Abstract
We present models of heterotic compactification on Calabi-Yau threefolds and compute the non-perturbative superpotential for vector bundle moduli. The key feature of these models is that the threefolds, which are elliptically fibered over del Pezzo surfaces, have homology classes with a unique holomorphic, isolated genus-zero curve. Using the spectral cover construction, we present vector bundles for which we can explicitly calculate the Pfaffians associated with string instantons on these curves. These are shown to be non-zero, thus leading to a non-vanishing superpotential in the 4D effective action. We discuss, in detail, why such compactifications avoid the Beasley-Witten residue theorem.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Lukas, B.A. Ovrut and D. Waldram, The ten-dimensional effective action of strongly coupled heterotic string theory, Nucl. Phys. B 540 (1999) 230 [hep-th/9801087] [INSPIRE].
A. Lukas, B.A. Ovrut, K.S. Stelle and D. Waldram, Heterotic M-theory in five-dimensions, Nucl. Phys. B 552 (1999) 246 [hep-th/9806051] [INSPIRE].
V. Braun, Y.-H. He, B.A. Ovrut and T. Pantev, A standard model from the E 8 × E 8 heterotic superstring, JHEP 06 (2005) 039 [hep-th/0502155] [INSPIRE].
V. Braun, Y.-H. He, B.A. Ovrut and T. Pantev, Vector bundle extensions, sheaf cohomology and the heterotic standard model, Adv. Theor. Math. Phys. 10 (2006) 525 [hep-th/0505041] [INSPIRE].
V. Braun, Y.-H. He, B.A. Ovrut and T. Pantev, The exact MSSM spectrum from string theory, JHEP 05 (2006) 043 [hep-th/0512177] [INSPIRE].
V. Bouchard and R. Donagi, An SU(5) heterotic standard model, Phys. Lett. B 633 (2006) 783 [hep-th/0512149] [INSPIRE].
V. Bouchard, M. Cvetič and R. Donagi, Tri-linear couplings in an heterotic minimal supersymmetric standard model, Nucl. Phys. B 745 (2006) 62 [hep-th/0602096] [INSPIRE].
L.B. Anderson, J. Gray, Y.-H. He and A. Lukas, Exploring Positive Monad Bundles And A New Heterotic Standard Model, JHEP 02 (2010) 054 [arXiv:0911.1569] [INSPIRE].
L.B. Anderson, J. Gray, A. Lukas and E. Palti, Two Hundred Heterotic Standard Models on Smooth Calabi-Yau Threefolds, Phys. Rev. D 84 (2011) 106005 [arXiv:1106.4804] [INSPIRE].
L.B. Anderson, J. Gray, A. Lukas and E. Palti, Heterotic standard models from smooth Calabi-Yau three-folds, PoS(CORFU2011)096.
L.B. Anderson, J. Gray, A. Lukas and E. Palti, Heterotic Line Bundle Standard Models, JHEP 06 (2012) 113 [arXiv:1202.1757] [INSPIRE].
E.I. Buchbinder, A. Constantin and A. Lukas, A heterotic standard model with B − L symmetry and a stable proton, JHEP 06 (2014) 100 [arXiv:1404.2767] [INSPIRE].
E.I. Buchbinder, A. Constantin and A. Lukas, Non-generic Couplings in Supersymmetric Standard Models, Phys. Lett. B 748 (2015) 251 [arXiv:1409.2412] [INSPIRE].
L. Battarra, M. Koehn, J.-L. Lehners and B.A. Ovrut, Cosmological Perturbations Through a Non-Singular Ghost-Condensate/Galileon Bounce, JCAP 07 (2014) 007 [arXiv:1404.5067] [INSPIRE].
R. Deen, B.A. Ovrut and A. Purves, Supersymmetric Sneutrino-Higgs Inflation, Phys. Lett. B 762 (2016) 441 [arXiv:1606.00431] [INSPIRE].
R. Deen and B. Ovrut, N = 1 supergravitational heterotic galileons, JHEP 11 (2017) 026 [arXiv:1707.05305] [INSPIRE].
Y. Cai, R. Deen, B.A. Ovrut and A. Purves, Perturbative reheating in Sneutrino-Higgs cosmology, JHEP 09 (2018) 001 [arXiv:1804.07848] [INSPIRE].
L.B. Anderson, J. Gray, A. Lukas and B. Ovrut, The Edge Of Supersymmetry: Stability Walls in Heterotic Theory, Phys. Lett. B 677 (2009) 190 [arXiv:0903.5088] [INSPIRE].
