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We study the infrared renormalon in the gluon condensate in the $SU(N)$ gauge theory with $n_W$-flavor adjoint Weyl fermions (QCD(adj.)) on~$mathbb{R}^3times S^1$ with the $mathbb{Z}_N$ twisted boundary conditions. We rely on the so-called large-$beta_0$ approximation as a conventional tool to analyze the renormalon, in which only Feynman diagrams that dominate in the large-$n_W$ limit are considered while the coefficient of the vacuum polarization is set by hand to the one-loop beta function~$beta_0=11/3-2n_W/3$. In the large~$N$ limit within the large-$beta_0$ approximation, the W-boson, which acquires the twisted Kaluza--Klein momentum, produces the renormalon ambiguity corresponding to the Borel singularity at~$u=2$. This provides an example that the system in the compactified space~$mathbb{R}^3times S^1$ possesses the renormalon ambiguity identical to that in the uncompactified space~$mathbb{R}^4$. We also discuss the subtle issue that the location of the Borel singularity can change depending on the order of two necessary operations.
We present additional observations to previous studies on the infrared (IR) renormalon in $SU(N)$ QCD(adj.), the $SU(N)$ gauge theory with $n_W$-flavor adjoint Weyl fermions on~$mathbb{R}^3times S^1$ with the $mathbb{Z}_N$ twisted boundary condition.
In the leading order of the large-$N$ approximation, we study the renormalon ambiguity in the gluon (or, more appropriately, photon) condensate in the 2D supersymmetric $mathbb{C}P^{N-1}$ model on~$mathbb{R}times S^1$ with the $mathbb{Z}_N$ twisted b
By employing the $1/N$ expansion, we compute the vacuum energy~$E(deltaepsilon)$ of the two-dimensional supersymmetric (SUSY) $mathbb{C}P^{N-1}$ model on~$mathbb{R}times S^1$ with $mathbb{Z}_N$ twisted boundary conditions to the second order in a SUS
We study the domain walls in hot $4$-D $SU(N)$ super Yang-Mills theory and QCD(adj), with $n_f$ Weyl flavors. We find that the $k$-wall worldvolume theory is $2$-D QCD with gauge group $SU(N-k)times SU(k) times U(1)$ and Dirac fermions charged under
We explicitly calculate the topological terms that arise in IR effective field theories for $SU(N)$ gauge theories on $mathbb{R}^3 times S^1$ by integrating out all but the lightest modes. We then show how these terms match all global-symmetry t Hoof