Abstract
Long ago, Nemeschansky and Sen demonstrated that the Ricci-flat metric on a Calabi-Yau manifold could be corrected, order by order in perturbation theory, to produce a conformally invariant (2, 2) nonlinear sigma model. Here we extend this result to (0, 2) sigma models for stable holomorphic vector bundles over Calabi-Yaus.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L. Álvarez-Gaumé, S.R. Coleman and P.H. Ginsparg, Finiteness of Ricci Flat N = 2 Supersymmetric σ Models, Commun. Math. Phys. 103 (1986) 423 [INSPIRE].
M.T. Grisaru, A.E.M. van de Ven and D. Zanon, Four Loop β-function for the N = 1 and N =2 Supersymmetric Nonlinear σ-model in Two-Dimensions,Phys. Lett. B 173(1986) 423 [INSPIRE].
D. Nemeschansky and A. Sen, Conformal Invariance of Supersymmetric σ Models on Calabi-Yau Manifolds, Phys. Lett. B 178 (1986) 365 [INSPIRE].
M. Dine, N. Seiberg, X.G. Wen and E. Witten, Nonperturbative Effects on the String World Sheet, Nucl. Phys. B 278 (1986) 769 [INSPIRE].
E. Witten, New Issues in Manifolds of SU(3) Holonomy, Nucl. Phys. B 268 (1986) 79 [INSPIRE].
L. Witten and E. Witten, Large Radius Expansion of Superstring Compactifications, Nucl. Phys. B 281 (1987) 109 [INSPIRE].
J. Distler and B.R. Greene, Aspects of (2, 0) String Compactifications, Nucl. Phys. B 304 (1988) 1 [INSPIRE].
A. Basu and S. Sethi, World sheet stability of (0, 2) linear σ-models, Phys. Rev. D 68 (2003) 025003 [hep-th/0303066] [INSPIRE].
C. Beasley and E. Witten, Residues and world sheet instantons, JHEP 10 (2003) 065 [hep-th/0304115] [INSPIRE].
M. Bertolini and M.R. Plesser, Worldsheet instantons and (0, 2) linear models, JHEP 08 (2015) 081 [arXiv:1410.4541] [INSPIRE].
L.B. Anderson, J. Gray and E. Sharpe, Algebroids, Heterotic Moduli Spaces and the Strominger System, JHEP 07 (2014) 037 [arXiv:1402.1532] [INSPIRE].
X. de la Ossa and E.E. Svanes, Holomorphic Bundles and the Moduli Space of N = 1 Supersymmetric Heterotic Compactifications, JHEP 10 (2014) 123 [arXiv:1402.1725] [INSPIRE].
M. Dine and N. Seiberg, Nonrenormalization Theorems in Superstring Theory, Phys. Rev. Lett. 57 (1986) 2625 [INSPIRE].
C.M. Hull and E. Witten, Supersymmetric σ-models and the Heterotic String, Phys. Lett. B 160 (1985) 398 [INSPIRE].
A. Sen, (2, 0) Supersymmetry and Space-Time Supersymmetry in the Heterotic String Theory, Nucl. Phys. B 278 (1986) 289 [INSPIRE].
S. Groot Nibbelink and L. Horstmeyer, Super Weyl invariance: BPS equations from heterotic worldsheets, JHEP 07 (2012) 054 [arXiv:1203.6827] [INSPIRE].
J. Gillard, G. Papadopoulos and D. Tsimpis, Anomaly, fluxes and (2, 0) heterotic string compactifications, JHEP 06 (2003) 035 [hep-th/0304126] [INSPIRE].
C. Quigley, S. Sethi and M. Stern, Novel Branches of (0, 2) Theories, JHEP 09 (2012) 064 [arXiv:1206.3228] [INSPIRE].
A. Strominger, Superstrings with Torsion, Nucl. Phys. B 274 (1986) 253 [INSPIRE].
K. Becker and K. Dasgupta, Heterotic strings with torsion, JHEP 11 (2002) 006 [hep-th/0209077] [INSPIRE].
K. Becker, M. Becker, P.S. Green, K. Dasgupta and E. Sharpe, Compactifications of heterotic strings on non-Kähler complex manifolds. 2, Nucl. Phys. B 678 (2004) 19 [hep-th/0310058] [INSPIRE].
I.V. Melnikov, R. Minasian and S. Sethi, Heterotic fluxes and supersymmetry, JHEP 06 (2014) 174 [arXiv:1403.4298] [INSPIRE].
X. de la Ossa and E.E. Svanes, Connections, Field Redefinitions and Heterotic Supergravity, JHEP 12 (2014) 008 [arXiv:1409.3347] [INSPIRE].
K. Dasgupta, G. Rajesh and S. Sethi, M theory, orientifolds and G-flux, JHEP 08 (1999) 023 [hep-th/9908088] [INSPIRE].
D. Huybrechts and M. Lehn, The geometry of moduli spaces of sheaves, Cambridge Mathematical Library, Cambridge University Press, Cambridge, U.K. (2010).
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: 1801.04336
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
Jardine, I.T., Quigley, C. Conformal invariance of (0, 2) sigma models on Calabi-Yau manifolds. J. High Energ. Phys. 2018, 90 (2018). https://doi.org/10.1007/JHEP03(2018)090
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2018)090