Strings with Negative Stiffness and Hyperfine Structure

Abstract

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 ...

QCD-Like Behavior of High-Temperature Confining Strings

“…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. In this paper we will study the high-temperature behaviour of the string model defined in [16]. We will show that this model has a high-temperature behaviour that agrees in temperature dependence, sign and reality properties with the large-N QCD result [6].…”

“…In this paper we will study the high-temperature behaviour of the string model defined in [16]. We will show that this model has a high-temperature behaviour that agrees in temperature dependence, sign and reality properties with the large-N QCD result [6].…”

“…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 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.…”

“…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.…”

Non-critical confining strings and the renormalization group

“…12 11 This actually covers the whole domain of the Louville variable in the non zz-invariant situation when λ > 0 because then α 0 < a 0 always. 12 Please note that owing to our identification (8) between the renormalization group scale µ and the…”