Closed flux tubes and their string description in D=2+1 SU(N) gauge theories
We carry out lattice calculations of the spectrum of confining flux tubes that wind around a spatial torus of variable length l , in 2 + 1 dimensions. We compare the energies of the lowest ∼30 states to the free string Nambu-Goto model and to recent results on the universal properties of effective s...
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Published in | The journal of high energy physics Vol. 2011; no. 5 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Berlin/Heidelberg
Springer-Verlag
01.05.2011
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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Summary: | We carry out lattice calculations of the spectrum of confining flux tubes that wind around a spatial torus of variable length
l
, in 2 + 1 dimensions. We compare the energies of the lowest ∼30 states to the free string Nambu-Goto model and to recent results on the universal properties of effective string actions. Our most useful calculations are in SU(6) at a small lattice spacing, which we check is very close to the
N
→ ∞ continuum limit. We find that the energies,
E
n
(
l
), are remarkably close to the predictions of the free string Nambu-Goto model, even well below the critical length at which the expansion of the Nambu-Goto energy in powers of 1/
l
2
diverges and the series needs to be resummed. Our analysis of the ground state supports the universality of the
O
(1/
l
) and the
O
(1/
l
3
) corrections to
σl
, and we find that the deviations from Nambu-Goto at small
l
prefer a leading correction that is
O
(1/
l
7
), consistent with theoretical expectations. We find that the low-lying states that contain a single phonon excitation are also consistent with the leading
O
(1/
l
7
) correction dominating down to the smallest values of
l
. By contrast our analysis of the other light excited states clearly shows that for these states the corrections at smaller
l
resum to a much smaller effective power. Finally, and in contrast to our recent calculations in
D
= 3 + 1, we find no evidence for the presence of any non-stringy states that could indicate the excitation of massive flux tube modes. |
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ISSN: | 1029-8479 1029-8479 |
DOI: | 10.1007/JHEP05(2011)042 |