Manifest covariance and the Hamiltonian approach to mass gap in (2+1)-dimensional Yang-Mills theory

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

doi:10.1103/physrevd.64.025011

Cited by 24 publications

(29 citation statements)

References 28 publications

(37 reference statements)

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“…An elegant prescription for doing that was proposed in [3]. In this section we provide a brief review of the analytic continuation suggested in [3].…”

Section: Minkowski Continuationmentioning

confidence: 99%

“…A construction that is very reminiscent of fuzzy spheres was carried out in [3] to regulate the integrals over the Lorentz group. One constructs states with a fixed value of Q which we denote by M − 1.…”

Section: Minkowski Continuationmentioning

confidence: 99%

“…In particular we focus on how the equations of motion of the theory can be brought to a form that involve only local variables, even though the AN mass-term is highly non-local. We also review the Minkowski space continuation of this mass term as suggested in [3]. In the next section we focus on the dimensional reduction of the mass-deformed Hamiltonian by Toroidal compactification of the spacial dimensions.…”

Section: Introductionmentioning

confidence: 99%

“…In the gauge invariant Hamiltonian formulation of the theory, the gap is ultimately related to the volume measure on the configuration space of the gauge theory, which can be computed and expressed as a hermitian Wess-Zumino-Witten model [4,7]. Though it is not completely clear how to pass from the non-local Hamiltonian formalism due to KKN to a covariant path-integral framework, a prescription for doing so, based upon the covariantization of the KKN formalism was proposed in [3]. Requiring manifest Lorentz covariance of the formalism led to two different possibilities for potential gauge invariant mass-terms that one may consider in the path integral framework, and one of these was the term proposed in [2] from finite temperature QCD considerations.…”

Section: Introductionmentioning

confidence: 99%

“…There now exists a very robust and powerful Hamiltonian formalism for Yang-Mills theory in D = 2 + 1 due to Kim, Karabali and Nair (KKN) [7,4,5,3], that can account for several non-perturbative features of the gauge theory including the existence of a mass-gap in its spectrum. Indeed, the term proposed by Alexanian and Nair is closely tied to the mechanism leading to the non-perturbative mass gap in the spectrum of the gauge theory in the KKN Hamiltonian formalism.…”

Section: Introductionmentioning

confidence: 99%

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Mass Deformations of Super Yang–mills Theories in D = 2 + 1, and Super-Membranes: A Note

Agarwal

2009

Mod. Phys. Lett. A

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Mass deformations of supersymmetric Yang-Mills theories in three spacetime dimensions are considered. The gluons of the theories are made massive by the inclusion of a non-local gauge and Poincare invariant mass term due to Alexanian and Nair, while the matter fields are given standard Gaussian mass-terms. It is shown that the dimensional reduction of such mass deformed gauge theories defined on R 3 or R × T 2 produces matrix quantum mechanics with massive spectra. In particular, all known massive matrix quantum mechanical models obtained by the deformations of dimensional reductions of minimal super Yang-Mills theories in diverse dimensions are shown also to arise from the dimensional reductions of appropriate massive Yang-Mills theories in three spacetime dimensions. Explicit formulae for the gauge theory actions are provided.

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“…An elegant prescription for doing that was proposed in [3]. In this section we provide a brief review of the analytic continuation suggested in [3].…”

Section: Minkowski Continuationmentioning

confidence: 99%

Section: Minkowski Continuationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Mass Deformations of Super Yang–mills Theories in D = 2 + 1, and Super-Membranes: A Note

Agarwal

2009

Mod. Phys. Lett. A

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Non-local symmetries for Yang-Mills theories and their massive counterparts in two and three dimensions

Agarwal

Fayyazuddin

2012

J. High Energ. Phys.

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We identify a non-local symmetry for Yang-Mills theories in 1 + 1 and 2 + 1 spacetime dimensions. The symmetry mixes a vector current with the gauge field. The current involved in the symmetry is required to satisfy certain constraints. The explicit solution for the current obeying these constraints, is obtained in two spacetime dimensions and in the abelian case in three dimensions. We conjecture that the current is generated from a non-local gauge and Lorentz invariant mass term in three dimensions and provide some evidence for it. We also posit a conserved current associated with the symmetry generators and derive some of its properties. In the Abelian case, we compute the symmetry algebra and show that additional symmetry generators have to be included for the algebra to close. The algebra contains an SO(2,1) subalgebra. We also comment on the implications of this symmetry for N = 1 supersymmetry.hep-th/yymmnnn *

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Confining strings in three-dimensional gauge theories beyond the Nambu-Gotō approximation

Caselle,

Magnoli,

Nada

et al. 2024

J. High Energ. Phys.

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We carry out a systematic study of the effective bosonic string describing confining flux tubes in SU(N) Yang-Mills theories in three spacetime dimensions. While their low-energy properties are known to be universal and are described well by the Nambu-Gotō action, a non-trivial dependence on the gauge group is encoded in a series of undetermined subleading corrections in an expansion around the limit of an arbitrarily long string. We quantify the first two of these corrections by means of high-precision Monte Carlo simulations of Polyakov-loop correlators in the lattice regularization. We compare the results of novel lattice simulations for theories with N = 3 and 6 color charges, and report an improved estimate for the N = 2 case, discussing the approach to the large-N limit. Our results are compatible with analytical bounds derived from the S-matrix bootstrap approach. In addition, we also present a new test of the Svetitsky-Yaffe conjecture for the SU(3) theory in three dimensions, finding that the lattice results for the Polyakov-loop correlation function are in excellent agreement with the predictions of the Svetitsky-Yaffe mapping, which are worked out quantitatively applying conformal perturbation theory to the three-state Potts model in two dimensions. The implications of these results are discussed.

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Manifest covariance and the Hamiltonian approach to mass gap in (2+1)-dimensional Yang-Mills theory

Cited by 24 publications

References 28 publications

Mass Deformations of Super Yang–mills Theories in D = 2 + 1, and Super-Membranes: A Note

Mass Deformations of Super Yang–mills Theories in D = 2 + 1, and Super-Membranes: A Note

Non-local symmetries for Yang-Mills theories and their massive counterparts in two and three dimensions

Confining strings in three-dimensional gauge theories beyond the Nambu-Gotō approximation

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