors for one gauge transformation, we study the generalized Abelian and non-Abelian (Yang-Mills theory) gauge theories. We first…
A clear separation of the time scales governing the dynamics of "slow" and "fast" degrees of freedom often serves as a prerequisite for the emergence of an independent low-energy theory. Here, we consider (slow) classical spins exchange…
In the present paper we study the limit of zero mass in nonabelian gauge theories both with Higgs mechanism and in the nonlinear realization of the gauge group (Stueckelberg mass). We argue that in the first case the longitudinal modes…
We show that baryon number symmetry is spontaneously broken in a class of three-dimensional, ${\cal N}=1$ supersymmetric theories with a discrete mass spectrum. These models serve as lower-dimensional, less-supersymmetric analogs of the…
We argue that extra dimensions with a properly chosen compactification scheme could be a natural source for emergent gauge symmetries. Actually, some proposed vector field potential terms or polynomial vector field constraints introduced in…