Abstract
We calculate, numerically, the low-lying spectrum of closed confining flux tubes that carry flux in different representations of SU(N). We do so for SU(6) at β = 171, where the calculated low-energy physics is very close to the continuum limit and, in many respects, also close to N = ∞. We focus on the adjoint, 84, 120, k = 2A, 2S and k = 3A,3M,3S representations and provide evidence that the corresponding flux tubes, albeit mostly unstable, do in fact exist. We observe that the ground state of a flux tube with momentum along its axis appears to be well defined in all cases and is well described by the Nambu-Goto spectrum (in flat space-time), all the way down to very small lengths, just as it is for flux tubes carrying fundamental flux. Excited states, however, typically show very much larger deviations from Nambu-Goto than the corresponding excitations of fundamental flux tubes and, indeed, cannot be extracted in many cases. We discuss whether what we are seeing here are separate stringy and massive modes or simply large corrections to energy levels that will become string-like at larger lengths.
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M. Lüscher, K. Symanzik and P. Weisz, Anomalies of the Free Loop Wave Equation in the WKB Approximation, Nucl. Phys. B 173 (1980) 365 [INSPIRE].
M. Lüscher, Symmetry Breaking Aspects of the Roughening Transition in Gauge Theories, Nucl. Phys. B 180 (1981) 317 [INSPIRE].
J. Polchinski and A. Strominger, Effective string theory, Phys. Rev. Lett. 67 (1991) 1681 [INSPIRE].
O. Aharony and Z. Komargodski, The Effective Theory of Long Strings, JHEP 05 (2013) 118 [arXiv:1302.6257] [INSPIRE].
A. Monin and M. Voloshin, Spontaneous and Induced Decay of Metastable Strings and Domain Walls, Annals Phys. 325 (2010) 16 [arXiv:0904.1728] [INSPIRE].
A. Monin and M. Voloshin, Destruction of a metastable string by particle collisions, Phys. Atom. Nucl. 73 (2010) 703 [arXiv:0902.0407] [INSPIRE].
A. Monin and M. Voloshin, Breaking of a metastable string at finite temperature, Phys. Rev. D 78 (2008) 125029 [arXiv:0809.5286] [INSPIRE].
A. Monin and M. Voloshin, The spontaneous breaking of a metastable string, Phys. Rev. D 78 (2008) 065048 [arXiv:0808.1693] [INSPIRE].
M. Shifman and A. Yung, Metastable strings in Abelian Higgs models embedded in nonAbelian theories: Calculating the decay rate, Phys. Rev. D 66 (2002) 045012 [hep-th/0205025] [INSPIRE].
A. Armoni and M. Shifman, Remarks on stable and quasistable k strings at large-N, Nucl. Phys. B 671 (2003) 67 [hep-th/0307020] [INSPIRE].
S. Bolognesi, M. Shifman and M. Voloshin, Quantum Fusion of Strings (Flux Tubes) and Domain Walls, Phys. Rev. D 80 (2009) 045010 [arXiv:0905.1664] [INSPIRE].
A. Athenodorou, B. Bringoltz and M. Teper, Closed flux tubes and their string description in D=2+1 SU(N) gauge theories, JHEP 05 (2011) 042[arXiv:1103.5854] [INSPIRE].
A. Athenodorou, B. Bringoltz and M. Teper, On the spectrum of closed k = 2 flux tubes in D=2+1 SU(N) gauge theories, JHEP 05 (2009) 019[arXiv:0812.0334] [INSPIRE].
B. Bringoltz and M. Teper, Closed k-strings in SU(N) gauge theories : 2+1 dimensions, Phys. Lett. B 663 (2008) 429 [arXiv:0802.1490] [INSPIRE].
J. Arvis, The Exact Q \( \overline{q} \) Potential In Nambu String Theory, Phys. Lett. B 127 (1983) 106 [INSPIRE].
M. Lüscher and P. Weisz, String excitation energies in SU(N) gauge theories beyond the free-string approximation, JHEP 07 (2004) 014 [hep-th/0406205] [INSPIRE].
J. Drummond, Universal subleading spectrum of effective string theory, hep-th/0411017 [INSPIRE].
O. Aharony, M. Field and N. Klinghoffer, The effective string spectrum in the orthogonal gauge, JHEP 04 (2012) 048 [arXiv:1111.5757] [INSPIRE]
O. Aharony and M. Dodelson, Effective String Theory and Nonlinear Lorentz Invariance, JHEP 02 (2012) 008 [arXiv:1111.5758] [INSPIRE].
O. Aharony and N. Klinghoffer, Corrections to Nambu-Goto energy levels from the effective string action, JHEP 12 (2010) 058 [arXiv:1008.2648] [INSPIRE].
O. Aharony and M. Field, On the effective theory of long open strings, JHEP 01 (2011) 065 [arXiv:1008.2636] [INSPIRE].
O. Aharony and E. Karzbrun, On the effective action of confining strings, JHEP 06 (2009) 012 [arXiv:0903.1927] [INSPIRE].
