The question of which effective string theory describes the confining flux-tube
has been a subject of extensive investigation during the last two decades.
We extracted by means of numerical simulations using lattice techniques the
spectrum of confining SU(N) torelons (flux-tubes that wind around a spatial torus) of
variable length L, in 2+1 and 3+1 dimensions, in the fundamental representation of
colour and for several combinations of parity and longitudinal momentum.
We compare the energies of the low-lying states to the free string
Nambu-Goto model and to recent results on the universal properties of
effective string actions. The main aim of this talk will be to
provide convincing evidence that Nambu-Goto string is the best known
description for the confining fundamental flux-tube in 2+1 and 3+1 dimensions.
I am planning to spend most of the time demonstrating our results for 2+1 dimensions
since this is a much less complicated case than that for 3+1 dimensions.
For 3+1 dimensions I will only provide a brief summary of our findings
most of which resemble those in 2+1 dimensions apart from some states
with particular quantum numbers which have large deviations from Nambu-Goto.
Finally, and if there is time left, I will present our very recent results on the spectrum of 2+1
dimensional closed flux-tubes in higher irreducible-representations of colour.