QCD-Like Behavior of High-Temperature Confining Strings

Abstract

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...

Confining Strings at High Temperature

“…So, any string theory that is equivalent to QCD must reproduce this behaviour. As shown in [13], contrary to previous string models, the high-temperature behaviour of confining strings reproduces exactly the correct large-N QCD result, a necessary condition for any string model of confinement.…”

“…In [13], the correct high-temperature behaviour of the confining string action was derived for a specific truncation. In this paper we will show that this property is largely independent of the specific truncation we choose, but holds true for all ghost-and tachyonfree truncations.…”

3d Georgi–glashow Model and Confining Strings at Zero and Finite Temperatures

“…Contrary to all previous string models for QCD, it is able to reproduce the large-N QCD behavior, found by Polchinski and Yang in [89], in both sign and reality properties [45].…”

“…The high-temperature behavior of the confining-string model proposed in [40] has been studied in [45], where it has been shown that this model has a high-temperature behavior that agrees in temperature dependence, sign and reality properties with the large-N QCD result [46]. The starting point will be again (6.2).…”

“…[36,42,43]), and some of these will be discussed in this review. A separate section will be devoted to the finite-temperature properties of confining strings [45].…”