On the vacuum wavefunction and string tension of Yang-Mills theories in (2+1) dimensions

Karabali, Dimitra; Kim, C.; Nair, V. P.

doi:10.1016/s0370-2693(98)00751-5

Cited by 147 publications

(160 citation statements)

References 9 publications

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“…This, in turn, restricts the allowed values of the (dimensionless) ratio m/2g 2 ; in particular, at the one-loop level our toy model provides the lower bound m 2g 2 0.14, (2.19) in agreement with a plethora of independent studies based on a variety of approaches in the continuum [53][54][55][56] and on the lattice 3 [58][59][60][61].…”

Section: The Maximum Of the Gluon Propagatorssupporting

confidence: 61%

Effects of divergent ghost loops on the Green’s functions of QCD

et al. 2014

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In the present work we discuss certain characteristic features encoded in some of the fundamental QCD Green's functions, whose origin can be traced back to the nonperturbative masslessness of the ghost field, in the Landau gauge. Specifically, the ghost loops that contribute to these Green's functions display infrared divergences, akin to those encountered in the perturbative treatment, in contradistinction to the gluonic loops, whose perturbative divergences are tamed by the dynamical generation of an effective gluon mass. In d = 4, the aforementioned divergences are logarithmic, thus causing a relatively mild impact, whereas in d = 3 they are linear, giving rise to enhanced effects. In the case of the gluon propagator, these effects do not interfere with its finiteness, but make its first derivative diverge at the origin, and introduce a maximum in the region of infrared momenta. The three-gluon vertex is also affected, and the induced divergent behavior is clearly exposed in certain special kinematic configurations, usually considered in lattice simulations; the sign of the corresponding divergence is unambiguously determined. The main underlying concepts are developed in the context of a simple toy model, which demonstrates clearly the interconnected nature of the various effects. The picture that emerges is subsequently corroborated by a detailed nonperturbative analysis, combining lattice results with the dynamical integral equations governing the relevant ingredients, such as the nonperturbative ghost loop and the momentum-dependent gluon mass.

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Section: The Maximum Of the Gluon Propagatorssupporting

confidence: 61%

Effects of divergent ghost loops on the Green’s functions of QCD

et al. 2014

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“…Nevertheless, recall that S wzw (H) in the exponent of the measure is crucial for the convergence of volume integrations. This is true if we start with Ψ 0 = 1 as the eigenstate of the kinetic energy operator and improve on it, as done in [1], or in evaluating expectation values using the chiral boson version as done in [6]. The absence of such a factor for N ≥ 2 also points in the direction of an unstable vacuum.…”

Section: Expectations For Supersymmetric Theoriesmentioning

confidence: 99%

“…For example, systematic computations of the string tension [6], screening effects [7] and the inclusion of the effects of non-trivial spatial geometries [8] have been studied within this framework. The Hamiltonian approach, with some variations, has also been employed to estimate the glueball spectrum in [9].…”

mentioning

confidence: 99%

Supersymmetry and mass gap in2+1dimensions: A gauge invariant Hamiltonian analysis

Agarwal

Nair

2012

Phys. Rev. D

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A Hamiltonian formulation of Yang-Mills-Chern-Simons theories with 0 ≤ N ≤ 4 supersymmetry in terms of gauge-invariant variables is presented, generalizing earlier work on nonsupersymmetric gauge theories. Special attention is paid to the volume measure of integration (over the gauge orbit space of the fields) which occurs in the inner product for the wave functions and arguments relating it to the renormalization of the Chern-Simons level number and to mass-gaps in the spectrum of the Hamiltonians are presented. The expression for the integration measure is consistent with the absence of mass gap for theories with extended supersymmetry (in the absence of additional matter hypermultiplets and/or Chern-Simons couplings), while for the minimally supersymmetric case, there is a mass-gap, the scale of which is set by a renormalized level number, in agreement with indications from existing literature. The realization of the supersymmetry algebra and the Hamiltonian in terms of the gauge invariant variables is also presented.

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“…It has been argued [37] that m 3 /g 2 3 for SU (N ) is very closely approximated by the simple analytic function…”

Section: The Final Conjecture and Its Consequences A Heuristic Mmentioning

confidence: 99%

“…Moreover, by appealing to known d = 3 gauge dynamics, we can estimate the d = 4 coupling strength in terms of the renormalization constant Z. In d = 3 the coupling g 2 3 has dimensions of mass, and there is a unique [for given SU (N )] dynamically-determined ratio M/g 2 3 , which has been estimated by a number of authors [27,28,29,30,31,32,33,34,35,36,37]. Knowing only this ratio we can estimate the d = 4 QCD coupling α s (M 2 ), getting a value around 0.4Z.…”

Section: Introductionmentioning

confidence: 99%

Conjecture on the infrared structure of the vacuum Schrödinger wave functional of QCD

Cornwall

2007

Phys. Rev. D

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The Schrödinger wave functional ψ = exp −S{A a i ( x)} for the d = 3+1 QCD vacuum is a partition function constructed in d = 4; the exponent 2S [in |ψ| 2 = exp(−2S)] plays the role of a d = 3 Euclidean action. We start from a simple conjecture for S based on dynamical generation of a gluon mass M in d = 4, then use earlier techniques of the author to extend (in principle) the conjectured form to full non-Abelian gauge invariance. We argue that the exact leading term, of O(M ), in an expansion of S in inverse powers of M is a d = 3 gauge-invariant mass term (gauged non-linear sigma model); the next leading term, of O(1/M ), is a conventional Yang-Mills action. The d = 3 action that is (twice) the sum of these two terms has center vortices as classical solutions. The d = 3 gluon mass m3, which we constrain to be the same as M , and d = 3 coupling g 2 3 are related through the conjecture to the d = 4 coupling strength, but at the same time the dimensionless ratio m3/g 2 3 can be estimated from d = 3 dynamics. This allows us to estimate the d = 4 coupling αs(M 2 ) in terms of the strictly d = 3 ratio m3/g 2 3 ; we find a value of about 0.4, in good agreement with an earlier theoretical value but somewhat low compared to the QCD phenomenological value of 0.7 ± 0.3. The wave functional for d = 2 + 1 QCD has an exponent that is a d = 2 infrared-effective action having both the gauge-invariant mass term and the field strength squared term, and so differs from the conventional QCD action in two dimensions, which has no mass term. This conventional d = 2 QCD would lead in d = 3 to confinement of all color-group representations. But with the mass term (again leading to center vortices), only N -ality ≡ 0 mod N representations can be confined (for gauge group SU (N )), as expected.

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On the vacuum wavefunction and string tension of Yang-Mills theories in (2+1) dimensions

Cited by 147 publications

References 9 publications

Effects of divergent ghost loops on the Green’s functions of QCD

Effects of divergent ghost loops on the Green’s functions of QCD

Supersymmetry and mass gap in2+1dimensions: A gauge invariant Hamiltonian analysis

Conjecture on the infrared structure of the vacuum Schrödinger wave functional of QCD

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