Strings and Aharonov–Bohm effect in Abelian Higgs model

Chernodub, M. N.; Polikarpov, M.I.; Veselov, A.I.; Zubkov, M. A.

doi:10.1016/s0370-2693(98)00622-4

Cited by 12 publications

(20 citation statements)

References 12 publications

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“…As first noticed in [18], the long-range orientational order in this model is due to an antiferromagnetic interaction between normals to the surface, a mechanism confirmed by numerical simulations [19]. Moreover, it was shown in [17] that this infared fixed point does not depend on the truncation and is present for all ghost-and tachyonfree truncations, and that the effective theory describing the infrared behaviour is a conformal field theory with central charge c = 1.…”

Section: Pacs: 1125pmsupporting

confidence: 76%

“…In [16,17] it was shown that, in the large-D approximation, this model has an infrared fixed point at zero stiffness, corresponding to a tensionless smooth string whose world-sheet has Hausdorff dimension 2, exactly the desired properties to describe QCD flux tubes. As first noticed in [18], the long-range orientational order in this model is due to an antiferromagnetic interaction between normals to the surface, a mechanism confirmed by numerical simulations [19]. Moreover, it was shown in [17] that this infared fixed point does not depend on the truncation and is present for all ghost-and tachyonfree truncations, and that the effective theory describing the infrared behaviour is a conformal field theory with central charge c = 1.…”

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confidence: 76%

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QCD-Like Behavior of High-Temperature Confining Strings

Diamantini

Trugenberger

2002

Phys. Rev. Lett.

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We show that, contrary to previous string models, the high-temperature behaviour of the recently proposed confining strings reproduces exactly the correct large-N QCD result, a necessary condition for any string model of confinement. PACS: 11.25PmAlthough fundamental strings [1] can be quantized only in critical dimensions, strings in four space-time dimensions are of great interest since there is a large body of evidence [2], recently confirmed by numerical tests [3], that they can describe the confining phase of non-Abelian gauge theories. However, a consistent quantum theory describing these strings has not yet been found: the simplest model, the Nambu-Goto string, can be quantized only in space-time dimension D = 26 or D ≤ 1 because of the conformal anomaly; it is inappropriate to describe the expected smooth strings dual to QCD [4], since large Euclidean world-sheets are crumpled. In the rigid string [5], the marginal term proportional to the square of the extrinsic curvature, introduced to cure this problem, turns out to be infrared irrelevant and, thus, unable to prevent crumpling.Both these models also fail to describe the correct hightemperature behaviour of large-N QCD [6]. As shown in [7], the deconfining transition in QCD is due to the condensation of Wilson lines, and the partition function of QCD flux tubes can be continued above the deconfining transition; this high-temperature continuation can be evaluated perturbatively. So, any string theory that is equivalent to QCD must reproduce this behaviour. However, the Nambu-Goto action has the wrong temperature dependence, while the rigid string has the correct high-temperature behaviour but with a wrong sign and an imaginary part signalling a world-sheet instability [6]. At low temperatures, the behaviour of the rigid string was studied in [8].Recently, two new models have been proposed: a first one, the confining string [9], is based on an induced string action explicitly derivable for compact QED [10] and for Abelian-projected SU(2) [11]; a second one, originally proposed in [12], is based on a five-dimensional, curved space-time string action with the quarks living on a fourdimensional horizon [13]. The interrelation between these two models has been analysed in [14].The confining string action possesses, in its world-sheet formulation, a non-local action with a negative stiffness [10,15] that can be expressed as a derivative expansion of the interaction between surface elements. To perform an analytic analysis of the geometric properties of these strings, this expansion must be truncated: this clearly makes the model non-unitary, but in a spurious way. Moreover, since the stiffness is negative, a stable truncation must, at least, include a sixth-order term in the derivatives [16]. In [16,17] it was shown that, in the large-D approximation, this model has an infrared fixed point at zero stiffness, corresponding to a tensionless smooth string whose world-sheet has Hausdorff dimension 2, exactly the desired properties to describe QCD flux tubes.As fi...