F. Gliozzi and M. Meineri, Lorentz completion of effective string (and p-brane) action, JHEP 08 (2012) 056 [arXiv:1207.2912] [INSPIRE].
M. Billó, M. Caselle, F. Gliozzi, M. Meineri and R. Pellegrini, The Lorentz-invariant boundary action of the confining string and its universal contribution to the inter-quark potential, JHEP 05 (2012) 130 [arXiv:1202.1984] [INSPIRE].
H.B. Meyer, Poincaré invariance in effective string theories, JHEP 05 (2006) 066 [hep-th/0602281] [INSPIRE].
S. Dubovsky, R. Flauger and V. Gorbenko, Evidence for a new particle on the worldsheet of the QCD flux tube, arXiv:1301.2325 [INSPIRE].
S. Dubovsky, R. Flauger and V. Gorbenko, Effective String Theory Revisited, JHEP 09 (2012) 044 [arXiv:1203.1054] [INSPIRE].
S. Dubovsky, R. Flauger and V. Gorbenko, Solving the Simplest Theory of Quantum Gravity, JHEP 09 (2012) 133 [arXiv:1205.6805] [INSPIRE].
B. Lucini and M. Teper, Confining strings in SU(N) gauge theories, Phys. Rev. D 64 (2001) 105019 [hep-lat/0107007] [INSPIRE].
B. Lucini and M. Teper, The k = 2 string tension in four dimensional SU(N) gauge theories, Phys. Lett. B 501 (2001) 128 [hep-lat/0012025] [INSPIRE].
L. Del Debbio, H. Panagopoulos, P. Rossi and E. Vicari, K string tensions in SU(N) gauge theories, Phys. Rev. D 65 (2002) 021501 [hep-th/0106185] [INSPIRE].
B. Lucini, M. Teper and U. Wenger, Glueballs and k-strings in SU(N) gauge theories: Calculations with improved operators, JHEP 06 (2004) 012 [hep-lat/0404008] [INSPIRE].
D. Karabali, C.-j. Kim and V. Nair, On the vacuum wave function and string tension of Yang-Mills theories in (2+1)-dimensions, Phys. Lett. B 434 (1998) 103 [hep-th/9804132] [INSPIRE].
D. Karabali, V. Nair and A. Yelnikov, The Hamiltonian Approach to Yang-Mills (2+1): An Expansion Scheme and Corrections to String Tension, Nucl. Phys. B 824 (2010) 387 [arXiv:0906.0783] [INSPIRE].
S. Deldar, Static SU(3) potentials for sources in various representations, Phys. Rev. D 62 (2000) 034509 [hep-lat/9911008] [INSPIRE].
S. Deldar, Potentials between static SU(3) sources in the fat center vortices model, JHEP 01 (2001) 013 [hep-ph/9912428] [INSPIRE].
S. Deldar, A new lattice measurement for potentials between static SU(3) sources, Eur. Phys. J. C 47 (2006) 163 [hep-lat/0607025] [INSPIRE].
G.S. Bali, Casimir scaling of SU(3) static potentials, Phys. Rev. D 62 (2000) 114503 [hep-lat/0006022] [INSPIRE].
S. Kratochvila and P. de Forcrand, Observing string breaking with Wilson loops, Nucl. Phys. B 671 (2003) 103 [hep-lat/0306011] [INSPIRE].
M. Pepe and U.-J. Wiese, From Decay to Complete Breaking: Pulling the Strings in SU(2) Yang-Mills Theory, Phys. Rev. Lett. 102 (2009) 191601 [arXiv:0901.2510] [INSPIRE].
A. Athenodorou and M. Teper, in progress.
H. Meyer and M. Teper, Confinement and the effective string theory in SU(N → ∞): A Lattice study, JHEP 12 (2004) 031 [hep-lat/0411039] [INSPIRE].
M. Teper, An Improved Method for Lattice Glueball Calculations, Phys. Lett. B 183 (1987) 345 [INSPIRE].
B. Lucini and M. Teper, SU(N) gauge theories in (2+1)-dimensions: Further results, Phys. Rev. D 66 (2002) 097502 [hep-lat/0206027] [INSPIRE].
M.J. Teper, SU(N) gauge theories in (2+1)-dimensions, Phys. Rev. D 59 (1999) 014512 [hep-lat/9804008] [INSPIRE].
C. Itzykson and M. Nauenberg, Unitary Groups: Representation And Decompositions, Rev. Mod. Phys. 38 (1966) 95 [INSPIRE].
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ArXiv ePrint: 1303.5946
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Athenodorou, A., Teper, M. Closed flux tubes in higher representations and their string description in D=2+1 SU(N) gauge theories. J. High Energ. Phys. 2013, 53 (2013). https://doi.org/10.1007/JHEP06(2013)053
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DOI: https://doi.org/10.1007/JHEP06(2013)053