Hagedorn transition, vortices and D0 branes: lessons from 2+1 confining strings

Kogan, Ian I.; Schvellinger, Martín; Kovner, Alex

doi:10.1088/1126-6708/2001/07/019

Cited by 13 publications

(10 citation statements)

References 34 publications

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“…The phase diagram of these systems has an exceedingly rich structure [6]. It also has interesting analogs in gauge theory systems as was pointed out in a recent work [7].…”

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confidence: 81%

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The target space depenedence of the Hagedorn temperature

Grignani

Orselli

Semenoff

2001

J. High Energy Phys.

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The effect of certain simple backgrounds on the Hagedorn temperature in theories of closed strings is examined. The background of interest are a constant Neveu-Schwarz B-field, a constant offset of the space-time metric and a compactified spatial dimension. We find that the Hagedorn temperature of string theory depends on the parameters of the background. We comment on an interesting non-extensive feature of the Hagedorn transition, including a subtlety with decoupling of closed strings in the NCOS limit of open string theory and on the large radius limit of discrete light-cone quantized closed strings.

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“…The phase diagram of these systems has an exceedingly rich structure [6]. It also has interesting analogs in gauge theory systems as was pointed out in a recent work [7].…”

mentioning

confidence: 81%

“…where z = exp(2πiτ ). Using (7) and (8), the τ 1 integral in (6) can be easily performed ∞ r,r ′ =0 d(r)d(r ′ )e −2πτ 2 (r+r ′ )…”

Section: Derivation Of T Hmentioning

confidence: 99%

The target space depenedence of the Hagedorn temperature

Grignani

Orselli

Semenoff

2001

J. High Energy Phys.

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“…This result depends entirely on the higher order term and is totally independent of the stiffness. Finite-temperature confining strings in (2+1) dimensions and in the presence of D0-branes have been studied in [20].In Euclidean space, the action proposed in [16] is:where 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 ). The first term in the bracket provides a bare surface tension 2t, while the second accounts for the rigidity, with a stiffness parameter s that we set to its fixed-point value s = 0.…”

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confidence: 99%

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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“…Let us now derive the action of a fluctuating string in a More direct way. 19 We work with the Polyakov effective Lagrangian (14). Since the string world sheet is identified with the domain wall in the effective action, we will integrate in the partition function over all degrees of freedom apart from those that mark the position of the domain wall.…”

Section: The Confining String For Pedestriansmentioning

confidence: 99%

Monopoles, Vortices and Strings: Confinement and Deconfinement in 2+1 Dimensions at Weak Coupling

Kogan¹,

Kovner²

2002

At the Frontier of Particle Physics

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We consider, from several complementary perspectives, the physics of confinement and deconfinement in the 2+1 dimensional Georgi-Glashow model. Polyakov's monopole plasma and 't Hooft's vortex condensation are discussed first. We then discuss the physics of confining strings at zero temperature. We review the Hamiltonian variational approach and show how the linear confining potential arises in this framework. The second part of this review is devoted to study of the deconfining phase transition. We show that the mechanism of the transition is the restoration of 't Hooft's magnetic symmetry in the deconfined phase. The heavy charged W bosons play a crucial role in the dynamics of the transition, and we discuss the interplay between the charged W plasma and the binding of monopoles at high temperature. Finally we discuss the phase transition from the point of view of confining strings. We show that from this point of view the transition is not driven by the Hagedorn mechanism (proliferation of arbitrarily long strings), but rather by the "disintegration" of the string due to the proliferation of 0 branes.

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Hagedorn transition, vortices and D0 branes: lessons from 2+1 confining strings

Cited by 13 publications

References 34 publications

The target space depenedence of the Hagedorn temperature

The target space depenedence of the Hagedorn temperature

QCD-Like Behavior of High-Temperature Confining Strings

Monopoles, Vortices and Strings: Confinement and Deconfinement in 2+1 Dimensions at Weak Coupling

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