Abstract
Most of the massive states in superstring theory are expected to undergo mass renormalization at one loop order. Typically these corrections should contain imaginary parts, indicating that the states are unstable against decay into lighter particles. However in such cases, direct computation of the renormalized mass using superstring perturbation theory yields divergent result. Previous approaches to this problem involve various analytic continuation techniques, or deforming the integral over the moduli space of the torus with two punctures into the complexified moduli space near the boundary. In this paper we use insights from string field theory to describe a different approach that gives manifestly finite result for the mass shift satisfying unitarity relations. The procedure is applicable to all states of (compactified) type II and heterotic string theories. We illustrate this by computing the one loop correction to the mass of the first massive state on the leading Regge trajectory in SO(32) heterotic string theory.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
B. Sundborg, Selfenergies of Massive Strings, Nucl. Phys. B 319 (1989) 415 [INSPIRE].
K. Amano and A. Tsuchiya, Mass Splittings and the Finiteness Problem of Mass Shifts in the Type II Superstring at One Loop, Phys. Rev. D 39 (1989) 565 [INSPIRE].
B. Sundborg, Infinite mass shifts of open superstrings as a possible signal of confinement, Nucl. Phys. B 338 (1990) 101 [INSPIRE].
E. D’Hoker and D.H. Phong, Momentum analyticity and finiteness of the one loop superstring amplitude, Phys. Rev. Lett. 70 (1993) 3692 [hep-th/9302003] [INSPIRE].
E. D’Hoker and D.H. Phong, Dispersion relations in string theory, Theor. Math. Phys. 98 (1994)306 [hep-th/9404128] [INSPIRE].
E. D’Hoker and D.H. Phong, The Box graph in superstring theory, Nucl. Phys. B 440 (1995) 24 [hep-th/9410152] [INSPIRE].
A. Berera, Unitary string amplitudes, Nucl. Phys. B 411 (1994) 157 [INSPIRE].
E. Witten, The Feynman iϵ in String Theory, JHEP 04 (2015) 055 [arXiv:1307.5124] [INSPIRE].
K. Amano, A Finite String Loop Amplitude in a Finite Form, Nucl. Phys. B 328 (1989) 510 [INSPIRE].
J.L. Montag and W.I. Weisberger, A Finite representation for a superstring scattering amplitude and its low-energy limit, Nucl. Phys. B 363 (1991) 527 [INSPIRE].
N. Marcus, Unitarity and Regularized Divergences in String Amplitudes, Phys. Lett. B 219 (1989) 265 [INSPIRE].
R. Iengo and J. Kalkkinen, Decay modes of highly excited string states and Kerr black holes, JHEP 11 (2000) 025 [hep-th/0008060] [INSPIRE].
R. Iengo and J.G. Russo, The decay of massive closed superstrings with maximum angular momentum, JHEP 11 (2002) 045 [hep-th/0210245] [INSPIRE].
C.B. Chiu and S. Matsuda, Intermediate Mass Distribution of Dual Resonance Pomeron, Nucl. Phys. B 134 (1978) 463 [INSPIRE].
V.A. Miransky, V.P. Shelest, B.V. Struminskii and G.M. Zinovjev, Dual resonance model and statistical bootstrap, Phys. Lett. B 43 (1973) 73.
M.B. Green and G. Veneziano, Average properties of dual resonances, Phys. Lett. B 36 (1971) 477 [INSPIRE].
D. Mitchell, N. Turok, R. Wilkinson and P. Jetzer, The Decay of Highly Excited Open Strings, Nucl. Phys. B 315 (1989) 1 [Erratum ibid. B 322 (1989) 628] [INSPIRE].
J. Dai and J. Polchinski, The Decay of Macroscopic Fundamental Strings, Phys. Lett. B 220 (1989) 387 [INSPIRE].
H. Okada and A. Tsuchiya, The Decay Rate of the Massive Modes in Type I Superstring, Phys. Lett. B 232 (1989) 91 [INSPIRE].
D. Mitchell, B. Sundborg and N. Turok, Decays of Massive Open Strings, Nucl. Phys. B 335 (1990) 621 [INSPIRE].
D. Amati and J.G. Russo, Fundamental strings as black bodies, Phys. Lett. B 454 (1999) 207 [hep-th/9901092] [INSPIRE].
J.L. Manes, Emission spectrum of fundamental strings: An algebraic approach, Nucl. Phys. B 621 (2002) 37 [hep-th/0109196] [INSPIRE].
R. Pius and A. Sen, Cutkosky Rules for Superstring Field Theory, JHEP 10 (2016) 024 [arXiv:1604.01783] [INSPIRE].
S. Mandelstam, Interacting String Picture of Dual Resonance Models, Nucl. Phys. B 64 (1973)205 [INSPIRE].
S. Mandelstam, Interacting String Picture of the Neveu-Schwarz-Ramond Model, Nucl. Phys. B 69 (1974) 77 [INSPIRE].
J. Greensite and F.R. Klinkhamer, New Interactions for Superstrings, Nucl. Phys. B 281 (1987)269 [INSPIRE].
J. Greensite and F.R. Klinkhamer, Contact Interactions in Closed Superstring Field Theory, Nucl. Phys. B 291 (1987) 557 [INSPIRE].
J. Greensite and F.R. Klinkhamer, Superstring Amplitudes and Contact Interactions, Nucl. Phys. B 304 (1988) 108 [INSPIRE].
M.B. Green and N. Seiberg, Contact Interactions in Superstring Theory, Nucl. Phys. B 299 (1988) 559 [INSPIRE].
N. Ishibashi, Light-cone gauge superstring field theory in linear dilaton background, arXiv:1605.04666 [INSPIRE].
A. Sen, S-duality Improved Superstring Perturbation Theory, JHEP 11 (2013) 029 [arXiv:1304.0458] [INSPIRE].
E. Witten, Superstring Perturbation Theory Revisited, arXiv:1209.5461 [INSPIRE].
A. Sen, Off-shell Amplitudes in Superstring Theory, Fortsch. Phys. 63 (2015) 149 [arXiv:1408.0571] [INSPIRE].
H. Hata and B. Zwiebach, Developing the covariant Batalin-Vilkovisky approach to string theory, Annals Phys. 229 (1994) 177 [hep-th/9301097] [INSPIRE].
R. Pius, A. Rudra and A. Sen, Mass Renormalization in String Theory: General States, JHEP 07 (2014) 062 [arXiv:1401.7014] [INSPIRE].
A. Sen, Unitarity of Superstring Field Theory, arXiv:1607.08244 [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: 1607.06500
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, 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 license, and indicate if changes were made.
About this article
Cite this article
Sen, A. One loop mass renormalization of unstable particles in superstring theory. J. High Energ. Phys. 2016, 50 (2016). https://doi.org/10.1007/JHEP11(2016)050
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2016)050