Related papers: From 4d Yang-Mills to 2d $\mathbb{CP}^{N-1}$ model…
By making use of the background field method, we derive a novel reformulation of the Yang-Mills theory which was proposed recently by the author to derive quark confinement in QCD. This reformulation identifies the Yang-Mills theory with a…
It is shown that in a formulation of Yang-Mills theory in two dimensions in terms of $A=if^{-1}\pa f$, $\bar A=i\bar f\bpa\bar f^{-1}$ with $f(z,\bar z)$, $\bar f(z,\bar z)\in[SU(N_C)]^c$ the complexification of $SU(N_C)$ , reveals certain…
We investigate to derive off-shell invariant twisted super Yang-Mills for N=2 in 2-dimensions and N=4 in 4-dimensions with a central charge by super connection ansatz formalism. We find off-shell invariant N=2 algebra with and without an…
The gauge-independent phenomenon of color confinement in Yang-Mills theory manifests itself differently in different gauges. Therefore, the gauge dependence of quantities related to the infrared structure of the theory becomes important for…
We investigate the symmetry structure of five-dimensional Yang-Mills theories with $\mathfrak{su}(N)$ gauge algebra. These theories feature intertwined 0-, 1-, and 2-form symmetries, depending on the global variant one is considering. In…
We consider SU($N$) Yang-Mills theory on ${\mathbb R}^{2,1}\times S^1$, where $S^1$ is a spatial circle. In the infrared limit of a small-circle radius the Yang-Mills action reduces to the action of a sigma model on ${\mathbb R}^{2,1}$…
We investigate the two-dimensional $\mathcal{N}=(2,2)$ supersymmetric Yang-Mills (SYM) theory on the discretized curved space (polyhedra). We first revisit that the number of supersymmetries of the continuum $\mathcal{N}=(2,2)$ SYM theory…
A model for the infrared sector of SU(2) Yang-Mills theory, based on magnetic vortices represented by (closed) random surfaces, is presented. The model quantitatively describes both confinement and the topological aspects of Yang-Mills…
We compute and analyse the low-lying spectrum of 2+1 dimensional $SU(N)$ Yang-Mills theory on a spatial torus of size $l\times l$ with twisted boundary conditions. This paper extends our previous work \cite{Perez:2013dra}. In that paper we…
We study $\mathcal{N}=1$ supersymmetric Yang-Mills theory (SYM) on the lattice. The non-perturbative nature of supersymmetric field theories is still largely unknown. Similarly to QCD, SYM is confining and contains strongly bound states.…
The scattering-matrix for planar Yang-Mills with N=4 supersymmetry relies on the assumption that integrability holds to all orders in perturbation theory. In this note we define a map from the spectral variables x^{\pm}, parameterizing the…
A formulation of $\mathcal{N} = 2$ supersymmetric Yang-Mills theory with a spacetime-dependent gauge coupling allows to study the breaking of conformal symmetry at the quantum level. The theory has an energy-momentum tensor that is only…
We study the pattern of chiral symmetry breaking ($\chi$SB) in the $\psi\chi\eta$ model (with the chiral fermion sector containing $ \psi^{\{ij\}}$, $\chi_{[ij]}$, and $\eta_{i}^{A}$, see [1]) on $\mathbb{R}^3 \times S^{1}_{L}$ and derive…
Commutative four dimensional supersymmetric Yang-Mills (SYM) is known to be renormalizable for ${\mathcal N} = 1, 2$, and finite for ${\mathcal N} = 4$. However, in the noncommutative version of the model the UV/IR mechanism gives rise to…
A center vortex model for the infrared sector of SU(4) Yang-Mills theory is constructed such as to reproduce both the ratio between the zero-temperature quark and diquark string tensions known from lattice Yang-Mills theory, as well as the…
The N=4 superconformal Yang-Mills theory on flat four-dimensional Minkowski space is a de-confined gauge theory in the sense that the string tension for fundamental representation coloured quarks vanishes. In fact, static fundamental…
Upon compactification on a circle, SU(N) gauge theory with all fields in the adjoint representation acquires a $Z_N$ global symmetry because the center of the gauge group is $Z_N$. For N=4 super Yang-Mills theory, we show how this $Z_N$…
We consider the (1+1)-dimensional ${\cal N}=(2,2)$ super Yang--Mills theory which is obtained by dimensionally reducing ${\cal N}=1$ super Yang--Mills theory in four dimension to two dimensions. We do our calculations in the large-$N_c$…
$SU(N)$ Yang-Mills theory in three dimensions, with a Chern-Simons term of level $k$ (an integer) added, has two dimensionful coupling constants, $g^2 k$ and $g^2 N$; its possible phases depend on the size of $k$ relative to $N$. For $k \gg…
Compactifying type $A_{N-1}$ 6d ${\cal N}{=}(2,0)$ supersymmetric CFT on a product manifold $M^4\times\Sigma^2=M^3\times\tilde{S}^1\times S^1\times{\cal I}$ either over $S^1$ or over $\tilde{S}^1$ leads to maximally supersymmetric 5d gauge…