N) gauge theories (original) (raw)

The k=2 string tension in four-dimensional SU( N) gauge theories

Physics Letters B, 2001

We calculate the k=2 string tension in SU(4) and SU(5) gauge theories in 3+1 dimensions, and compare it to the k=1 fundamental string tension. We find, from the continuum extrapolation of our lattice calculations, that σk=2/σf=1.40±0.08 in the SU(4) gauge theory, and that σk=2/σf=1.56±0.10 in SU(5). We remark upon the way this might constrain the dynamics of confinement and the intriguing implications it might have for the mass spectrum of SU(N) gauge theories. We also note that these results agree closely with the MQCD-inspired conjecture that the SU(N) string tension varies as σk∝ sin(πk/N).

k -string tensions in SU ( N ) gauge theories

Physical Review D, 2001

In the context of four-dimensional SU(N ) gauge theories, we study the spectrum of the confining strings. We compute, for the SU(6) gauge theory formulated on a lattice, the three independent string tensions σ k related to sources with ZN charge k = 1, 2, 3, using Monte Carlo simulations. Our results, whose uncertainty is approximately 2% for k = 2 and 4% for k = 3, are consistent with the sine formula σ k /σ = sin k π N / sin π N for the ratio between σ k and the standard string tension σ, and show deviations from the Casimir scaling. The sine formula is known to emerge in supersymmetric SU(N ) gauge theories and in M-theory. We comment on an analogous behavior exhibited by two-dimensional SU(N ) × SU(N ) chiral models.

SU(N) gauge theories in four dimensions: exploring the approach to N = infinity

2001

We calculate the string tension, K, and some of the lightest glueball masses, M, in 3+1 dimensional SU(N) lattice gauge theories for N=2,3,4,5 . From the continuum extrapolation of the lattice values, we find that the mass ratios, M/sqrt(K), appear to show a rapid approach to the large-N limit, and, indeed, can be described all the way down to SU(2) using just a leading O(1/NxN) correction. We confirm that the smooth large-N limit we find, is obtained by keeping a constant 't Hooft coupling. We also calculate the topological charge of the gauge fields. We observe that, as expected, the density of small-size instantons vanishes rapidly as N increases, while the topological susceptibility appears to have a non-zero N=infinity limit.

SU (N) gauge theories in four dimensions: exploring the approach to N=∞

Journal of High Energy Physics, 2001

We calculate the string tension, σ, and some of the lightest glueball masses, m G , in 3+1 dimensional SU(N) lattice gauge theories for 2 ≤ N ≤ 5. From the continuum extrapolation of the lattice values, we find that the mass ratios m G / √ σ appear to show a rapid approach to the large-N limit, and, indeed, can be described all the way down to SU(2) using just a leading O(1/N 2 ) correction. We confirm that the smooth large-N limit we find, is obtained by keeping a constant 't Hooft coupling. We also calculate the topological charge of the gauge fields. We observe that, as expected, the density of small-size instantons vanishes rapidly as N increases, while the topological susceptibility appears to have a non-zero N = ∞ limit.

Confining strings in SU(N) gauge theories

Physical Review D, 2001

We calculate the string tensions of kkk-strings in SU($N$) gauge theories in both 3 and 4 dimensions. In D=3+1, we find that the ratio of the k=2k=2k=2 string tension to the k=1k = 1k=1 fundamental string tension is consistent, at the 2sigma2 \sigma2sigma level, with both the M(-theory)QCD-inspired conjecture and with `Casimir scaling'. In D=2+1 we see a definite deviation from the MQCD formula, as well as a much smaller but still significant deviation from Casimir scaling. We find that in both D=2+1 and D=3+1 the high temperature spatial kkk-string tensions also satisfy approximate Casimir scaling. We point out that approximate Casimir scaling arises naturally if the cross-section of the flux tube is nearly independent of the flux carried, and that this will occur in an effective dual superconducting description, if we are in the deep-London limit. We estimate, numerically, the intrinsic width of kkk-strings in D=2+1 and indeed find little variation with kkk. In addition to the stable kkk-strings we investigate some ofthe unstable strings, finding in D=2+1 that they satisfy (approximate) Casimir scaling. We also investigate the basic assumption that confining flux tubes are described by an effective string theory at large distances. We estimate the coefficient of the universal L\"uscher correction from periodic strings that are longer than 1 fermi, and find cL=0.98(4)c_L=0.98(4)cL=0.98(4) in D=3+1 and cL=0.558(19)c_L=0.558(19)cL=0.558(19) in D=2+1. These values are within 2sigma2 \sigma2sigma of the simple bosonic string values and are inconsistent with other simple effective string theories.

