Abstract
We study heterotic supergravity on the conifold and its ℤ 2 orbifold with Abelian gauge fields and three-form flux. By taking a limit of large five brane charge, we are able suppress non-linear curvature corrections and construct exact supersymmetric solutions. At large distances, these solutions are generically locally Ricci-flat, have a magnetic flux through the two-sphere at infinity as well as non-zero five-brane charge. For a given flux, our family of solutions has three real parameters, the size of the pair of two spheres in the IR and the dilaton zero mode. We present an explicit analytic solution for a decoupled near horizon region which is not asymptotically locally Ricci-flat and where for a given flux, the size of the cycles is frozen and the only parameter is the dilaton zero mode. We also present an exactly solvable worldsheet CFT for this near horizon region. When one of the two cycles has vanishing size, the near horizon region no longer exists but nonetheless we obtain a solution on the (unorbifolded) resolved conifold.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
K. Dasgupta, G. Rajesh and S. Sethi, M-theory, orientifolds and G-flux, JHEP 08 (1999) 023 [hep-th/9908088] [INSPIRE].
E. Goldstein and S. Prokushkin, Geometric model for complex non-Kähler manifolds with SU(3) structure, Commun. Math. Phys. 251 (2004) 65 [hep-th/0212307] [INSPIRE].
J.-X. Fu and S.-T. Yau, The theory of superstring with flux on non-Kähler manifolds and the complex Monge-Ampère equation, J. Diff. Geom. 78 (2008) 369 [hep-th/0604063] [INSPIRE].
K. Becker and S. Sethi, Torsional heterotic geometries, Nucl. Phys. B 820 (2009) 1 [arXiv:0903.3769] [INSPIRE].
A. Adams, M. Ernebjerg and J.M. Lapan, Linear models for flux vacua, Adv. Theor. Math. Phys. 12 (2008) 817 [hep-th/0611084] [INSPIRE].
M. Blaszczyk, S. Groot Nibbelink and F. Ruehle, Green-Schwarz mechanism in heterotic (2, 0) gauged linear sigma models: torsion and NS5 branes, JHEP 08 (2011) 083 [arXiv:1107.0320] [INSPIRE].
C. Quigley and S. Sethi, Linear sigma models with torsion, JHEP 11 (2011) 034 [arXiv:1107.0714] [INSPIRE].
C. Quigley, S. Sethi and M. Stern, Novel branches of (0, 2) theories, JHEP 09 (2012) 064 [arXiv:1206.3228] [INSPIRE].
A. Adams, E. Dyer and J. Lee, GLSMs for non-Kähler geometries, JHEP 01 (2013) 044 [arXiv:1206.5815] [INSPIRE].
P. Candelas and X.C. de la Ossa, Comments on conifolds, Nucl. Phys. B 342 (1990) 246 [INSPIRE].
A. Strominger, Massless black holes and conifolds in string theory, Nucl. Phys. B 451 (1995) 96 [hep-th/9504090] [INSPIRE].
R. Gopakumar and C. Vafa, On the gauge theory/geometry correspondence, Adv. Theor. Math. Phys. 3 (1999) 1415 [hep-th/9811131] [INSPIRE].
I.R. Klebanov and E. Witten, Superconformal field theory on three-branes at a Calabi-Yau singularity, Nucl. Phys. B 536 (1998) 199 [hep-th/9807080] [INSPIRE].
I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: duality cascades and χSB resolution of naked singularities, JHEP 08 (2000) 052 [hep-th/0007191] [INSPIRE].
J.M. Maldacena and C. Núñez, Towards the large N limit of pure N = 1 super Yang-Mills theory, Phys. Rev. Lett. 86 (2001) 588 [hep-th/0008001] [INSPIRE].
M. Atiyah, J.M. Maldacena and C. Vafa, An M-theory flop as a large N duality, J. Math. Phys. 42 (2001) 3209 [hep-th/0011256] [INSPIRE].
L. Carlevaro, D. Israël and P.M. Petropoulos, Double-scaling limit of heterotic bundles and dynamical deformation in CFT, Nucl. Phys. B 827 (2010) 503 [arXiv:0812.3391] [INSPIRE].