L.B. Anderson, J. Gray, A. Lukas and B. Ovrut, Stabilizing the Complex Structure in Heterotic Calabi-Yau Vacua, JHEP 02 (2011) 088 [arXiv:1010.0255] [INSPIRE].
L.B. Anderson, J. Gray, A. Lukas and B. Ovrut, Stabilizing All Geometric Moduli in Heterotic Calabi-Yau Vacua, Phys. Rev. D 83 (2011) 106011 [arXiv:1102.0011] [INSPIRE].
L.B. Anderson, J. Gray, A. Lukas and B. Ovrut, The Atiyah Class and Complex Structure Stabilization in Heterotic Calabi-Yau Compactifications, JHEP 10 (2011) 032 [arXiv:1107.5076] [INSPIRE].
R. Donagi, B.A. Ovrut and D. Waldram, Moduli spaces of five-branes on elliptic Calabi-Yau threefolds, JHEP 11 (1999) 030 [hep-th/9904054] [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].
M. Dine, N. Seiberg, X.G. Wen and E. Witten, Nonperturbative Effects on the String World Sheet. 2., Nucl. Phys. B 289 (1987) 319 [INSPIRE].
J. Distler, Resurrecting (2,0) compactifications, Phys. Lett. B 188 (1987) 431 [INSPIRE].
J. Distler and B.R. Greene, Aspects of (2,0) String Compactifications, Nucl. Phys. B 304 (1988) 1 [INSPIRE].
P.S. Aspinwall and D.R. Morrison, Chiral rings do not suffice: N = (2, 2) theories with nonzero fundamental group, Phys. Lett. B 334 (1994) 79 [hep-th/9406032] [INSPIRE].
E. Silverstein and E. Witten, Criteria for conformal invariance of (0,2) models, Nucl. Phys. B 444 (1995) 161 [hep-th/9503212] [INSPIRE].
K. Becker, M. Becker and A. Strominger, Five-branes, membranes and nonperturbative string theory, Nucl. Phys. B 456 (1995) 130 [hep-th/9507158] [INSPIRE].
E. Witten, World sheet corrections via D instantons, JHEP 02 (2000) 030 [hep-th/9907041] [INSPIRE].
J.A. Harvey and G.W. Moore, Superpotentials and membrane instantons, hep-th/9907026 [INSPIRE].
E. Lima, B.A. Ovrut, J. Park and R. Reinbacher, Nonperturbative superpotential from membrane instantons in heterotic M-theory, Nucl. Phys. B 614 (2001) 117 [hep-th/0101049] [INSPIRE].
E.I. Buchbinder, R. Donagi and B.A. Ovrut, Superpotentials for vector bundle moduli, Nucl. Phys. B 653 (2003) 400 [hep-th/0205190] [INSPIRE].
E.I. Buchbinder, R. Donagi and B.A. Ovrut, Vector bundle moduli superpotentials in heterotic superstrings and M-theory, JHEP 07 (2002) 066 [hep-th/0206203] [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].
C. Beasley and E. Witten, New instanton effects in string theory, JHEP 02 (2006) 060 [hep-th/0512039] [INSPIRE].
V. Braun, M. Kreuzer, B.A. Ovrut and E. Scheidegger, Worldsheet instantons, torsion curves and non-perturbative superpotentials, Phys. Lett. B 649 (2007) 334 [hep-th/0703134] [INSPIRE].
V. Braun, M. Kreuzer, B.A. Ovrut and E. Scheidegger, Worldsheet instantons and torsion curves, part A: Direct computation, JHEP 10 (2007) 022 [hep-th/0703182] [INSPIRE].
V. Braun, M. Kreuzer, B.A. Ovrut and E. Scheidegger, Worldsheet Instantons and Torsion Curves, Part B: Mirror Symmetry, JHEP 10 (2007) 023 [arXiv:0704.0449] [INSPIRE].
P.S. Aspinwall and M.R. Plesser, Elusive Worldsheet Instantons in Heterotic String Compactifications, Proc. Symp. Pure Math. 85 (2012) 33 [arXiv:1106.2998] [INSPIRE].
E.I. Buchbinder and B.A. Ovrut, Non-vanishing Superpotentials in Heterotic String Theory and Discrete Torsion, JHEP 01 (2017) 038 [arXiv:1611.01922] [INSPIRE].
E. Buchbinder, A. Lukas, B. Ovrut and F. Ruehle, Heterotic Instanton Superpotentials from Complete Intersection Calabi-Yau Manifolds, JHEP 10 (2017) 032 [arXiv:1707.07214] [INSPIRE].
