Abstract
We compute leading order quantum corrections to the Regge trajectory of a rotating string with massive endpoints using semiclassical methods. We expand the bosonic string action around a classical rotating solution to quadratic order in the fluctuations and perform the canonical quantization of the resulting theory. For a rotating string in D dimensions the intercept receives contributions from D − 3 transverse modes and one mode in the plane of rotation, in addition to a contribution due to the Polchinski-Strominger term of the non-critical effective string action when D ≠ 26. The intercept at leading order is proportional to the expectation value of the worldsheet Hamiltonian of the fluctuations, and this is shown explicitly in several cases. All contributions to the intercept are considered, and we show a simple physical method to renormalize the divergences in them. The intercept converges to known results at the massless limit, and corrections from the masses are explicitly calculated at the long string limit. In the process we also determine the quantum spectrum of the string with massive endpoints, and analyze the asymmetric case of two different endpoint masses.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Chodos and C.B. Thorn, Making the Massless String Massive, Nucl. Phys. B 72 (1974) 509 [INSPIRE].
P.H. Frampton, String Approaches to Hadron Structure, Phys. Rev. D 12 (1975) 538 [INSPIRE].
I. Bars and A.J. Hanson, Quarks at the Ends of the String, Phys. Rev. D 13 (1976) 1744 [INSPIRE].
W.A. Bardeen, I. Bars, A.J. Hanson and R.D. Peccei, A Study of the Longitudinal Kink Modes of the String, Phys. Rev. D 13 (1976) 2364 [INSPIRE].
K. Kikkawa and M.-a. Sato, Lattice Gauge Theory, String Model and Hadron Spectrum, Phys. Rev. Lett. 38 (1977) 1309 [INSPIRE].
M. Ida, Relativistic Motion of Massive Quarks Joined by a Massless String, Prog. Theor Phys. 59 (1978) 1661 [INSPIRE].
M. Kruczenski, L.A. Pando Zayas, J. Sonnenschein and D. Vaman, Regge trajectories for mesons in the holographic dual of large-N c QCD, JHEP 06 (2005) 046 [hep-th/0410035] [INSPIRE].
J. Sonnenschein, Holography Inspired Stringy Hadrons, Prog. Part. Nucl. Phys. 92 (2017) 1 [arXiv:1602.00704] [INSPIRE].
J. Sonnenschein and D. Weissman, Rotating strings confronting PDG mesons, JHEP 08 (2014) 013 [arXiv:1402.5603] [INSPIRE].
J. Sonnenschein and D. Weissman, A rotating string model versus baryon spectra, JHEP 02 (2015) 147 [arXiv:1408.0763] [INSPIRE].
G.S. Sharov, Instability of the Y string baryon model within classical dynamics, Phys. Atom. Nucl. 65 (2002) 906 [INSPIRE].
G. ’t Hooft, Minimal strings for baryons, in Hadrons and Strings Workshop: A Trento ECT Workshop Trento, Italy, 12-17 July 2004 [hep-th/0408148] [INSPIRE].
J. Sonnenschein and D. Weissman, A tetraquark or not a tetraquark? A holography inspired stringy hadron (HISH) perspective, Nucl. Phys. B 920 (2017) 319 [arXiv:1606.02732] [INSPIRE].
L. Blech, N. Sircar and J. Sonnenschein, Charged stringy mesons.
R.D. Pisarski and J.D. Stack, Spin Dependent Potential for Heavy Fermions on the Ends of a String, Nucl. Phys. B 286 (1987) 657 [INSPIRE].
M.G. Olsson and K. Williams, QCD and the relativistic flux tube with fermionic ends, Phys. Rev. D 48 (1993) 417 [INSPIRE].
A. Sever and A. Zhiboedov, On Fine Structure of Strings: The Universal Correction to the Veneziano Amplitude, JHEP 06 (2018) 054 [arXiv:1707.05270] [INSPIRE].
L.D. Solovev, Relativistic quantum model of confinement and the current quark masses, Phys. Rev. D 58 (1998) 035005 [hep-ph/9803483] [INSPIRE].
