Two-dimensional Yang-Mills theory: perturbative and instanton contributions, and its relation to QCD in higher dimensions

Bassetto, A.

doi:10.1016/s0920-5632(00)00767-2

Cited by 5 publications

(7 citation statements)

References 32 publications

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“…σ(k 2 ) ≤ 1 as stated in the original article by Gribov [17]. Since M 2 must be positive 2 , we clearly see from (32) that…”

Section: The Second (Main) Reason Why ϕϕ − ωω Is Problematic In 2d: T...mentioning

confidence: 58%

“…However, a drawback of the superrenormalizability is the appearance of severe infrared instabilities and therefore an infrared regulator, usually put in by hand, is necessary. We emphasize that caution is anyhow at place when performing calculations in 2D gauge theories as discussed in [2]. Let us also mention that certain studies questioned some of the results of [1] by recalculating the fermion propagator using other infrared regularization methods, and the corresponding results were qualitatively different [3,4,5].…”

Section: Introductionmentioning

confidence: 99%

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The effects of Gribov copies in 2D gauge theories

et al. 2009

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In previous works, we have shown that the Gribov-Zwanziger action, which implements the restriction of the domain of integration in the path integral to the Gribov region, generates extra dynamical effects which influence the infrared behaviour of the gluon and ghost propagator in SU(N) Yang-Mills gauge theories. The latter are in good agreement with the most recent lattice data obtained at large volumes, both in 4D and in 3D. More precisely, the gluon propagator is suppressed and does not vanish at zero momentum, while the ghost propagator keeps a 1/p^2 behaviour for p^2\approx0. Instead, in 2D, the lattice data revealed a vanishing zero momentum gluon propagator and an infrared enhanced ghost, in support of the usual Gribov-Zwanziger scenario. We will now show that the 2D version of the Gribov-Zwanziger action still gives results in qualitative agreement with these lattice data, as the peculiar infrared nature of 2D gauge theories precludes the analogue of the dynamical effect otherwise present in 4D and 3D. Simultaneously, we also observe that the Gribov-Zwanziger restriction serves as an infrared regulating mechanism.Comment: 10 pages, 1 .eps figur

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“…σ(k 2 ) ≤ 1 as stated in the original article by Gribov [17]. Since M 2 must be positive 2 , we clearly see from (32) that…”

Section: The Second (Main) Reason Why ϕϕ − ωω Is Problematic In 2d: T...mentioning

confidence: 58%

Section: Introductionmentioning

confidence: 99%

The effects of Gribov copies in 2D gauge theories

et al. 2009

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“…On the other hand, if in Eq. (64) we perform the decompactification limit A Ä , we exactly recover the perturbative result in which we have used the WML propagator [33,6,34]. Memory of the k th topological sector has been completely lost.…”

Section: The Instanton Representationmentioning

confidence: 91%

“…From the mathematical viewpoint, the zero-instanton sector is reproduced if integration over the group manifold is replaced by integration over the tangent group algebra [34].…”

Section: The Instanton Representationmentioning

confidence: 99%

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Wilson Loops in the Adjoint Representation and Multiple Vacua in Two-Dimensional Yang–Mills Theory

Bassetto

Vian

2000

Annals of Physics

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QCD 2 with fermions in the adjoint representation is invariant under SU(N )ÂZ N and thereby is endowed with a nontrivial vacuum structure (k-sectors). The static potential between adjoint charges, in the limit of infinite mass, can be therefore obtained by computing Wilson loops in the pure Yang Mills theory with the same nontrivial structure. When the (Euclidean) space-time is compacted on a sphere S 2 , Wilson loops can be exactly expressed in terms of an infinite series of topological excitations (instantons). The presence of k-sectors modifies the energy spectrum of the theory and its instanton content. For the exact solution, in the limit in which the sphere is decompacted, a k-sector can be mimicked by the presence of k-fundamental charges at , according to Witten's suggestion. However, this property does not hold before decompaction or for the genuine perturbative solution which corresponds to the zero-instanton contribution on S 2 . Academic Press

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Quantum ’t Hooft Loops of SYM $${{\mathcal N}=4}$$ as Instantons of YM2 in Dual Groups SU(N) and SU(N)/ZN

Bassetto

Thambyahpillai

2011

Lett Math Phys

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A relation between circular 1/2 BPS 't Hooft operators in 4d N = 4 SYM and instantonic solutions in 2d Yang-Mills theory (YM 2 ) has recently been conjectured. Localization indeed predicts that those 't Hooft operators in a theory with gauge group G are captured by instanton contributions to the partition function of YM 2 , belonging to representations of the dual group L G. This conjecture has been tested in the case G = U (N ) = L G and for fundamental representations. In this paper we examine this conjecture for the case of the groups G = SU (N ) and L G = SU (N )/Z N and loops in different representations. Peculiarities when groups are not self-dual and representations not "minimal" are pointed out.Mathematics Subject Classifications (2010). 22E46, 81T13, 81T40.

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Two-dimensional Yang-Mills theory: perturbative and instanton contributions, and its relation to QCD in higher dimensions

Cited by 5 publications

References 32 publications

The effects of Gribov copies in 2D gauge theories

The effects of Gribov copies in 2D gauge theories

Wilson Loops in the Adjoint Representation and Multiple Vacua in Two-Dimensional Yang–Mills Theory

Quantum ’t Hooft Loops of SYM $${{\mathcal N}=4}$$ as Instantons of YM2 in Dual Groups SU(N) and SU(N)/ZN

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