L.B. Anderson, Y.-H. He and A. Lukas, Monad Bundles in Heterotic String Compactifications, JHEP 07 (2008) 104 [arXiv:0805.2875] [INSPIRE].
R.Y. Donagi, Principal bundles on elliptic fibrations, Asian J. Math. 1 (1997) 214 [alg-geom/9702002] [INSPIRE].
R. Friedman, J. Morgan and E. Witten, Vector bundles and F-theory, Commun. Math. Phys. 187 (1997) 679 [hep-th/9701162] [INSPIRE].
R. Friedman, J.W. Morgan and E. Witten, Vector bundles over elliptic fibrations, alg-geom/9709029 [INSPIRE].
E. Buchbinder, R. Donagi and B.A. Ovrut, Vector bundle moduli and small instanton transitions, JHEP 06 (2002) 054 [hep-th/0202084] [INSPIRE].
R. Donagi, Y.-H. He, B.A. Ovrut and R. Reinbacher, The particle spectrum of heterotic compactifications, JHEP 12 (2004) 054 [hep-th/0405014] [INSPIRE].
E.I. Buchbinder, B.A. Ovrut and R. Reinbacher, Instanton moduli in string theory, JHEP 04 (2005) 008 [hep-th/0410200] [INSPIRE].
L.B. Anderson, X. Gao, J. Gray and S.-J. Lee, Fibrations in CICY Threefolds, JHEP 10 (2017) 077 [arXiv:1708.07907] [INSPIRE].
D. Cox, J. Little and H. Schenck, Toric Varieties, Graduate studies in mathematics. American Mathematical Soc., (2011).
R. Wazir, Arithmetic on elliptic threefolds, Compos. Math. 140 (2004) 567.
R. Donagi, A. Grassi and E. Witten, A nonperturbative superpotential with E 8 symmetry, Mod. Phys. Lett. A 11 (1996) 2199 [hep-th/9607091] [INSPIRE].
G. Curio and D. Lüst, A class of N = 1 dual string pairs and its modular superpotential, Int. J. Mod. Phys. A 12 (1997) 5847 [hep-th/9703007] [INSPIRE].
L.B. Anderson, F. Apruzzi, X. Gao, J. Gray and S.-J. Lee, Instanton superpotentials, Calabi-Yau geometry and fibrations, Phys. Rev. D 93 (2016) 086001 [arXiv:1511.05188] [INSPIRE].
M. Cvetič, R. Donagi, J. Halverson and J. Marsano, On Seven-Brane Dependent Instanton Prefactors in F-theory, JHEP 11 (2012) 004 [arXiv:1209.4906] [INSPIRE].
A.P. Braun, M. Del Zotto, J. Halverson, M. Larfors, D.R. Morrison and S. Schäfer-Nameki, Infinitely Many M2-instanton Corrections to M-theory on G 2 -manifolds, arXiv:1803.02343 [INSPIRE].
P. Candelas and A. Font, Duality between the webs of heterotic and type-II vacua, Nucl. Phys. B 511 (1998) 295 [hep-th/9603170] [INSPIRE].
B. Andreas, N = 1 heterotic/F theory duality, Fortsch. Phys. 47 (1999) 587 [hep-th/9808159] [INSPIRE].
P. Berglund and P. Mayr, Heterotic string/F theory duality from mirror symmetry, Adv. Theor. Math. Phys. 2 (1999) 1307 [hep-th/9811217] [INSPIRE].
L.B. Anderson and W. Taylor, Geometric constraints in dual F-theory and heterotic string compactifications, JHEP 08 (2014) 025 [arXiv:1405.2074] [INSPIRE].
M. Cvetič, A. Grassi, D. Klevers, M. Poretschkin and P. Song, Origin of Abelian Gauge Symmetries in Heterotic/F-theory Duality, JHEP 04 (2016) 041 [arXiv:1511.08208] [INSPIRE].
M. Cvetič, A. Grassi and M. Poretschkin, Discrete Symmetries in Heterotic/F-theory Duality and Mirror Symmetry, JHEP 06 (2017) 156 [arXiv:1607.03176] [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: 1806.04669
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
Buchbinder, E.I., Lin, L. & Ovrut, B.A. Non-vanishing heterotic superpotentials on elliptic fibrations. J. High Energ. Phys. 2018, 111 (2018). https://doi.org/10.1007/JHEP09(2018)111
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2018)111