Physical String Tension Research Articles

Blockspin renormalization-group study of color confinement due to violation of the non-Abelian Bianchi identity

Block-spin transformation of topological defects is applied to the violation of the non-Abelian Bianchi identity (VMABI) on lattice defined as Abelian monopoles. To get rid of lattice artifacts, we introduce various techniques smoothing the vacuum. The effective action can be determined by adopting the inverse Monte-Carlo method. The coupling constants $F(i)$ of the effective action depend on the coupling of the lattice action $\beta$ and the number of the blocking step $n$. But it is found that $F(i)$ satisfy a beautiful scaling, that is, they are a function of the product $b=na(\beta)$ alone for lattice coupling constants $3.0\le\beta\le3.9$ and the steps of blocking $1\le n\le 12$. The effective action showing the scaling behavior can be regarded as an almost perfect action corresponding to the continuum limit, since $a\to 0$ as $n\to\infty$ for fixed $b$. The almost perfect action showing the scaling is found to be independent of the smooth gauges adopted here. Then we compare the results with those obtained by the analytic blocking method of topological defects from the continuum. The infrared monopole action can be transformed into that of the string model. The physical string tension and the lowest glueball mass can be evaluated \textit{analytically} by the strong-coupling expansion of the string model. We get $\sqrt{\sigma}\simeq 1.3\sqrt{\sigma_{phys}}$ for $b\ge 1.0\ \ (\sigma_{phys}^{-1/2})$, whereas the scalar glueball mass is kept to be near $M(0^{++})\sim 3.7\sqrt{\sigma_{phys}}$. Also we can almost reproduce \textit{analytically} the scaling function of the squared monopole density determined numerically for large $b$ region $b>1.2\ (\sigma_{phys}^{-1/2})$.

Axion string dynamics I: 2+1D

If the axion exists and if the initial axion field value is uncorrelated at causally disconnected points, then it should be possible to predict the efficiency of cosmological axion production, relating the axionic dark matter density to the axion mass. The main obstacle to making this prediction is correctly treating the axion string cores. We develop a new algorithm for treating the axionic string cores correctly in 2+1 dimensions. When the axionic string cores are given their full physical string tension, axion production is about twice as efficient as in previous simulations. We argue that the string network in 2+1 dimensions should behave very differently than in 3+1 dimensions, so this result cannot be simply carried over to the physical case. We outline how to extend our method to 3+1D axion string dynamics.

Coulomb versus physical string tension on the lattice

From continuum studies it is known that the Coulomb string tension $\sigma_C$ gives an upper bound for the physical (Wilson) string tension $\sigma_W$ [D. Zwanziger, Phys. Rev. Lett. 90, 102001 (2003)]. How does however such relationship translate to the lattice? In this paper we give evidence that there, while the two string tensions are related at zero temperature, they decouple at finite temperature. More precisely, we show that on the lattice the Coulomb gauge confinement scenario is always tied to the spatial string tension, which is known to survive the deconfinement phase transition and to cause screening effects in the quark-gluon plasma. Our analysis is based on the identification and elimination of center vortices which allows to control the physical string tension and study its effect on the Coulomb gauge observables. We also show how alternative definitions of the Coulomb potential may sense the deconfinement transition; however a true static Coulomb gauge order parameter for the phase transition is still elusive on the lattice.

Instantaneous interquark potential in generalized Landau gauge in SU(3) lattice QCD: A linkage between the Landau and the Coulomb gauges

We investigate in detail "instantaneous interquark potentials", interesting gauge-dependent quantities defined from the spatial correlators of the temporal link-variable $U_4$, in generalized Landau gauge using SU(3) quenched lattice QCD. The instantaneous Q$\bar{\rm Q}$ potential has no linear part in the Landau gauge, and it is expressed by the Coulomb plus linear potential in the Coulomb gauge, where the slope is 2-3 times larger than the physical string tension. Using the generalized Landau gauge, we find that the instantaneous potential can be continuously described between the Landau and the Coulomb gauges, and its linear part rapidly grows in the neighborhood of the Coulomb gauge. We also investigate the instantaneous 3Q potential in the generalized Landau gauge, and obtain similar results to the Q$\bar{\rm Q}$ case. $T$-length terminated Polyakov-line correlators and their corresponding "finite-time potentials" are also investigated in generalized Landau gauge.

P-vortices and drama of Gribov copies

We present results of the careful study of the Gribov copies problem in SU(2) lattice gauge theory for the direct maximal center projection widely used in confinement studies. Applying simulated annealing algorithm we demonstrate that this problem is more severe than it was thought before. The projected (gauge noninvariant) string tension is not in the agreement with the physical string tension. We do not find any indications that P-vortices reproduce the full SU(2) string tension neither in the infinite volume limit nor in the continuum limit.

Various representations of infrared effective lattice QCD

We study various representations of the infrared effective theory of SU(2) gluodynamics starting from the monopole action derived recently. We determine the coupling constants in the abelian-Higgs model directly from lattice QCD and evaluate the type of the QCD vacuum. The string action is derived using the BKT transformation on the lattice. At the classical level this action reproduces the physical string tension with a good accuracy.

Further investigations of the crumpling transition in dynamically triangulated random surfaces

We examine further the critical behaviour of dynamically triangulated random surfaces (DTRS) with extrinsic curvature at their second-order crumpling transition. We show that the string tension in these models may be scaling near the transition in such a way that the physical string tension is finite, unlike models containing only a Polyakov term, suggesting that one can use DTRS as a discretization of subcritical string theory. We explore the universality properties of DTRS, showing that an apparently irrelevant term can affect the phase transition. We also find that the observed phase transition persists when the surfaces are embedded in higher dimensions, contradicting the naive expectations of a saddle point expansion.

String tension in a lattice model of random surfaces

The model of planar random surfaces without spikes shows nontrivial critical behaviour on a four-dimensional lattice. In this article we address ourselves to the question of whether the string tension has a finite continuum limit at the critical point. To this end we calculated the first few terms of its strong coupling expansion and analysed them with the help of Padé approximants. The results indicate a nonvanishing critical string tension in lattice units which implies that the physical string tension would diverge in the continuum limit. We applied the method to the susceptibility too and found values for its critical exponent which are consistent with the Monte Carlo results, supporting the reliability of the method.

Static potential for smooth strings in the large-D limit.

The static potential V(R) in Polyakov's model of smooth strings is studied in the large-D limit. The physical string tension is calculated analytically as a function of the bare string tension and the extrinsic curvature coupling. A systematic saddle-point method for computing the loop expansion of V(R) is developed and carried out explicitly to two loops. There are no corrections to the 1/R Luscher term to this order. The leading short-distance behavior of V(R) is also proportional to 1/R with twice the coefficient of the Luscher term.

Static potential for smooth strings.

The static potential is studied in Helfrich and Polyakov's model of smooth strings. For large separations R, the potential is linear in R with corrections of order 1/R. While the physical string tension is renormalized by the extrinsic curvature coupling, the coefficient of the 1/R term has L\"uscher's universal value to any finite order in the loop expansion. For very small separations, the leading term in the potential is proportional to 1/R, with a coefficient exactly twice that of the L\"uscher term, and with corrections that are logarithmically small.

Static potential in a string model with extrinsic curvatures

The static quark potential in a string model including extrinsic curvature effects is studied in the large d limit, where d is the dimensionality of euclidean space. At large distances it is explicitly shown that the physical string tension is dynamically generated. Examining the large-distance “Coulomb” term in the potential, we show that the non-perturbative effects in general generate non-gaussian effective theories in the infrared regime. At large distances the d → ∞ saddle point is stable for a large range of parameters.