zbMATH — the first resource for mathematics

Monad constructions of omalous bundles. (English) Zbl 1280.81109
Summary: We consider a particular class of holomorphic vector bundles relevant for supersymmetric string theory, called omalous, over nonsingular projective varieties. We use monads to construct examples of such bundles over 3-fold hypersurfaces in \(\mathbb P^4\), complete intersection Calabi-Yau manifolds in \(\mathbb P^k\), blow-ups of \(\mathbb P^2\) at \(n\) distinct points, and products \(\mathbb P^m \times \mathbb P^n\).

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
81T60 Supersymmetric field theories in quantum mechanics
Full Text: DOI arXiv
[1] Candelas, P.; Horowitz, G. T.; Strominger, A.; Witten, E., Vacuum configurations for superstrings, Nuclear Phys. B, 258, 46-74, (1985)
[2] Green, M. B.; Schwarz, J. H.; Witten, E., (Superstring Theory Vol. 2: Loop Amplitudes, Anomalies and Phenomenology, Cambridge Monographs on Mathematical Physics, (1987), Cambridge University Press) · Zbl 0619.53002
[3] Guffin, J., Quantum sheaf cohomology, a précis, Mat. Contemp., 41, 17-26, (2012) · Zbl 1290.32024
[4] Witten, E.; Witten, L., Large radius expension of superstring compactification, Nuclear Phys. B, 281, 109-126, (1987)
[5] Donagi, R.; Lukas, A.; Ovrut, B. A.; Waldram, D., Holomorphic vector bundles and non-perturbative vacua in \(M\)-theory, J. High Energy Phys., 034, (1999), JHEP 9906 (1999) 034 · Zbl 0952.14033
[6] Guffin, J.; Katz, S., Deformed quantum cohomology and \((0, 2)\) mirror symmetry, J. High Energy Phys., 109, (2010) · Zbl 1290.81120
[7] Andreas, B.; Garcia-Fernandez, M., Solutions of the Strominger system via stable bundles on Calabi-Yau threefolds, Comm. Math. Phys., 315, 153-168, (2012) · Zbl 1252.32031
[8] Brambilla, M. C., Semistability of certain bundles on a quintic Calabi-Yau threefold, Rev. Mat. Complut., 22, 53-61, (2009) · Zbl 1161.14031
[9] Douglas, M. R.; Zhou, C.-G., Chirality change in string theory, J. High Energy Phys., 014, (2004), JHEP 06 (2004) 014
[10] Anderson, L. B.; He, Y. H.; Lukas, A., Heterotic compactification, an algorithm approach, J. High Energy Phys., 49, (2007), JHEP 0707:049
[11] Anderson, L. B.; He, Y. H.; Lukas, A., Monad bundles in heterotic string compactification, J. High Energy Phys., 104, (2008), JHEP 0807:104
[12] Anderson, L. B.; Gray, J.; He, Y. H.; Lukas, A., Exploring positive monad bundles and a new heterotic standard model, J. High Energy Phys., 054, (2010), JHEP 1002:054 · Zbl 1270.81146
[13] Blumenhagen, R., Target space duality for \((0, 2)\) compactifications, Nuclear Phys. B, 513, 573-590, (1998) · Zbl 0939.32017
[14] Kachru, S., Some three generation \((0, 2)\) Calabi-Yau models, Phys. Lett. B, 349, 76-82, (1995)
[15] Jardim, M.; Miró-Roig, R. M., On the stability of instanton sheaves over certain projective varieties, Comm. Algebra, 36, 288-298, (2008) · Zbl 1131.14046
[16] Jardim, M., Stable bundles on 3-fold hypersurfaces, Bull. Braz. Math. Soc. (N.S.), 38, 649-659, (2007) · Zbl 1139.14035
[17] Floystad, G., Monads on projective spaces, Comm. Algebra, 28, 5503-5516, (2000) · Zbl 0977.14007
[18] Griffith, P.; Harris, J., Principles of algebraic geometry, (1994), Wiley & Sons
[19] Hoppe, H., Generischer spaltungstyp und zweite chernklasse stabiler vectorraumbündel vom rang 4 auf \(\mathbb{P}^4\), Math. Z., 187, 345-360, (1984) · Zbl 0567.14011
[20] A.A. Henni, Monads for torsion-free sheaves on multi-blow-ups of the projective plane. Preprint arXiv:0903.3190. · Zbl 1330.14016
[21] Buchdahl, N. P., Monads and bundles on rational surfaces, Rocky Mountain J. Math., 34, 513-540, (2004) · Zbl 1061.14039
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.