Abstract
Even at tree level, the first quantized string theory suffers from apparent short distance singularities associated with collision of vertex operators that prevent us from straightforward numerical computation of various quantities. Examples include string theory S-matrix for generic external momenta and computation of the spectrum of string theory under a marginal deformation of the world-sheet theory. The former requires us to define the S-matrix via analytic continuation or as limits of contour integrals in complexified moduli space, while the latter requires us to use an ultraviolet cut-off at intermediate steps. In contrast, string field theory does not suffer from such divergences. In this paper we show how string field theory can be used to generate an explicit algorithm for computing tree level amplitudes in any string theory that does not suffer from any short distance divergence from integration over the world-sheet variables. We also use string field theory to compute second order mass shift of string states under a marginal deformation without having to use any cut-off at intermediate steps. We carry out the analysis in a broad class of string field theories, thereby making it manifest that the final results are independent of the extra data that go into the formulation of string field theory. We also comment on the generalization of this analysis to higher genus amplitudes.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M. Schnabl, Analytic solution for tachyon condensation in open string field theory, Adv. Theor. Math. Phys.10 (2006) 433 [hep-th/0511286] [INSPIRE].
C. de Lacroix, H. Erbin, S.P. Kashyap, A. Sen and M. Verma, Closed Superstring Field Theory and its Applications, Int. J. Mod. Phys.A 32 (2017) 1730021 [arXiv:1703.06410] [INSPIRE].
D. Friedan, E.J. Martinec and S.H. Shenker, Conformal Invariance, Supersymmetry and String Theory, Nucl. Phys.B 271 (1986) 93 [INSPIRE].
E. Witten, Noncommutative Geometry and String Field Theory, Nucl. Phys.B 268 (1986) 253 [INSPIRE].
M. Saadi and B. Zwiebach, Closed String Field Theory from Polyhedra, Annals Phys.192 (1989) 213 [INSPIRE].
T. Kugo, H. Kunitomo and K. Suehiro, Nonpolynomial Closed String Field Theory, Phys. Lett.B 226 (1989) 48 [INSPIRE].
T. Kugo and K. Suehiro, Nonpolynomial Closed String Field Theory: Action and Its Gauge Invariance, Nucl. Phys.B 337 (1990) 434 [INSPIRE].
H. Sonoda and B. Zwiebach, Closed String Field Theory Loops With Symmetric Factorizable Quadratic Differentials, Nucl. Phys.B 331 (1990) 592 [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].
B. Zwiebach, Oriented open-closed string theory revisited, Annals Phys.267 (1998) 193 [hep-th/9705241] [INSPIRE].
R. Saroja and A. Sen, Picture changing operators in closed fermionic string field theory, Phys. Lett.B 286 (1992) 256 [hep-th/9202087] [INSPIRE].
T. Erler, S. Konopka and I. Sachs, Resolving Witten‘s superstring field theory, JHEP04 (2014) 150 [arXiv:1312.2948] [INSPIRE].
T. Erler, S. Konopka and I. Sachs, NS-NS Sector of Closed Superstring Field Theory, JHEP08 (2014) 158 [arXiv:1403.0940] [INSPIRE].
A. Sen, BV Master Action for Heterotic and Type II String Field Theories, JHEP02 (2016) 087 [arXiv:1508.05387] [INSPIRE].
T. Erler, Y. Okawa and T. Takezaki, Complete Action for Open Superstring Field Theory with Cyclic A∞ Structure, JHEP08 (2016) 012 [arXiv:1602.02582] [INSPIRE].
S. Konopka and I. Sachs, Open Superstring Field Theory on the Restricted Hilbert Space, JHEP04 (2016) 164 [arXiv:1602.02583] [INSPIRE].
N. Berkovits, SuperPoincaré invariant superstring field theory, Nucl. Phys.B 450 (1995) 90 [Erratum ibid.B 459 (1996) 439] [hep-th/9503099] [INSPIRE].
N. Berkovits, The Ramond sector of open superstring field theory, JHEP11 (2001) 047 [hep-th/0109100] [INSPIRE].
Y. Okawa and B. Zwiebach, Heterotic string field theory, JHEP07 (2004) 042 [hep-th/0406212] [INSPIRE].
N. Berkovits, Y. Okawa and B. Zwiebach, WZW-like action for heterotic string field theory, JHEP11 (2004) 038 [hep-th/0409018] [INSPIRE].
H. Kunitomo and Y. Okawa, Complete action for open superstring field theory, PTEP2016 (2016) 023B01 [arXiv:1508.00366] [INSPIRE].
A.J. Hanson and J.-P. Sha, A contour integral representation for the dual five-point function and a symmetry of the genus-4 surface in R6 , J. Phys.A 39 (2006) 2509 [math-ph/0510064] [INSPIRE].
E. Witten, The Feynman iE in String Theory, JHEP04 (2015) 055 [arXiv:1307.5124] [INSPIRE].
S. Mizera, Combinatorics and Topology of Kawai-Lewellen-Tye Relations, JHEP08 (2017) 097 [arXiv:1706.08527] [INSPIRE].
W. Siegel, Covariantly Second Quantized String. 2, Phys. Lett.149B (1984) 157 [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. Sen and B. Zwiebach, A proof of local background independence of classical closed string field theory, Nucl. Phys.B 414 (1994) 649 [hep-th/9307088] [INSPIRE].