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Section: Pacs: 1125pmsupporting

confidence: 76%

supporting

confidence: 76%

QCD-Like Behavior of High-Temperature Confining Strings

Diamantini

Trugenberger

2002

Phys. Rev. Lett.

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“…In fact this model has an infrared fixed point at zero stiffness [8,9], corresponding to a tensionless smooth string whose world-sheet has Hausdorff dimension 2, exactly the desired properties to describe QCD flux tubes. The long-range orientational order in this model is due to an antiferromagnetic interaction between normals to the surface [10], a mechanism confirmed by numerical simulations [11]. Moreover, it was shown in [9] that this infared fixed point does not depend on the truncation and is present for all ghost-and tachyon-free truncations, and that the effective theory describing the infrared behaviour is a conformal field theory with central charge c = 1.…”

Section: Introductionsupporting

confidence: 64%

Confining Strings at High Temperature

Diamantini

Trugenberger

2002

J. High Energy Phys.

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“…Moreover, it has been proposed [16] as a mechanism leading to smooth strings, with "long-range" orientational correlations, a fact confirmed by recent numerical simulations [17].…”

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confidence: 63%

Strings with Negative Stiffness and Hyperfine Structure

1999

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We propose a new string model by adding a higher-order gradient term to the rigid string, so that the stiffness can be positive or negative without loosing stability. In the large-D approximation, the model has three phases, one of which with a new type of generalized "antiferromagnetic" orientational correlations. We find an infrared-stable fixed point describing world-sheets with vanishing tension and Hausdorff dimension DH = 2. Crumpling is prevented by the new term which suppresses configurations with rapidly changing extrinsic curvature.PACS: 11.25.Pm 1. So far, fundamental strings [1] can be quantized only in critical spacetime dimensions D c , due to the difficulty of handling the Liouville field, which does not decouple in dimensions different from D c . Strings in four space-time dimensions, however, are of great physical importance since they are supposed to describe the confining phase of non-Abelian gauge theories [2], as confirmed by recent precision numerical tests [3]. As yet, there exists no consistent quantum theory of such strings. Attempts in this direction based on discrete models for the Liouville field failed [4], since these could not be generalized beyond one dimension. Further hope was based on strings with extrinsic curvature stiffness [5], but the infrared irrelevance of stiffness did not prevent the worldsheets from crumpling [6].Recent progress in this field is based on a new type of action. In its local formulation [7], the string action is induced by an antisymmetric tensor field. This action realizes explicitly the necessary zig-zag invariance of confining strings [8]. It can be derived without extra assumptions [9] for the confining phase of compact U (1) gauge theories [10]. The resulting strings are dual versions of the magnetic strings of the Abelian Higgs model [11,12]. Moreover, the action is a specific form of an earlier-proposed class of actions which would generate surfaces with non-trivial elastic properties [13].The characteristic of the effective string action obtained by integrating out the tensor field is a non-local interaction with negative stiffness between world-sheet elements. Such an interaction has been shown [14] to produce the correct high-temperature behavior of confining strings known from large-N QCD calculations [15].Moreover, it has been proposed [16] as a mechanism leading to smooth strings, with "long-range" orientational correlations, a fact confirmed by recent numerical simulations [17].In this letter we report on further progress in this field by considering the simplest possible model in this class of actions, obtained by adding to the rigid string the nextorder gradient term. The new model is defined in euclidean space by the actionwhere D a are covariant derivatives with respect to the induced metric g ab = ∂ a x µ ∂ b x µ on the surface x (ξ 0 , ξ 1 ) and we have used units c = 1,h = 1. Here, the bracket has to be considered as representing the first few terms in the expansion of the non-local interaction mediated by the original antisymmetric ...

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Strings and Aharonov–Bohm effect in Abelian Higgs model

Cited by 12 publications

References 12 publications

QCD-Like Behavior of High-Temperature Confining Strings

QCD-Like Behavior of High-Temperature Confining Strings

Confining Strings at High Temperature

Strings with Negative Stiffness and Hyperfine Structure

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