We consider the heterotic string on Calabi-Yau manifolds admitting a Strominger-Yau-Zaslow fibration. Upon reducing the system in the T3-directions, the Hermitian Yang-Mills conditions can then be reinterpreted as a complex flat connection on ℝ3 satisfying a certain co-closure condition. We give a number of abelian and non-abelian examples, and also compute the back-reaction on the geometry through the non-trivial α′-corrected heterotic Bianchi identity, which includes an important correction to the equations for the complex flat connection. These are all new local solutions to the Hull-Strominger system on T3 × ℝ3. We also propose a method for computing the spectrum of certain non-abelian models, in close analogy with the Morse-Witten complex of the abelian models.
P. Candelas, G.T. Horowitz, A. Strominger and E. Witten, Vacuum configurations for superstrings, Nucl. Phys. B 258 (1985) 46 [INSPIRE].
A. Strominger, Superstrings with torsion, Nucl. Phys. B 274 (1986) 253 [INSPIRE].
C.M. Hull, Compactifications of the heterotic superstring, Phys. Lett. B 178 (1986) 357 [INSPIRE].
S. Donaldson, Adiabatic limits of co-associative Kovalev-Lefschetz fibrations, in Algebra, geometry, and physics in the 21st century, D. Auroux et al. eds., Springer, Germany (2017).
A. Kovalev, Twisted connected sums and special Riemannian holonomy, J. Reine Angew. Math. 565 (2003) 125.
A. Corti, M. Haskins, J. Nordström and T. Pacini, Asymptotically cylindrical Calabi-Yau 3-folds from weak Fano 3-folds, Geom. Topol. 17 (2013) 1955.
C.M. Hull, Anomalies, ambiguities and superstrings, Phys. Lett. B 167 (1986) 51 [INSPIRE].
C.M. Hull and P.K. Townsend, World sheet supersymmetry and anomaly cancellation in the heterotic string, Phys. Lett. B 178 (1986) 187 [INSPIRE].
A. Sen, (2, 0) supersymmetry and space-time supersymmetry in the heterotic string theory, Nucl. Phys. B 278 (1986) 289 [INSPIRE].
M.B. Green and J.H. Schwarz, Anomaly cancellation in supersymmetric D = 10 gauge theory and superstring theory, Phys. Lett. B 149 (1984) 117 [INSPIRE].
S.K. Donaldson, Anti self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles, Proc. London Math. Soc. 50 (1985) 1.
K. Uhlenbeck and S.T. Yau, On the existence of Hermitian-Yang-mills connections in stable vector bundles, Commun. Pure Appl. Math. 39 (1986) S257.
G. t Hooft, Magnetic monopoles in unified theories, Nucl. Phys. B 79 (1974) 276 [CERN-TH-1876].
A. M. Polyakov, Particle spectrum in quantum field theory, in 30 years of the landau institute — Selected papers, I.M. Khalatnikov ed., World Scientific, Singapore (1996).
K. Corlette et al., Flat g-bundles with canonical metrics, J. Diff. Geom. 28 (1988) 361.
M. Gagliardo and K. Uhlenbeck, Geometric aspects of the Kapustin-Witten equations, J. Fix. Point Theor. Appl. 11 (2012) 185.
A. Ashmore, X. De La Ossa, R. Minasian, C. Strickland-Constable and E.E. Svanes, Finite deformations from a heterotic superpotential: holomorphic Chern-Simons and an L∞ algebra, JHEP 10 (2018) 179 [arXiv:1806.08367] [INSPIRE].
M.K. Prasad and C.M. Sommerfield, An exact classical solution for the ’t Hooft monopole and the Julia-Zee dyon, Phys. Rev. Lett. 35 (1975) 760 [INSPIRE].
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2010.07438
About this article
Cite this article
Acharya, B.S., Kinsella, A. & Svanes, E.E. T 3-invariant heterotic Hull-Strominger solutions. J. High Energ. Phys. 2021, 197 (2021). https://doi.org/10.1007/JHEP01(2021)197
- Superstring Vacua
- Superstrings and Heterotic Strings
- Flux compactifications
- Solitons Monopoles and Instantons