Abstract
We consider SU(N) Yang–Mills theory on R2,1×S1, where S1 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 R2,1 whose target space is a 2(N−1)-dimensional torus modulo the Weyl-group action. We argue that there is freedom in the choice of the framing of the gauge bundles, which leads to more general options. In particular, we show that this low-energy limit can give rise to a target space SU(N)×SU(N)/ZN. The latter is the direct product of SU(N) and its Langlands dual SU(N)/ZN, and it contains the above-mentioned torus as its maximal Abelian subgroup. An analogous result is obtained for any non-Abelian gauge group.
Highlights
Introduction and summaryPure Yang–Mills or QCD-like theories in four spacetime dimensions are strongly coupled in the infrared limit
It is known that one can partially overcome this difficulty by compactifying Yang–Mills theory on a circle with small radius
In our paper we focus on the derivation of kinetic terms in the low-energy limit of pure Yang–Mills theory
Summary
Pure Yang–Mills or QCD-like theories in four spacetime dimensions are strongly coupled in the infrared limit. In the adiabatic limit, when the metric on is scaled down, the d = 4 SU(N) Yang–Mills action can be reduced (already on the classical level) to the action of a d = 3 sigma model whose target space is T ×T ∨/W. Can be reduced to a sigma model on R2,1 with non-Abelian target space M or a subgroup thereof including the torus T ×T ∨ ∼= U(1)2(N−1). For a general gauge group G with weight lattice w , the sigma-model target space will be M = G×G∨, where G∨ denotes the Langlands dual group, whose weight lattice. The Abelian dual superconductor approach has various limitations, like any other confinement mechanism The suggestion of this paper aims in the same direction
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