New evidence for \((0,2)\) target space duality. (English) Zbl 1357.81146

Anderson, Lara B.; Feng, He

J. Phys. A, Math. Theor. 50, No. 6, Article ID 064004, 53 p. (2017).

Summary: In the context of \((0,2)\) gauged linear sigma models, we explore chains of perturbatively dual heterotic string compactifications. The notion of target space duality originates in non-geometric phases and can be used to generate distinct GLSMs with shared geometric phases leading to apparently identical target space theories. To date, this duality has largely been studied at the level of counting states in the effective theories. We extend this analysis to the effective potential and loci of enhanced symmetry in dual theories. By engineering vector bundles with non-trivial constraints arising from slope-stability (i.e. D-terms) and holomorphy (i.e. F-terms) the detailed structure of the vacuum space of the dual theories can be explored. Our results give new evidence that GLSM target space duality may provide important hints towards a more complete understanding of \((0,2)\) string dualities.

MSC:

81T30

String and superstring theories; other extended objects (e.g., branes) in quantum field theory

Keywords:

heterotic string theory; string duality; gauged linear sigma models

Software:

STRINGVACUA

References:

[1]	Adams A, Basu A and Sethi S 2003 (0, 2) duality Adv. Theor. Math. Phys.7 865 · Zbl 1058.81064
[2]	Blumenhagen R, Schimmrigk R and Wisskirchen A 1997 (0, 2) mirror symmetry Nucl. Phys. B 486 598 · Zbl 0925.14014
[3]	Melnikov I, Sethi S and Sharpe E 2012 Recent developments in (0, 2) mirror symmetry SIGMA8 068 · Zbl 1271.32020
[4]	Melnikov I V and Plesser M R 2011 A (0, 2) mirror map J. High Energy Phys.JHEP02(2011) 001 · Zbl 1294.81223
[5]	Kapustin A, Kreuzer M and Schlesinger K G 2009 Homological Mirror Symmetry: New Developments and Perspectives (Berlin: Springer)
[6]	Distler J and Kachru S 1995 Duality of (0, 2) string vacua Nucl. Phys. B 442 64 · Zbl 0990.81659
[7]	Blumenhagen R 1998 Target space duality for (0, 2) compactifications Nucl. Phys. B 513 573 · Zbl 0939.32017
[8]	Blumenhagen R 1998 (0, 2) Target space duality, CICYs and reflexive sheaves Nucl. Phys. B 514 688 · Zbl 0920.14017
[9]	Blumenhagen R and Rahn T 2011 Landscape study of target space duality of (0, 2) heterotic string models J. High Energy Phys.JHEP09(2011) 098 · Zbl 1301.81188
[10]	Rahn T 2012 Target space dualities of heterotic grand unified theories Proc. Symp. Pure Math.85 423
[11]	Strominger A 1995 Massless black holes and conifolds in string theory Nucl. Phys. B 451 96 · Zbl 0925.83071
[12]	Sharpe E R 1999 Kahler cone substructure Adv. Theor. Math. Phys.2 1441 · Zbl 1059.14500
[13]	Anderson L B, Gray J, Lukas A and Ovrut B 2009 Stability Walls in heterotic theories J. High Energy Phys.JHEP09(2009) 026
[14]	Anderson L B, Gray J, Lukas A and Ovrut B 2009 The edge Of supersymmetry: stability Walls in heterotic theory Phys. Lett. B 677 190
[15]	Anderson L B, Gray J, Lukas A and Ovrut B 2011 The Atiyah class and complex structure stabilization in heterotic Calabi-Yau compactifications J. High Energy Phys.JHEP10(2011) 032 · Zbl 1303.81139
[16]	Anderson L B, Gray J, Lukas A and Ovrut B 2013 Vacuum varieties, holomorphic bundles and complex structure stabilization in heterotic theories J. High Energy Phys.JHEP07(2013) 017 · Zbl 1342.81391
