Abstract
String theory gives a well defined procedure for computing the S-matrix of BPS or a class of massless states, but similar calculation for general massive states is plagued with difficulties due to mass renormalization effect. In this paper we describe a procedure for computing the renormalized masses and S-matrix elements in bosonic string theory for a special class of massive states which do not mix with unphysical states under renormalization. Even though this requires working with off-shell amplitudes which are ambiguous, we show that the renormalized masses and S-matrix elements are free from these ambiguities. We also argue that the masses and S-matrix elements for general external states can be found by examining the locations of the poles and the residues of the S-matrix of special states. Finally we discuss generalizations to heterotic and superstring theories.
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References
E. Witten, Superstring perturbation theory revisited, arXiv:1209.5461 [INSPIRE].
A. Belopolsky, De Rham cohomology of the supermanifolds and superstring BRST cohomology, Phys. Lett. B 403 (1997) 47 [hep-th/9609220] [INSPIRE].
A. Belopolsky, New geometrical approach to superstrings, hep-th/9703183 [INSPIRE].
A. Belopolsky, Picture changing operators in supergeometry and superstring theory, hep-th/9706033 [INSPIRE].
E. D’Hoker and D.H. Phong, Two loop superstrings. 1. Main formulas, Phys. Lett. B 529 (2002) 241 [hep-th/0110247] [INSPIRE].
E. D’Hoker and D.H. Phong, Two loop superstrings. 2. The chiral measure on moduli space, Nucl. Phys. B 636 (2002) 3 [hep-th/0110283] [INSPIRE].
E. D’Hoker and D.H. Phong, Two loop superstrings. 3. Slice independence and absence of ambiguities, Nucl. Phys. B 636 (2002) 61 [hep-th/0111016] [INSPIRE].
E. D’Hoker and D.H. Phong, Two loop superstrings 4: The cosmological constant and modular forms, Nucl. Phys. B 639 (2002) 129 [hep-th/0111040] [INSPIRE].
E. D’Hoker and D.H. Phong, Two-loop superstrings. V. Gauge slice independence of the N-point function, Nucl. Phys. B 715 (2005) 91 [hep-th/0501196] [INSPIRE].
E. D’Hoker and D.H. Phong, Two-loop superstrings VI: Non-renormalization theorems and the 4-point function, Nucl. Phys. B 715 (2005) 3 [hep-th/0501197] [INSPIRE].
E. D’Hoker and D.H. Phong, Two-loop superstrings. VII. Cohomology of chiral amplitudes, Nucl. Phys. B 804 (2008) 421 [arXiv:0711.4314] [INSPIRE].
E. Witten, Notes on supermanifolds and integration, arXiv:1209.2199 [INSPIRE].
E. Witten, Notes on super riemann surfaces and their moduli, arXiv:1209.2459 [INSPIRE].
E. Witten, More on superstring perturbation theory, arXiv:1304.2832 [INSPIRE].
E. Witten, Notes on holomorphic string and superstring theory measures of low genus, arXiv:1306.3621 [INSPIRE].
E. Witten, The feynman iϵ in string theory, arXiv:1307.5124 [INSPIRE].
R. Donagi and E. Witten, Supermoduli space is not projected, arXiv:1304.7798 [INSPIRE].
S. Weinberg, Radiative corrections in string theory, in The Oregon Meeting, Proceedings of the Annual Meeting of the Division of Particles and Fields of the APS, Eugene, Oregon, 1985, R.C. Hwa ed., World Scientific, Singapore (1986).
N. Seiberg, Anomalous dimensions and mass renormalization in string theory, Phys. Lett. B 187 (1987) 56 [INSPIRE].
H. Ooguri and N. Sakai, String loop corrections from fusion of handles and vertex operators, Phys. Lett. B 197 (1987) 109 [INSPIRE].
H. Yamamoto, One loop mass shifts in O(32) open superstring theory, Prog. Theor. Phys. 79 (1988) 189 [INSPIRE].
A. Sen, Mass renormalization and BRST anomaly in string theories, Nucl. Phys. B 304 (1988) 403 [INSPIRE].
S.R. Das, Renormalizing handles and holes in string theory, Phys. Rev. D 38 (1988) 3105 [INSPIRE].
S.-J. Rey, Unified view of BRST anomaly and its cancellation in string amplitudes, Nucl. Phys. B 316 (1989) 197 [INSPIRE].
B. Sundborg, Selfenergies of massive strings, Nucl. Phys. B 319 (1989) 415 [INSPIRE].
N. Marcus, Unitarity and regularized divergences in string amplitudes, Phys. Lett. B 219 (1989) 265 [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].
C.J.H. Lee, BRST anomalies and mass renormalization with anomalous U(1) gauge symmetries in string theory, UMI-92-24830 (1992) [INSPIRE].
A. Berera, The mass renormalization of string theory, Phys. Rev. D 49 (1994) 6674 [INSPIRE].
L. Del Debbio, E. Kerrane and R. Russo, Mass corrections in string theory and lattice field theory, Phys. Rev. D 80 (2009) 025003 [arXiv:0812.3129] [INSPIRE].
D. Chialva, String mass shifts, Nucl. Phys. B 819 (2009) 225 [arXiv:0903.3979] [INSPIRE].
P.C. Nelson, Covariant insertion of general vertex operators, Phys. Rev. Lett. 62 (1989) 993 [INSPIRE].
A.G. Cohen, G.W. Moore, P.C. Nelson and J. Polchinski, An off-shell propagator for string theory, Nucl. Phys. B 267 (1986) 143 [INSPIRE].
A.G. Cohen, G.W. Moore, P.C. Nelson and J. Polchinski, Semi off-shell string amplitudes, Nucl. Phys. B 281 (1987) 127 [INSPIRE].
L. Álvarez-Gaumé, C. Gomez, G.W. Moore and C. Vafa, Strings in the operator formalism, Nucl. Phys. B 303 (1988) 455 [INSPIRE].
L. Álvarez-Gaumé, C. Gomez, P.C. Nelson, G. Sierra and C. Vafa, Fermionic strings in the operator formalism, Nucl. Phys. B 311 (1988) 333 [INSPIRE].
B. Zwiebach, Closed string field theory: quantum action and the B-V master equation, Nucl. Phys. B 390 (1993) 33 [hep-th/9206084] [INSPIRE].
N. Berkovits, Y. Okawa and B. Zwiebach, WZW-like action for heterotic string field theory, JHEP 11 (2004) 038 [hep-th/0409018] [INSPIRE].
P. Di Vecchia et al., N point g loop vertex for a free bosonic theory with vacuum charge Q, Nucl. Phys. B 322 (1989) 317 [INSPIRE].
J. Polchinski, Factorization of bosonic string amplitudes, Nucl. Phys. B 307 (1988) 61 [INSPIRE].
H. Hata and B. Zwiebach, Developing the covariant Batalin-Vilkovisky approach to string theory, Annals Phys. 229 (1994) 177 [hep-th/9301097] [INSPIRE].
A. LeClair, M.E. Peskin and C.R. Preitschopf, String field theory on the conformal plane. 1. Kinematical principles, Nucl. Phys. B 317 (1989) 411 [INSPIRE].
A. LeClair, M.E. Peskin and C.R. Preitschopf, String field theory on the conformal plane. 2. Generalized gluing, Nucl. Phys. B 317 (1989) 464 [INSPIRE].
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Pius, R., Rudra, A. & Sen, A. Mass renormalization in string theory: special states. J. High Energ. Phys. 2014, 58 (2014). https://doi.org/10.1007/JHEP07(2014)058
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DOI: https://doi.org/10.1007/JHEP07(2014)058