Abstract
In some string theories, e.g. SO(32) heterotic string theory on Calabi-Yau manifolds, a massless field with a tree level potential can acquire a tachyonic mass at the one loop level, forcing us to quantize the theory around a new background that is not a solution to the classical equations of motion and hence is not described by a conformally invariant world-sheet theory. We describe a systematic procedure for carrying out string perturbation theory around such backgrounds.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M. Dine, N. Seiberg and E. Witten, Fayet-Iliopoulos Terms in String Theory, Nucl. Phys. B 289 (1987) 589 [INSPIRE].
J.J. Atick, L.J. Dixon and A. Sen, String Calculation of Fayet-Iliopoulos d Terms in Arbitrary Supersymmetric Compactifications, Nucl. Phys. B 292 (1987) 109 [INSPIRE].
M. Dine, I. Ichinose and N. Seiberg, F terms and d Terms in String Theory, Nucl. Phys. B 293 (1987) 253 [INSPIRE].
M.B. Green and N. Seiberg, Contact Interactions in Superstring Theory, Nucl. Phys. B 299 (1988) 559 [INSPIRE].
E. Witten, More On Superstring Perturbation Theory, arXiv:1304.2832 [INSPIRE].
N. Berkovits and E. Witten, Supersymmetry Breaking Effects using the Pure Spinor Formalism of the Superstring, JHEP 06 (2014) 127 [arXiv:1404.5346] [INSPIRE].
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. I. Main formulas, Phys. Lett. B 529 (2002) 241 [hep-th/0110247] [INSPIRE].
E. D’Hoker and D.H. Phong, Two loop superstrings. II. 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. III. 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. IV. 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, Notes On Holomorphic String And Superstring Theory Measures Of Low Genus, arXiv:1306.3621 [INSPIRE].
E. Witten, The Feynman i \( \epsilon \) in String Theory, arXiv:1307.5124 [INSPIRE].
R. Donagi and E. Witten, Supermoduli Space Is Not Projected, arXiv:1304.7798 [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].
W. Fischler and L. Susskind, Dilaton Tadpoles, String Condensates and Scale Invariance, Phys. Lett. B 171 (1986) 383 [INSPIRE].
W. Fischler and L. Susskind, Dilaton Tadpoles, String Condensates and Scale Invariance. 2., Phys. Lett. B 173 (1986) 262 [INSPIRE].
B.W. Lee, Renormalization of the σ-model, Nucl. Phys. B 9 (1969) 649 [INSPIRE].
K. Bardakci, Dual models and spontaneous symmetry breaking, Nucl. Phys. B 68 (1974) 331 [INSPIRE].
K. Bardakci, Dual models and spontaneous symmetry breaking II, Nucl. Phys. B 70 (1974) 397 [INSPIRE].
K. Bardakci and M.B. Halpern, Explicit Spontaneous Breakdown in a Dual Model, Phys. Rev. D 10 (1974) 4230 [INSPIRE].
E. Dudas, G. Pradisi, M. Nicolosi and A. Sagnotti, On tadpoles and vacuum redefinitions in string theory, Nucl. Phys. B 708 (2005) 3 [hep-th/0410101] [INSPIRE].
J.J. Atick and A. Sen, Two Loop Dilaton Tadpole Induced by Fayet-Iliopoulos D Terms in Compactified Heterotic String Theories, Nucl. Phys. B 296 (1988) 157 [INSPIRE].
E. D’Hoker and D.H. Phong, Two-loop vacuum energy for Calabi-Yau orbifold models, Nucl. Phys. B 877 (2013) 343 [arXiv:1307.1749] [INSPIRE].
E. D’Hoker, Topics in Two-Loop Superstring Perturbation Theory, arXiv:1403.5494 [INSPIRE].
R. Pius, A. Rudra and A. Sen, Mass Renormalization in String Theory: Special States, JHEP 07 (2014) 058 [arXiv:1311.1257] [INSPIRE].
R. Pius, A. Rudra and A. Sen, Mass Renormalization in String Theory: General States, JHEP 07 (2014) 062 [arXiv:1401.7014] [INSPIRE].
J.J. Atick, G.W. Moore and A. Sen, Catoptric Tadpoles, Nucl. Phys. B 307 (1988) 221 [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: 1404.6254
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
Pius, R., Rudra, A. & Sen, A. String perturbation theory around dynamically shifted vacuum. J. High Energ. Phys. 2014, 70 (2014). https://doi.org/10.1007/JHEP10(2014)070
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2014)070