[17]	Anderson L B, Gray J and Ovrut B A 2011 Transitions in the web of heterotic vacua Fortsch. Phys.59 327 · Zbl 1215.81076
[18]	Lukas A and Stelle K S 2000 Heterotic anomaly cancellation in five-dimensions J. High Energy Phys.JHEP01(2000) 010 · Zbl 0989.81595
[19]	Blumenhagen R, Honecker G and Weigand T 2005 Loop-corrected compactifications of the heterotic string with line bundles J. High Energy Phys.JHEP06(2005) 020
[20]	Horrocks G and Mumford D 1973 A rank 2 vector bundle on P4 with 15 000 symmetries Topology12 63-81 · Zbl 0255.14017
[21]	Beilinson A 1978 Coherent sheaves on Pn and problems in linear algebra, Funkt. Anal. Prilozhen.12 68-9 · Zbl 0427.57013
[22]	Anderson L B 2008 Heterotic and M-theory compactifications for string phenomenology PhD Thesis University of Oxford
[23]	Anderson L B, He Y H and Lukas A 2007 Heterotic compactification, an algorithmic approach J. High Energy Phys.JHEP07(2007) 049
[24]	Anderson L B, He Y H and Lukas A 2008 Monad bundles in heterotic string compactifications J. High Energy Phys.JHEP07(2008) 104
[25]	Anderson L B, Gray J, He Y H and Lukas A 2010 Exploring positive monad bundles and a new heterotic standard Model J. High Energy Phys.JHEP02(2010) 054 · Zbl 1270.81146
[26]	Witten E 1993 Phases of N = 2 theories in two-dimensions Nucl. Phys. B 403 159 · Zbl 0910.14020
[27]	Distler J 1994 Notes on (0, 2) superconformal field theories Trieste HEP Cosmology1994 322-51
[28]	Distler J, Greene B R and Morrison D R 1996 Resolving singularities in (0, 2) models Nucl. Phys. B 481 289 · Zbl 0925.14011
[29]	Chiang T M, Distler J and Greene B R 1997 Some features of (0, 2) moduli space Nucl. Phys. B 496 590 · Zbl 0951.81061
[30]	Blumenhagen R, Jurke B, Rahn T and Roschy H 2010 Cohomology of line bundles: a computational algorithm J. Math. Phys.51 103525 · Zbl 1314.55012
[31]	Anderson L B, Gray J, He Y-H, Lee S-J and Lukas A 2009 ‘CICY package’, based on methods described in (arXiv:0911.1569, arXiv:0911.0865, arXiv:0805.2875, hep-th/0703249, hep-th/ 0702210)
[32]	Hubsch T 1987 Calabi-Yau manifolds: motivations and constructions Commun. Math. Phys.108 291 · Zbl 0602.53061
[33]	Candelas P, Dale A M, Lutken C A and Schimmrigk R 1988 Complete intersection Calabi-Yau manifolds Nucl. Phys. B 298 493
[34]	Hubsch T 1994 Calabi-Yau Manifolds: a Bestiary for Physicists (Singapore: World Scientific)
[35]	Green M B, Schwarz J H and Witten E 1987 Superstring Theory. Vol. 2: Loop Amplitudes, Anomalies And Phenomenology(Cambridge Monographs On Mathematical Physics) (Cambridge: Cambridge University Press) 596P
[36]	Witten E 1986 New Issues in Manifolds of SU(3) Holonomy Nucl. Phys. B 268 79
[37]	Uhlenbeck K and Yau S T 1986 On the existence of Hermitian Yang-Mills connections in stable bundles Commun. Pure App. Math.39 257 · Zbl 0615.58045
[38]	Donaldson S 1985 Anti self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles Proc. Lond. Math. Soc.3 1 · Zbl 0529.53018
[39]	Anderson L B, Gray J, Lukas A and Ovrut B 2011 Stabilizing all geometric moduli in heterotic Calabi-Yau vacua Phys. Rev. D 83 106011
[40]	Anderson L B, Gray J, Lukas A and Ovrut B 2011 Stabilizing the complex structure in heterotic Calabi-Yau vacua J. High Energy Phys.JHEP02(2011) 088 · Zbl 1294.81153
[41]	Atiyah M F 1957 Complex analytic connections in fibre bundles Trans. Am. Math. Soc.85 181-207 · Zbl 0078.16002
[42]	Gukov S, Vafa C and Witten E 2000 CFT’s from Calabi-Yau four folds Nucl. Phys. B 584 69 · Zbl 0984.81143