L. Carlevaro and D. Israël, Heterotic resolved conifolds with torsion, from supergravity to CFT, JHEP 01 (2010) 083 [arXiv:0910.3190] [INSPIRE].
J.-X. Fu, L.-S. Tseng and S.-T. Yau, Local heterotic torsional models, Commun. Math. Phys. 289 (2009) 1151 [arXiv:0806.2392] [INSPIRE].
C.G. Callan Jr., J.A. Harvey and A. Strominger, Supersymmetric string solitons, hep-th/9112030 [INSPIRE].
O. Aharony, M. Berkooz, D. Kutasov and N. Seiberg, Linear dilatons, NS5-branes and holography, JHEP 10 (1998) 004 [hep-th/9808149] [INSPIRE].
A.H. Chamseddine and M.S. Volkov, Non-Abelian Bogomol’nyi-Prasad-Sommerfield monopoles in N = 4 gauged supergravity, Phys. Rev. Lett. 79 (1997) 3343 [hep-th/9707176] [INSPIRE].
A.H. Chamseddine and M.S. Volkov, Non-Abelian solitons in N = 4 gauged supergravity and leading order string theory, Phys. Rev. D 57 (1998) 6242 [hep-th/9711181] [INSPIRE].
S. Kachru, J. Pearson and H.L. Verlinde, Brane/flux annihilation and the string dual of a non-supersymmetric field theory, JHEP 06 (2002) 021 [hep-th/0112197] [INSPIRE].
F. Chen, K. Dasgupta, J.M. Lapan, J. Seo and R. Tatar, Gauge/gravity duality in heterotic string theory, Phys. Rev. D 88 (2013) 066003 [arXiv:1303.4750] [INSPIRE].
T. Fei, A construction of non-Kähler Calabi-Yau manifolds and new solutions to the Strominger system, arXiv:1507.00293 [INSPIRE].
T. Fei, Some torsional local models of heterotic strings, arXiv:1508.05566 [INSPIRE].
E.A. Bergshoeff and M. de Roo, The quartic effective action of the heterotic string and supersymmetry, Nucl. Phys. B 328 (1989) 439 [INSPIRE].
M.B. Green and J.H. Schwarz, Anomaly cancellations in supersymmetric D = 10 gauge theory and superstring theory, Phys. Lett. B 149 (1984) 117 [INSPIRE].
J.P. Gauntlett, D. Martelli and D. Waldram, Superstrings with intrinsic torsion, Phys. Rev. D 69 (2004) 086002 [hep-th/0302158] [INSPIRE].
J. Li and S.T. Yau, Hermitian Yang-Mills connection on non-Kähler manifolds, Conf. Proc. C 8607214 (1986) 560 [INSPIRE].
A.-A. Weil, Introduction à l’étude des variétés kählériennes, Hermann (1958).
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].
X. de la Ossa and E.E. Svanes, Connections, field redefinitions and heterotic supergravity, JHEP 12 (2014) 008 [arXiv:1409.3347] [INSPIRE].
S. Ivanov, Heterotic supersymmetry, anomaly cancellation and equations of motion, Phys. Lett. B 685 (2010) 190 [arXiv:0908.2927] [INSPIRE].
I.V. Melnikov, R. Minasian and S. Sethi, Heterotic fluxes and supersymmetry, JHEP 06 (2014) 174 [arXiv:1403.4298] [INSPIRE].
D.N. Page and C.N. Pope, Inhomogeneous Einstein metrics on complex line bundles, Class. Quant. Grav. 4 (1987) 213 [INSPIRE].
C.V. Johnson, Exact models of extremal dyonic four-dimensional black hole solutions of heterotic string theory, Phys. Rev. D 50 (1994) 4032 [hep-th/9403192] [INSPIRE].
C.V. Johnson, Heterotic cosets, in Proceedings of the High-Energy Physics and Cosmology Summer School, Trieste Italy, 13 Jun-29 Jul 1994 [hep-th/9409061] [INSPIRE].
C.V. Johnson, Heterotic coset models, Mod. Phys. Lett. A 10 (1995) 549 [hep-th/9409062] [INSPIRE].