The string and its tension in Su(3) lattice gauge theory: Towards definitive results

Physics Letters B, 1985

We consider the correlation of Polyakov loops It as shown that the ground-state energy recewes a umversal contribution-~r/3A (A being the length of the loop) arising from long wavelength fluctuations of the string. The correlation function is calculated for fl = 5.5, 5 7, 5 9 and 6 0 on lattices ranging in s~ze from 63 × 12 to 123 × 24 using the source method. The calculation is accurate enough to identify the asymptotic exponential decay wtuch makes sure that we are extracting the ground state energy and hence the (asymptotic) linearly nsmg p~ece of the potential We find the Coulomb-hke contribution to be remarkably consistent w~th-~r/3A The stnng tension violates asymptotic scaling by-60%, taken over the whole range of fl Tlus stands in sharp contrast to the fl dependence of the mass gap which ~s consistent with asymptouc scahng.

SU(N) gauge theories in 2+1 dimensions: Further results

Physical Review D, 2002

We calculate the string tension and part of the mass spectrum of SU(4) and SU(6) gauge theories in 2+1 dimensions using lattice techniques. We combine these new results with older results for N=2,...,5 so as to obtain more accurate extrapolations to N=infinity. The qualitative conclusions of the earlier work are unchanged: SU(N) theories in 2+1 dimensions are linearly confining as N->infinity; the limit is achieved by keeping g.g.N fixed; SU(3), and even SU(2), are `close' to SU(infinity). We obtain more convincing evidence than before that the leading large-N correction is O(1/N.N). We look for the multiplication of states that one expects in simple flux loop models of glueballs, but find no evidence for this.

SU (N) GAUGE THEORIES IN FOUR DIMENSIONS: EXPLORING THE APPROACH TO TV=∞

Topology and confinement in SU (< i> N) gauge theories

Nuclear Physics B-Proceedings Supplements, 2002

The large N limit of SU(N ) gauge theories in 3+1 dimensions is investigated on the lattice by extrapolating results obtained for 2 ≤ N ≤ 5. A numerical determination of the masses of the lowest-lying glueball states and of the topological susceptibility in the limit N → ∞ is provided. Ratios of the tensions of stable k-strings over the tension of the fundamental string are investigated in various regimes and the results are compared with expectations based on several scenarios -in particular MQCD and Casimir scaling. While not conclusive at zero temperature in D=3+1, in the other cases investigated our data seem to favour the latter.

The String Tension in Two-Dimensional Gauge Theories

International Journal of Modern Physics A, 1999

We review and elaborate on properties of the string tension in two-dimensional gauge theories. The first model we consider is massive QED in the m≪e limit. We evaluate the leading string tension both in the fermionic and bosonized descriptions. We discuss the next-to-leading corrections in m/e. The next-to-leading terms in the long distance behavior of the quark–antiquark potential, are evaluated in a certain region of external versus dynamical charges. The finite temperature behavior is also determined. In QCD 2 we review the results for the string tension of quarks in cases with dynamical quarks in the fundamental, adjoint, symmetric and antisymmetric representations. The screening nature of SYM 2 is re-derived.

The< i> k= 2 string tension in four-dimensional< i> SU(< i> N) gauge theories (original) (raw)

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