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/l^gamma) non-universal correction to the flux tube ground state energy does indeed have a power gamma greater than or equal to 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.
Highlights
Of the spectra and, in the case of SU(2), to see what happens when l is decreased past the value at which the Nambu-Goto ground state becomes tachyonic
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
We begin with a brief overview of the ‘Nambu-Goto spectrum’ since it has been found to provide a good approximation to the observed spectrum of closed fundamental flux tubes [1,2,3,4]. (See [16,17,18], and references therein, for a discussion of open flux tubes and Wilson loops.) This spectrum is obtained by the canonical light cone quantisation of a free bosonic string in D = 26 [19, 20]
Summary
The states are obtained by applying these creation operators to the ‘vacuum’ of the world sheet theory All this implies that the (transverse) parity of a state is given by the total number of phonons:. In addition the coefficients of these 1/l, 1/l3 and 1/l5 terms in the expansion of En(l) around σl are precisely the same as one obtains, to that order, by expanding the expression for ENL,NR(q, l) in eq (2.3) in powers of 1/l This explains why, in general, longer flux tubes are well described by the Nambu-Goto spectrum. By working backwards and searching for the classic signal of a phase shift passing through the value of π, this provides a powerful framework for determining whether the numerically determined flux tube spectrum contains the contribution of massive resonant states [14, 15]. A second focus of this paper is to add to what we can infer about that massive mode
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