A. Inopin and G.S. Sharov, Hadronic Regge trajectories: Problems and approaches, Phys. Rev. D 63 (2001) 054023 [hep-ph/9905499] [INSPIRE].
T.J. Allen, C. Goebel, M.G. Olsson and S. Veseli, Analytic quantization of the QCD string, Phys. Rev. D 64 (2001) 094011 [hep-ph/0106026] [INSPIRE].
M. Baker and R. Steinke, Semiclassical quantization of effective string theory and Regge trajectories, Phys. Rev. D 65 (2002) 094042 [hep-th/0201169] [INSPIRE].
O. Aharony and E. Karzbrun, On the effective action of confining strings, JHEP 06 (2009) 012 [arXiv:0903.1927] [INSPIRE].
O. Aharony and Z. Komargodski, The Effective Theory of Long Strings, JHEP 05 (2013) 118 [arXiv:1302.6257] [INSPIRE].
J. Zahn, Semiclassical energy of open Nambu-Goto strings, Phys. Rev. D 97 (2018) 066028 [arXiv:1605.07928] [INSPIRE].
J. Zahn, The semi-classical energy of the Chodos-Thorn string, arXiv:1703.03721 [INSPIRE].
S. Frolov and A.A. Tseytlin, Semiclassical quantization of rotating superstring in AdS 5 × S 5, JHEP 06 (2002) 007 [hep-th/0204226] [INSPIRE].
L.A. Pando Zayas, J. Sonnenschein and D. Vaman, Regge trajectories revisited in the gauge/string correspondence, Nucl. Phys. B 682 (2004) 3 [hep-th/0311190] [INSPIRE].
A.M. Polyakov, Quantum Geometry of Bosonic Strings, Phys. Lett. B 103 (1981) 207 [INSPIRE].
J. Polchinski and A. Strominger, Effective string theory, Phys. Rev. Lett. 67 (1991) 1681 [INSPIRE].
S. Hellerman and I. Swanson, String Theory of the Regge Intercept, Phys. Rev. Lett. 114 (2015) 111601 [arXiv:1312.0999] [INSPIRE].
G. Lambiase and V.V. Nesterenko, Quark mass correction to the string potential, Phys. Rev. D 54 (1996) 6387 [hep-th/9510221] [INSPIRE].
G. Lambiase, V.V. Nesterenko and M. Bordag, Casimir energy of a ball and cylinder in the zeta function technique, J. Math. Phys. 40 (1999) 6254 [hep-th/9812059] [INSPIRE].
J. Zahn, The excitation spectrum of rotating strings with masses at the ends, JHEP 12 (2013) 047 [arXiv:1310.0253] [INSPIRE].
S. Hellerman, S. Maeda, J. Maltz and I. Swanson, Effective String Theory Simplified, JHEP 09 (2014) 183 [arXiv:1405.6197] [INSPIRE].
O. Aharony and M. Field, On the effective theory of long open strings, JHEP 01 (2011) 065 [arXiv:1008.2636] [INSPIRE].
O. Aharony, M. Field and N. Klinghoffer, The effective string spectrum in the orthogonal gauge, JHEP 04 (2012) 048 [arXiv:1111.5757] [INSPIRE].
S. Hellerman and I. Swanson, Boundary Operators in Effective String Theory, JHEP 04 (2017) 085 [arXiv:1609.01736] [INSPIRE].
J. Sonnenschein and D. Weissman, The decay width of stringy hadrons, Nucl. Phys. B 927 (2018) 368 [arXiv:1705.10329] [INSPIRE].
J. Dai and J. Polchinski, The Decay of Macroscopic Fundamental Strings, Phys. Lett. B 220 (1989) 387 [INSPIRE].
D. Mitchell, B. Sundborg and N. Turok, Decays of Massive Open Strings, Nucl. Phys. B 335 (1990) 621 [INSPIRE].
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: 1801.00798
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
Sonnenschein, J., Weissman, D. Quantizing the rotating string with massive endpoints. J. High Energ. Phys. 2018, 148 (2018). https://doi.org/10.1007/JHEP06(2018)148
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2018)148