A. Sen and B. Zwiebach, Quantum background independence of closed string field theory, Nucl. Phys.B 423 (1994) 580 [hep-th/9311009] [INSPIRE].
A. Sen, Background Independence of Closed Superstring Field Theory, JHEP02 (2018) 155 [arXiv:1711.08468] [INSPIRE].
M. Schnabl, Comments on marginal deformations in open string field theory, Phys. Lett.B 654 (2007) 194 [hep-th/0701248] [INSPIRE].
M. Kiermaier, Y. Okawa, L. Rastelli and B. Zwiebach, Analytic solutions for marginal deformations in open string field theory, JHEP01 (2008) 028 [hep-th/0701249] [INSPIRE].
E. Fuchs, M. Kroyter and R. Potting, Marginal deformations in string field theory, JHEP09 (2007) 101 [arXiv:0704.2222] [INSPIRE].
M. Kiermaier, Y. Okawa and P. Soler, Solutions from boundary condition changing operators in open string field theory, JHEP03 (2011) 122 [arXiv:1009.6185] [INSPIRE].
T. Erler and C. Maccaferri, String Field Theory Solution for Any Open String Background, JHEP10 (2014) 029 [arXiv:1406.3021] [INSPIRE].
A. Sen, Gauge Invariant 1PI Effective Action for Superstring Field Theory, JHEP06 (2015) 022 [arXiv:1411.7478] [INSPIRE].
A. Sen, Supersymmetry Restoration in Superstring Perturbation Theory, JHEP12 (2015) 075 [arXiv:1508.02481] [INSPIRE].
S. Mukherji and A. Sen, Some all order classical solutions in nonpolynomial closed string field theory, Nucl. Phys. B 363 (1991) 639 [INSPIRE].
T. Kugo and B. Zwiebach, Target space duality as a symmetry of string field theory, Prog. Theor. Phys.87 (1992) 801 [hep-th/9201040] [INSPIRE].
M. Cho, S. Collier and X. Yin, Strings in Ramond-Ramond Backgrounds from the Neveu-Schwarz-Ramond Formalism, arXiv:1811.00032 [INSPIRE].
S.F. Moosavian and R. Pius, Hyperbolic Geometry of Superstring Perturbation Theory, arXiv:1703.10563 [INSPIRE].
S.F. Moosavian and R. Pius, Hyperbolic geometry and closed bosonic string field theory. Part I. The string vertices via hyperbolic Riemann surfaces, JHEP08 (2019) 157 [arXiv:1706.07366] [INSPIRE].
S.F. Moosavian and R. Pius, Hyperbolic geometry and closed bosonic string field theory. Part II. The rules for evaluating the quantum BV master action, JHEP08 (2019) 177 [arXiv:1708.04977] [INSPIRE].
S. Ghosh and S. Raju, Breakdown of String Perturbation Theory for Many External Particles, Phys. Rev. Lett.118 (2017) 131602 [arXiv:1611.08003] [INSPIRE].
P. Di Vecchia, R. Nakayama, J.L. Petersen and S. Sciuto, Properties of the Three Reggeon Vertex in String Theories, Nucl. Phys.B 282 (1987) 103 [INSPIRE].
A. Sen, Off-shell Amplitudes in Superstring Theory, Fortsch. Phys.63 (2015) 149 [arXiv:1408.0571] [INSPIRE].
A. Sen and E. Witten, Filling the gaps with PCO’s, JHEP09 (2015) 004 [arXiv:1504.00609] [INSPIRE].
J.J. Atick, G.W. Moore and A. Sen, Catoptric Tadpoles, Nucl. Phys.B 307 (1988) 221 [INSPIRE].
E. Witten, Superstring Perturbation Theory Revisited, arXiv:1209.5461 [INSPIRE].
R. Pius, A. Rudra and A. Sen, Mass Renormalization in String Theory: Special States, JHEP07 (2014) 058 [arXiv:1311.1257] [INSPIRE].
R. Pius, A. Rudra and A. Sen, Mass Renormalization in String Theory: General States, JHEP07 (2014) 062 [arXiv:1401.7014] [INSPIRE].
R. Pius, A. Rudra and A. Sen, String Perturbation Theory Around Dynamically Shifted Vacuum, JHEP10 (2014) 070 [arXiv:1404.6254] [INSPIRE].
R. Pius and A. Sen, Cutkosky rules for superstring field theory, JHEP10 (2016) 024 [Erratum ibid.09 (2018) 122] [arXiv:1604.01783] [INSPIRE].
A. Sen, Equivalence of Two Contour Prescriptions in Superstring Perturbation Theory, JHEP04 (2017) 025 [arXiv:1610.00443] [INSPIRE].
A. Sen, One Loop Mass Renormalization of Unstable Particles in Superstring Theory, JHEP11 (2016) 050 [arXiv:1607.06500] [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: 1902.00263
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
Sen, A. String field theory as world-sheet UV regulator. J. High Energ. Phys. 2019, 119 (2019). https://doi.org/10.1007/JHEP10(2019)119
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2019)119