[43]	Gukov S, Vafa C and Witten E 2001 Nucl. Phys. B 608 477 (erratum)
[44]	Wall C T C 1966 Classification problems in differential topology, V Inventiones Math.1 355-74 · Zbl 0149.20601
[45]	Anderson L B, Gray J, Lukas A and Palti E 2012 Heterotic line bundle standard models J. High Energy Phys.JHEP06(2012) 113 · Zbl 1397.81406
[46]	Anderson L B, Gray J, Lukas A and Palti E 2011 Two hundred heterotic standard models on smooth Calabi-Yau threefolds Phys. Rev. D 84 106005
[47]	Anderson L B, Constantin A, Gray J, Lukas A and Palti E 2014 A comprehensive scan for heterotic SU(5) GUT models J. High Energy Phys.JHEP01(2014) 047
[48]	Anderson L B, Constantin A, Lee S J and Lukas A 2015 Hypercharge flux in heterotic compactifications Phys. Rev. D 91 046008
[49]	Hartshorne R 1977 Algebraic Geometry(Graduate Texts in Mathematics vol 52) (Berlin: Springer)
[50]	Kachru S and Witten E 1993 Computing the complete massless spectrum of a Landau-Ginzburg orbifold Nucl. Phys. B 407 637 · Zbl 1043.81689
[51]	Closset C, Gu W, Jia B and Sharpe E 2016 Localization of twisted N=(0,2) gauged linear sigma models in two dimensions J. High Energy Phys.JHEP03(2016) 070 · Zbl 1388.81714
[52]	Donagi R, Guffin J, Katz S and Sharpe E 2012 (0, 2) quantum cohomology Proc. Symp. Pure Math.85 83
[53]	Aspinwall P S, Greene B R and Morrison D R 1994 Calabi-Yau moduli space, mirror manifolds and space-time topology change in string theory Nucl. Phys. B 416 414 · Zbl 0899.32006
[54]	Candelas P, de la Ossa X and McOrist J 2016 A metric for heterotic moduli (arXiv:1605.05256 [hep-th])
[55]	McOrist J 2016 On the effective field theory of heterotic vacua (arXiv:1606.05221 [hep-th])
[56]	Anderson L B, Gray J and Sharpe E 2014 Algebroids, heterotic moduli spaces and the strominger system J. High Energy Phys.JHEP07(2014) 037
[57]	de la Ossa X and Svanes E E 2014 Holomorphic bundles and the moduli space of N = 1 supersymmetric heterotic compactifications J. High Energy Phys.JHEP10(2014) 123 · Zbl 1333.81413
[58]	de la Ossa X, Hardy E and Svanes E E 2016 The heterotic superpotential and moduli J. High Energy Phys.JHEP01(2016) 049 · Zbl 1388.81192
[59]	de la Ossa X, Hardy E and Svanes E E 2016 The massless spectrum of heterotic compactifications Fortsch. Phys.64 365 · Zbl 1339.81079
[60]	Slansky R 1981 Group theory for unified model building Phys. Rep.79 1
[61]	Anderson L B, Gray J, Raghuram N and Taylor W 2016 Matter in transition J. High Energy Phys.JHEP04(2016) 080 · Zbl 1388.81022
[62]	Bertolini M and Plesser M R 2015 Worldsheet instantons and (0, 2) linear models J. High Energy Phys.JHEP08(2015) 081 · Zbl 1388.81284
[63]	Douglas M R and Zhou C G 2004 Chirality change in string theory J. High Energy Phys.JHEP06(2004) 014
[64]	Huybrechts D and Lehn M 1997 The Geometry of the Moduli Space of Stable of Sheaves(Aspects of Mathematics, E vol 31) (Cambridge: Cambridge University Press)
[65]	Okonek C, Schneider M and Spindler H 1980 Vector Bundles on Complex Projective Spaces (Boston, MA: Birkhuser)
[66]	Candelas P and de la Ossa X C 1990 Comments on Conifolds Nucl. Phys. B 342 246
[67]	Anderson L B, Apruzzi F, Gao X, Gray J and Lee S J 2016 Instanton superpotentials, Calabi-Yau geometry, and fibrations Phys. Rev. D 93 086001
[68]	Anderson L B, Apruzzi F, Gao X, Gray J and Lee S J 2016 A new construction of Calabi-Yau manifolds: generalized CICYs Nucl. Phys. B 906 441 · Zbl 1334.14023
[69]	Anderson L B, Clossett C, Gray J and Lee S J GLSMs for gCICYs (to appear)
