Quark confinement and the bosonic string

Abstract

Using a new type of simulation algorithm for the standard SU(3) lattice gauge theory that yields results with unprecedented precision, we confirm the presence of a γ/r correction to the static quark potential at large distances r, with a coefficient γ as predicted by the bosonic string theory. In both three and four dimensions, the transition from perturbative to string behaviour is evident from the data and takes place at surprisingly small distances. * On leave from Deutsches Elektronen-Synchrotron DESY,

The Casimir energy paradox of the QCD string

“…On the largest length scale of 3 fm, the spectrum exhibited string-like excitations with asymptotic π/R string gaps split by a fine structure. It is quite remarkable that the torelon spectrum, which is free of end effects, exhibits a similar fine structure, as reported for the first time at this conference [3].In a complementary study [2], the Casimir energy and the related effective conformal charge, C eff (R) = −12R 3 F ′ (R)/(π(D − 2)), were isolated where F(R) is the force between the static color sources and D is the space-time dimension of the gauge theory. With unparalleled accuracy, C eff (R) was determined for the gauge group * Talk presented by J. Kuti.…”

Linear broadening of the confining string in Yang-Mills theory at low temperature

“…Since the string ends at static quark charges separated by a distance r, its fluctuation field obeys the boundary condition h(0, t) = h(r, t) = 0. The boundary conditions explicitly break translation invariance and one might have expected boundary terms to be present in the effective action as well [6].…”

“…We have performed numerical simulations at the bare gauge coupling 4/g 2 = 9.0 on a 90 2 × 16 lattice, corresponding to T /T c ≈ 0.38. We have used the Lüscher-Weisz technique [6,17] with a single level and with slices of thickness 4. In table 1 we report the number of sub-lattice updates for various ranges of distances between the static sources.…”

“…Using the effective theory, Lüscher has calculated the leading correction to the linear quark-anti-quark potential V (r) = σr − π(d − 2) 24r + O(1/r 3 ), (1.1) where d is the space-time dimension and (d − 2) counts the directions transverse to the string world-sheet [1,2]. Accurate numerical simulations have shown the validity of that expectation [3][4][5][6][7][8][9][10][11][12]. The effective theory also accounts for the string width [13].…”

“…Since numerical lattice calculations of the string width in non-Abelian gauge theories are computationally very challenging, early calculations were affected by large statistical errors and did thus not yield conclusive results [16]. Only recently, using the very efficient Lüscher-Weisz multi-level algorithm [6,17], the logarithmically divergent string width has been accurately verified by simulating (2 + 1)-d SU (2) lattice Yang-Mills theory [18]. Recent results on the effective string description of the color flux tube in (2 + 1)-d SU (N ) Yang-Mills theory can be found in [19,20].…”