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Abstract:

We calculate the spectrum of light glueballs and the string tension in a number of SO(N) lattice gauge theories in 2+1 dimensions, with N in the range 3 ≤ N ≤ 16. After extrapolating to the continuum limit and then to N = ∞ we compare to the spectrum and string tension of the SU(N → ∞) gauge theory and find that the most reliably and precisely calculated physical quantities are consistent in that limit. We also compare the glueball spectra of those pairs of SO(N) and SU(N′) theories that possess the same Lie algebra, i.e. SO(3) and SU(2), SO(4) and SU(2)×SU(2), SO(6) and SU(4), and find that for the very lightest glueballs the spectra are consistent within each such pair, as are the string tensions and the couplings. Where there are apparent discrepancies they are typically for heavier glueballs, where the systematic errors are much harder to control. We calculate the SO(N) string tensions with a particular focus on the confining properties of SO(2N + 1) theories which, unlike SO(2N) theories, possess a trivial centre. We find that for both the light glueballs and for the string tension SO(2N) and SO(2N + 1) gauge theories appear to form a single smooth sequence.

Abstract:

There is numerical evidence that the world sheet action of the confining flux tube in D=3+1 SU(N) gauge theories contains a massive excitation with 0− quantum numbers whose mass shows some decrease as one goes from SU(3) to SU(5). Moreover it has been shown that the natural coupling of this pseudoscalar has a topological interpretation making it natural to call it the world-sheet ‘axion’. Recently it has been pointed out that if the mass of this ‘axion’ vanishes as N→∞ then it becomes possible for the world sheet theory to be integrable in the planar limit. In this paper we perform lattice calculations of this ‘axion’ mass from SU(2) to SU(12), which allows us to make a controlled extrapolation to N=∞ and so test this interesting possibility. We find that the ‘axion’ does not in fact become massless as N→∞. So if the theory is to possess planar integrability then it must be some other world sheet excitation that becomes massless in the planar limit.

Abstract:

There is numerical evidence that the world sheet action of the confining flux tube in D =3 +1SU(N)gauge theories contains a massive excitation with 0−quantum numbers whose mass shows some decrease as one goes from SU(3)to SU(5). Moreover it has been shown that the natural coupling of this pseudoscalar has a topological interpretation making it natural to call it the world-sheet ‘axion’. Recently it has been pointed out that if the mass of this ‘axion’ vanishes as N→∞then it becomes possible for the world sheet theory to be integrable in the planar limit. In this paper we perform lattice calculations of this ‘axion’ mass from SU(2)to SU(12), which allows us to make a controlled extrapolation to N=∞and so test this interesting possibility. We find that the ‘axion’ does not in fact become massless as N→∞. So if the theory is to possess planar integrability then it must be some other world sheet excitation that becomes massless in the planar limit.

Abstract:

We calculate the low-lying glueball spectrum and various string tensions in SU(N) lattice gauge theories in 2 + 1 dimensions, and extrapolate the results to the continuum limit. We do so for for the range N ∈ [2, 16] so as to control the N -dependence with a useful precision. We observe a number of striking near-degeneracies in the various JPC sectors of the glueball spectrum, in particular between C = + and C = − states. We calculate the string tensions of flux tubes in a number of representations, and provide evidence that the leading correction to the N -dependence of the k-string tensions is ∝ 1/N rather than ∝ 1/N2, and that the dominant binding of k fundamental flux tubes into a k-string is via pairwise interactions. We comment on the possible implications of our results for the dynamics of these gauge theories.

Abstract:

We extend our earlier calculations of the spectrum of closed flux tubes in SU(N) gauge theories in 2 + 1 dimensions, with a focus on questions raised by recent theoretical progress on the effective string action of long flux tubes and the world-sheet action for flux tubes of moderate lengths. Our new calculations in SU(4) and SU(8) provide evidence that the leading O(1/lγ) non-universal correction to the flux tube ground state energy does indeed have a power γ ≥ 7. We perform a study in SU(2), where we can traverse the length at which the Nambu-Goto ground state becomes tachyonic, to obtain an all-N view of the spectrum. Our comparison of the k = 2 flux tube excitation energies in SU(4) and SU(6) suggests that the massive world sheet excitation associated with the k = 2 binding has a scale that knows about the group and hence the theory in the bulk, and we comment on the potential implications of world sheet massive modes for the bulk spectrum. We provide a quantitative analysis of the surprising (near-)orthogonality of flux tubes carrying flux in different SU(N) representations, which implies that their screening by gluons is highly suppressed even at small N.