C. Klimč´ık and A.A. Tseytlin, Exact four-dimensional string solutions and Toda-like sigma models from ‘null-gauged’ WZNW theories, Nucl. Phys. B 424 (1994) 71 [hep-th/9402120] [INSPIRE].
D. Israël, Habilitation de recherche, UPMC, Sorbonne Universités (2014).
A.A. Tseytlin, Effective action of gauged WZW model and exact string solutions, Nucl. Phys. B 399 (1993) 601 [hep-th/9301015] [INSPIRE].
D. Marolf, Chern-Simons terms and the three notions of charge, in Proceedings of Quantization, Gauge Theory, and Strings. International Conference Dedicated to the Memory of Professor Efim Fradkin, Moscow Russia, 5-10 Jun 2000, Vol. 1+2, pp. 312-320 [hep-th/0006117] [INSPIRE].
O. Aharony, A. Hashimoto, S. Hirano and P. Ouyang, D-brane charges in gravitational duals of 2+1 dimensional gauge theories and duality cascades, JHEP 01 (2010) 072 [arXiv:0906.2390] [INSPIRE].
R. Rohm and E. Witten, The antisymmetric tensor field in superstring theory, Annals Phys. 170 (1986) 454 [INSPIRE].
S. Gukov, S. Kachru, X. Liu and L. McAllister, Heterotic moduli stabilization with fractional Chern-Simons invariants, Phys. Rev. D 69 (2004) 086008 [hep-th/0310159] [INSPIRE].
E. Witten, Global anomalies in string theory, in Proceedings of the Symposium on Anomalies, Geometry, Topology, Argonne U.S.A., 28-30 Mar 1985.
J.O. Conrad, On fractional instanton numbers in six-dimensional heterotic E 8 × E 8 orbifolds, JHEP 11 (2000) 022 [hep-th/0009251] [INSPIRE].
H. Nishi, SU(n)-Chern-Simons invariants of Seifert fibered 3-manifolds, Int. J. Math. 09 (1998) 295.
A. Butti, M. Graña, R. Minasian, M. Petrini and A. Zaffaroni, The baryonic branch of Klebanov-Strassler solution: a supersymmetric family of SU(3) structure backgrounds, JHEP 03 (2005) 069 [hep-th/0412187] [INSPIRE].
R. Casero, C. Núñez and A. Paredes, Towards the string dual of \( \mathcal{N}=1 \) SQCD-like theories, Phys. Rev. D 73 (2006) 086005 [hep-th/0602027] [INSPIRE].
J. Maldacena and D. Martelli, The unwarped, resolved, deformed conifold: fivebranes and the baryonic branch of the Klebanov-Strassler theory, JHEP 01 (2010) 104 [arXiv:0906.0591] [INSPIRE].
S.S. Gubser, Curvature singularities: the good, the bad and the naked, Adv. Theor. Math. Phys. 4 (2000) 679 [hep-th/0002160] [INSPIRE].
A. Brandhuber, G 2 holonomy spaces from invariant three-forms, Nucl. Phys. B 629 (2002) 393 [hep-th/0112113] [INSPIRE].
R. Bryand and S. Salamon, On the construction of some complete metrices with expectional holonomy, Duke Math. J. 58 (1989) 829 [INSPIRE].
G.W. Gibbons, D.N. Page and C.N. Pope, Einstein metrics on S 3 , R 3 and R 4 bundles, Commun. Math. Phys. 127 (1990) 529 [INSPIRE].
M. Atiyah and E. Witten, M-theory dynamics on a manifold of G 2 holonomy, Adv. Theor. Math. Phys. 6 (2003) 1 [hep-th/0107177] [INSPIRE].
B.S. Acharya and S. Gukov, M theory and singularities of exceptional holonomy manifolds, Phys. Rept. 392 (2004) 121 [hep-th/0409191] [INSPIRE].
N. Halmagyi, Missing mirrors: type IIA supergravity on the resolved conifold, arXiv:1003.2121 [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: 1601.07561
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
Halmagyi, N., Israël, D. & Svanes, E. The Abelian heterotic conifold. J. High Energ. Phys. 2016, 29 (2016). https://doi.org/10.1007/JHEP07(2016)029
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2016)029