Dr Michael Teper

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.