Abstract
I describe the recently proposed quantization of bosonic string about the meanfield ground state, paying special attention to the differences from the usual quantization about the classical vacuum which turns out to be unstable for d > 2. In particular, the string susceptibility index γstr is 1 in the usual perturbation theory, but equals 1/2 in the mean-field approximation that applies for 2 < d < 26. I show that the total central charge equals zero in the mean-field approximation and argue that fluctuations about the mean field do not spoil conformal invariance.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
V.A. Kazakov, A.A. Migdal and I.K. Kostov, Critical Properties of Randomly Triangulated Planar Random Surfaces, Phys. Lett. B 157 (1985) 295 [INSPIRE].
F. David, Planar Diagrams, Two-Dimensional Lattice Gravity and Surface Models, Nucl. Phys. B 257 (1985) 45 [INSPIRE].
J. Ambjørn, B. Durhuus and J. Fröhlich, Diseases of Triangulated Random Surface Models and Possible Cures, Nucl. Phys. B 257 (1985) 433 [INSPIRE].
V.G. Knizhnik, A.M. Polyakov and A.B. Zamolodchikov, Fractal Structure of 2D Quantum Gravity, Mod. Phys. Lett. A 3 (1988) 819 [INSPIRE].
F. David, Conformal Field Theories Coupled to 2D Gravity in the Conformal Gauge, Mod. Phys. Lett. A 3 (1988) 1651 [INSPIRE].
J. Distler and H. Kawai, Conformal Field Theory and 2D Quantum Gravity, Nucl. Phys. B 321 (1989) 509 [INSPIRE].
J. Ambjørn, B. Durhuus and T. Jonsson, Quantum geometry. A statistical field theory approach, Cambridge University Press, Cambridge U.K. (1997).
J. Ambjørn and B. Durhuus, Regularized bosonic strings need extrinsic curvature, Phys. Lett. B 188 (1987) 253 [INSPIRE].
Y. Makeenko, QCD String as an Effective String, in proceedings of the Low dimensional physics and gauge principles, Yerevan, Armenia and Tbilisi, Georgia, 21-29 September 2011, World Scientific (2012), pp. 211-222 [arXiv:1206.0922] [INSPIRE].
J. Polchinski and A. Strominger, Effective string theory, Phys. Rev. Lett. 67 (1991) 1681 [INSPIRE].
S. Dubovsky, R. Flauger and V. Gorbenko, Effective String Theory Revisited, JHEP 09 (2012) 044 [arXiv:1203.1054] [INSPIRE].
O. Aharony and Z. Komargodski, The Effective Theory of Long Strings, JHEP 05 (2013) 118 [arXiv:1302.6257] [INSPIRE].
S. Dubovsky, R. Flauger and V. Gorbenko, Flux Tube Spectra from Approximate Integrability at Low Energies, J. Exp. Theor. Phys. 120 (2015) 399 [arXiv:1404.0037] [INSPIRE].
S. Hellerman, S. Maeda, J. Maltz and I. Swanson, Effective String Theory Simplified, JHEP 09 (2014) 183 [arXiv:1405.6197] [INSPIRE].
B.B. Brandt and M. Meineri, Effective string description of confining flux tubes, Int. J. Mod. Phys. A 31 (2016) 1643001 [arXiv:1603.06969] [INSPIRE].
J.M. 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. Alvarez, The Static Potential in String Models, Phys. Rev. D 24 (1981) 440 [INSPIRE].
J.F. Arvis, The Exact q q Potential in Nambu String Theory, Phys. Lett. B 127 (1983) 106 [INSPIRE].
P. Olesen, Strings and QCD, Phys. Lett. B 160 (1985) 144 [INSPIRE].
J. Ambjørn and Y. Makeenko, String theory as a Lilliputian world, Phys. Lett. B 756 (2016) 142 [arXiv:1601.00540] [INSPIRE].
J. Ambjørn and Y. Makeenko, Scaling behavior of regularized bosonic strings, Phys. Rev. D 93 (2016) 066007 [arXiv:1510.03390] [INSPIRE].
J. Ambjørn and Y. Makeenko, Stability of the nonperturbative bosonic string vacuum, Phys. Lett. B 770 (2017) 352 [arXiv:1703.05382] [INSPIRE].
J. Ambjørn and Y. Makeenko, The use of Pauli-Villars regularization in string theory, Int. J. Mod. Phys. A 32 (2017) 1750187 [arXiv:1709.00995] [INSPIRE].
A.M. Polyakov, Quantum Geometry of Bosonic Strings, Phys. Lett. B 103 (1981) 207 [INSPIRE].
B. Durhuus, P. Olesen and J.L. Petersen, Polyakov’s Quantized String With Boundary Terms, Nucl. Phys. B 198 (1982) 157 [INSPIRE].
O. Alvarez, Theory of Strings with Boundaries: Fluctuations, Topology and Quantum Geometry, Nucl. Phys. B 216 (1983) 125 [INSPIRE].
Y. Makeenko, Methods of contemporary gauge theory, Cambridge University Press, Cambridge U.K. (2002), pp. 208-210.
Y. Makeenko, An interplay between static potential and Reggeon trajectory for QCD string, Phys. Lett. B 699 (2011) 199 [arXiv:1103.2269] [INSPIRE].
L. Brink and H.B. Nielsen, A Simple Physical Interpretation of the Critical Dimension of Space-Time in Dual Models, Phys. Lett. B 45 (1973) 332 [INSPIRE].
A.M. Polyakov, Gauge fields and strings, Harwood Academic Publishers, Reading U.K. (1987), pp. 173-174.
R.C. Brower, Spectrum generating algebra and no ghost theorem for the dual model, Phys. Rev. D 6 (1972) 1655 [INSPIRE].
P. Goddard and C.B. Thorn, Compatibility of the Dual Pomeron with Unitarity and the Absence of Ghosts in the Dual Resonance Model, Phys. Lett. B 40 (1972) 235 [INSPIRE].
A.B. Zamolodchikov, On the entropy of random surfaces, Phys. Lett. B 117 (1982) 87 [INSPIRE].
S. Chaudhuri, H. Kawai and S.H.H. Tye, Path Integral Formulation of Closed Strings, Phys. Rev. D 36 (1987) 1148 [INSPIRE].
I.K. Kostov and A. Krzywicki, On the Entropy of Random Surfaces With Arbitrary Genus, Phys. Lett. B 187 (1987) 149 [INSPIRE].
A. Zamolodchikov and A. Zamolodchikov, Lectures on Liouville theory and matrix models, (2008) and online pdf version at http://qft.itp.ac.ru/ZZ.pdf.
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1802.07541
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Makeenko, Y. Mean field quantization of effective string. J. High Energ. Phys. 2018, 104 (2018). https://doi.org/10.1007/JHEP07(2018)104
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2018)104