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Keywords
(13)
1/n expansion
Energy Spectrum
Finite Volume
Gauge Theory
Ground State Energy
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Closed flux tubes and their string description in D =3+1 SU( N ) gauge theories
Closed flux tubes and their string description in D =3+1 SU( N ) gauge theories,10.1007/JHEP02(2011)030,Journal of High Energy Physics,Andreas Athenod
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Closed flux tubes and their string description in D =3+1 SU( N ) gauge theories
(
Citations: 4
)
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Andreas Athenodorou
,
Barak Bringoltz
,
Michael Teper
We calculate the
energy spectrum
of ac onfining flux tube that is closed around a spatial torus, as a function of its length l. We do so for various SU(N) gauge theories in 3+ 1 dimensions, and for various values of spin, parity and longitudinal momentum. We are able to present usefully accurate results for about 20 of the lightest such states, for a range of l that begins close to the (finite volume) deconfining
phase transition
at l√σ ∼1.6, and extends up to l√σ ∼6 (where σ is the string tension). We find that most of these lowlying states are well described by the
spectrum
of the NambuGoto free
string theory
in flat spacetime. Remarkably, this is so not only at the larger values of l, where the gap between the
ground state energy
and the lowlying excitations becomes small compared to the mass gap, but also down to much shorter lengths where these excitation energies become large compared to √σ, the fluxtube no longer ‘looks’ anything like a thin string, and an expansion of the effective string action in powers of 1/l no longer converges. All this is for flux in the fundamental representation. We also calculate the k = 2 (anti)symmetric ground states and these show larger corrections at small l. So far all this closely resembles our earlier findings in 2+ 1 dimensions. However, and in contrast to the situation in D = 2+ 1, we also find that there are some states, with J P=0−quantum numbers, that show large deviations from the NambuGoto spectrum. We investigate the possibility that (some of) these states may encode the massive modes associated with the
internal structure
of the flux tube, and we discuss how the precocious free string behaviour of most states constrains the effective string action, on which much interesting theoretical progress has recently been made.
Journal:
Journal of High Energy Physics  J HIGH ENERGY PHYS
, vol. 2011, no. 2, pp. 163, 2011
DOI:
10.1007/JHEP02(2011)030
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Citation Context
(3)
...and indeed results from the lattice show a good agreement with this equation (see, for instance, [4]–[21]); a similar agreement is also seen for long closed strings (see, for instance, [22]–[
35
])...
Ofer Aharony
,
et al.
On the effective theory of long open strings
...For recent results on the closed string spectrum in 2 + 1 and 3 + 1 dimensional SU(N) gauge theory see [25,
26
]...
...Here P is the parity quantum number of the state and C what we call the quantum number of charge conjugation (called transverse and longitudinal parity respectively in [
26
])...
...This method is analogous to the method used in [
26
], where a variational criterion has been applied at each value of T seperately...
...In [25] and [
26
] this mixing is minimised by using a very large number of basis states...
...in [
26
] and [19]), we t the ground state data to the form...
...In addition they are consistent with the results from [15, 22{24] for smaller values ofR and with the results obtained for closed strings [25,
26
]...
...In the case of closed strings and in the nite temperature behavior of the string tension analogous deviations were observed in [
26
] and [41]...
Bastian B. Brandt
.
Probing boundarycorrections to NambuGoto open string energy levels i...
...We end in section 4 with a discussion of the extent to which our results can be compared to recent lattice results for 3 + 1 dimensional gauge theories [
7
, 8], showing some deviations from the NambuGoto energy levels...
...Recently, a deviation from the NambuGoto energy levels was reported for some specific closed string states in lattice simulations of 3+1 dimensional SU(N) YangMills theory [
7
, 8], which calculated the spectrum for the low levels of a closed fluxtube wrapping a compact dimension...
...Two useful parity operators used in [
7
, 8] to classify the states are P⊥ and Pk . P⊥ is a reflection about the X 2 axis, which takes � 2 → −� 2 or � ± → −� ∓ , and Pk is the parity...
...The results of [
7
, 8] show that even for rather small values of r (where the 1/r expansion is not expected to converge) almost all states agree very well with the NambuGoto formula for the energy levels, except for two states (one with q = 0 and one with q = 1) that are the lightest states with J P? = 0 − . These states show a large deviation from NambuGoto...
...There are thus two possible interpretations of the results of [
7
, 8]. One possibility is that when we sum the 1/r expansion (including all corrections coming from the c4 term and all terms related to it by Lorentz symmetry, and perhaps including additional corrections as well) we will find a very small deviation for almost all states, but a large deviation for the 0 − states...
Ofer Aharony
,
et al.
Corrections to NambuGoto energy levels from the effective string acti...
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Citations
(4)
On the effective theory of long open strings
(
Citations: 5
)
Ofer Aharony
,
Matan Field
Journal:
Journal of High Energy Physics  J HIGH ENERGY PHYS
, vol. 2011, no. 1, pp. 148, 2011
Probing boundarycorrections to NambuGoto open string energy levels in 3d SU(2) gauge theory
(
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Corrections to NambuGoto energy levels from the effective string action
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Citations: 8
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