Two-dimensional sigma models: Modelling non-perturbative effects in quantum chromodynamics

Novikov, V.A.; Shifman, M.; Vainshtein, A.I.; Захаров, В. И.

doi:10.1016/0370-1573(84)90021-8

Cited by 230 publications

(284 citation statements)

References 51 publications

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“…As well-known (e.g. [9,10]), the only supergeneralization of the bosonic CP (N − 1) is the N = (2, 2) supersymmetric CP (N − 1) model with four supercharges.…”

Section: Introductionmentioning

confidence: 98%

Erratum: Heterotic flux tubes inN=2supersymmetric QCD withN=1preserving deformations [Phys. Rev. D77, 125016 (2008)]

Shifman¹,

Yung²

2009

Phys. Rev. D

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We consider non-Abelian BPS-saturated flux tubes (strings) in N = 2 supersymmetric QCD deformed by superpotential terms of a special type breaking N = 2 supersymmetry down to N = 1 . Previously it was believed that worldsheet supersymmetry is "accidentally" enhanced due to the facts that N = (1, 1) SUSY is automatically elevated up to N = (2, 2) on CP (N − 1) and, at the same time, there are no N = (0, 2) generalizations of the bosonic CP (N − 1) model. Edalati and Tong noted that the target space is in fact CP (N − 1) × C rather than CP (N − 1). This allowed them to suggest a "heterotic" N = (0, 2) sigma model, with the CP (N − 1) target space for bosonic fields and an extra right-handed fermion which couples to the fermion fields of the N = (2, 2) CP (N −1) model. We derive the heterotic N = (0, 2) worldsheet model directly from the bulk theory. The relation between the bulk and worldsheet deformation parameters we obtain does not coincide with that suggested by Edalati and Tong at large values of the deformation parameter. For polynomial deformation superpotentials in the bulk we find nonpolynomial response in the worldsheet model. We find a geometric representation for the heterotic model. Supersymmetry is proven to be spontaneously broken for small deformations (at the quantum level). This confirms Tong's conjecture. A proof valid for large deformations will be presented in the subsequent publication.

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“…As well-known (e.g. [9,10]), the only supergeneralization of the bosonic CP (N − 1) is the N = (2, 2) supersymmetric CP (N − 1) model with four supercharges.…”

Section: Introductionmentioning

confidence: 98%

Erratum: Heterotic flux tubes inN=2supersymmetric QCD withN=1preserving deformations [Phys. Rev. D77, 125016 (2008)]

Shifman¹,

Yung²

2009

Phys. Rev. D

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“…The rôle of IR renormalons in the operator product expansion of two-point functions and their relationship with non-perturbative inverse power corrections has been extensively discussed in the literature [9][10][11][12][13][14][15][16]. This and further discussions which originate in the work of ref.…”

mentioning

confidence: 99%

“…i.e., an ambiguity which has the same 1 Q 4 pattern as the gluon condensate contribution that appears in the OPE evaluation of the Adler function [12,13]. Since the Adler function must be an unambiguous physical observable, there must exist another contribution that cancels (2.28).…”

mentioning

confidence: 99%

Low-energy QCD and ultraviolet renormalons

Peris¹,

Rafael²

1997

Nuclear Physics B

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We discuss the contribution of ultraviolet (UV) renormalons in QCD to two-point functions of quark current operators. This explicitly includes effects due to the exchange of one renormalon chain as well as two chains. It is shown that, when the external euclidean momentum of the two-point functions becomes smaller than the scale Λ L associated with the Landau singularity of the QCD one-loop running coupling constant, the positions of the UV renormalons in the Borel plane become true singularities in the integration range of the Borel transform. This introduces ambiguities in the evaluation of the corresponding two-point functions. The ambiguities associated with the leading UV renormalon singularity are of the same type as the contribution due to the inclusion of dimension d = 6 local operators in a low-energy effective Lagrangian valid at scales smaller than Λ L . We then discuss the inclusion of an infinite number of renormalon chains and argue that the previous ambiguity hints at a plausible approximation scheme for low-energy QCD, resulting in an effective Lagrangian similar to the one of the extended Nambu-Jona-Lasinio (ENJL) model of QCD at large N c .

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“…But since in these systems the vortex is infinitely long (stable), one can make use of the facts known about the infrared dynamics of 2D CP N −1 theory. It is in fact known that the quantum fluctuations of the CP N −1 modes become strongly coupled at long distances (a 2D analogue of confinement) [63,64]; it means that the vortex dynamically Abelianizes [35,[65][66][67]. The masses of the kink monopoles are now replaced by O(Λ), where Λ is the dynamical scale of the 2D CP N −1 theory.…”

Section: Jhep09(2014)039mentioning

confidence: 99%

Monopole-vortex complex at large distances and nonAbelian duality

Chatterjee

Konishi

2014

J. High Energ. Phys.

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Abstract:We discuss the large-distance approximation of the monopole-vortex complex soliton in a hierarchically broken gauge system, SU(N + 1) → SU(N ) × U(1) → 1, in a color-flavor locked SU(N ) symmetric vacuum. The ('t Hooft-Polyakov) monopole of the higher-mass-scale breaking appears as a point and acts as a source of the thin vortex generated by the lower-energy gauge symmetry breaking. The exact color-flavor diagonal symmetry of the bulk system is broken by each individual soliton, leading to nonAbelian orientational CP N −1 zeromodes propagating in the vortex worldsheet, well studied in the literature. But since the vortex ends at the monopoles these fluctuating modes endow the monopoles with a local SU(N ) charge. This phenomenon is studied by performing the duality transformation in the presence of the CP N −1 moduli space. The effective action is a CP N −1 model defined on a finite-width worldstrip.

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Two-dimensional sigma models: Modelling non-perturbative effects in quantum chromodynamics

Cited by 230 publications

References 51 publications

Erratum: Heterotic flux tubes inN=2supersymmetric QCD withN=1preserving deformations [Phys. Rev. D77, 125016 (2008)]

Erratum: Heterotic flux tubes inN=2supersymmetric QCD withN=1preserving deformations [Phys. Rev. D77, 125016 (2008)]

Low-energy QCD and ultraviolet renormalons

Monopole-vortex complex at large distances and nonAbelian duality

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