[70]	Berglund P and Hubsch T 2016 On Calabi-Yau generalized complete intersections from Hirzebruch varieties and novel K3-fibrations (arXiv:1606.07420 [hep-th])
[71]	Anderson L B, Gray J and Ovrut B 2010 Yukawa textures from heterotic stability Walls J. High Energy Phys.JHEP05(2010) 086 · Zbl 1287.81087
[72]	Kuriyama M, Nakajima H and Watari T 2009 Theoretical framework for R-parity violation Phys. Rev. D 79 075002
[73]	Luty M A and Taylor W 1996 Varieties of vacua in classical supersymmetric gauge theories Phys. Rev. D 53 3399
[74]	Huybrechts D and Lehn M 1997 The Geometry of Moduli Spaces of Sheaves (Cambridge: Cambridge University Press)
[75]	Candelas P, de la Ossa X, He Y H and Szendroi B 2008 Triadophilia: a special corner in the landscape Adv. Theor. Math. Phys.12 2, 429 · Zbl 1144.81499
[76]	Beasley C and Witten E 2003 Residues and world sheet instantons J. High Energy Phys.JHEP10(2003) 065
[77]	Beasley C and Witten E 2006 New instanton effects in string theory J. High Energy Phys.JHEP02(2006) 060
[78]	Li J and Yau S T 2005 The Existence of supersymmetric string theory with torsion J. Differ. Geom.70 143 · Zbl 1102.53052
[79]	Melnikov I V and Sharpe E 2011 On marginal deformations of (0, 2) non-linear sigma models Phys. Lett. B 705 529
[80]	Braun V, Brelidze T, Douglas M R and Ovrut B A 2008 Calabi-Yau metrics for quotients and complete intersections J. High Energy Phys.JHEP05(2008) 080
[81]	Douglas M R, Karp R L, Lukic S and Reinbacher R 2008 Numerical Calabi-Yau metrics J. Math. Phys.49 032302 · Zbl 1153.81351
[82]	Headrick M and Nassar A 2013 Energy functionals for Calabi-Yau metrics Adv. Theor. Math. Phys.17 867 · Zbl 1304.14050
[83]	Anderson L B, Braun V, Karp R L and Ovrut B A 2010 Numerical hermitian Yang-Mills connections and vector bundle stability in heterotic theories J. High Energy Phys.JHEP06(2010) 107 · Zbl 1288.81086
[84]	Blesneag S, Buchbinder E I, Candelas P and Lukas A 2016 Holomorphic Yukawa couplings in heterotic string theory J. High Energy Phys.JHEP01(2016) 152 · Zbl 1388.81776
[85]	Buchbinder E I, Constantin A, Gray J and Lukas A 2016 Yukawa unification in heterotic string theory (arXiv:1606.04032 [hep-th])
[86]	Anderson L B, Gray J, Grayson D, He Y H and Lukas A 2010 Yukawa couplings in heterotic compactification Commun. Math. Phys.297 95 · Zbl 1203.81130
[87]	Gray J, He Y H, Ilderton A and Lukas A 2009 STRINGVACUA: a mathematica package for studying vacuum configurations in string phenomenology Comput. Phys. Commun.180 107 · Zbl 1198.81156
[88]	Berglund P and Mayr P 1999 Heterotic string / F theory duality from mirror symmetry Adv. Theor. Math. Phys.2 1307 · Zbl 1041.81570
[89]	Friedman R, Morgan J and Witten E 1997 Vector bundles and F theory Commun. Math. Phys.187 679 · Zbl 0919.14010
[90]	Anderson L B and Taylor W 2014 Geometric constraints in dual F-theory and heterotic string compactifications J. High Energy Phys.JHEP08(2014) 025
[91]	Anderson L B 2016 Spectral covers, integrality conditions, and heterotic/F-theory duality J. Singularities15 1-13 · Zbl 1346.81109
[92]	Cvetic M, Grassi A and Poretschkin M 2016 Discrete symmetries in heterotic/F-theory duality and mirror symmetry (arXiv:1607.03176 [hep-th])
[93]	Cvetic M, Grassi A, Klevers D, Poretschkin M and Song P 2016 Origin of Abelian gauge symmetries in heterotic/F-theory duality J. High Energy Phys.JHEP04(2016) 041 · Zbl 1388.81169