Universality class of confining strings

Abstract

A recently proposed model of confining strings has a non-local world-sheet action induced by a space-time Kalb-Ramond tensor field. Here we show that, in the large-D approximation, an infinite set of ghost-and tachyon-free truncations of the derivative expansion of this action all lead to c = 1 models. Their infrared limit describes smooth strings with world-sheets of Hausdorff dimension D H = 2 and long-range orientational order, as expected for QCD strings. March 1999 * Supported by an A. v. Humboldt fellowship. On leave of absence from I.N.F.N. and University of Perugia;

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

“…If we now look at the behavior of ρ 1 at low temperatures, below the deconfining transition [41], we see that 1/ρ 1 is positive. The deconfining transition is indeed determined by the vanishing of 1/ρ 1 at β = β dec .…”

“…In [41] it has been proved that the answer to this question is no: the value of c and the smooth geometric properties are independent of an infinite set of truncations, provided that a solution for the polynomial "gap" equation exists. These properties are presumably common to a large class of non-local world-sheet interactions.…”

“…It is in fact the sixth-order term, forced by the negative stiffness, that suppresses the formation of spikes on the surfaces and leads to a smooth surface in the large-D approximation. In fact, in [40,41] it has been 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 [42,43], 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 [44].…”

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

“…Induced string action can be explicitly derived for compact QED [29,30] and it was found that this nonlocal action has derivative expansion describing rigid string [31]. For more details see [32] and references therein.…”

“…Thus, such a string theory must have a curvature term with the coefficient of order σ/M 2 γ . The derivative expansion for the confining string action has been discussed in the literature (see [32]) and references therein). It has in general the form…”