Invariant Solutions to the Strominger System on Complex Lie Groups and Their Quotients

Fei, Teng; Yau, Shing-Tung

doi:10.1007/s00220-015-2374-0

Invariant Solutions to the Strominger System on Complex Lie Groups and Their Quotients

Teng Fei
(
- MIT
)
,
Shing-Tung Yau
(
- Harvard U.
)

Jul 29, 2014

13 pages

Published in:

Commun.Math.Phys. 338 (2015) 3, 1183-1195

Published: May 3, 2015

e-Print:

1407.7641 [math-ph]

DOI:

10.1007/s00220-015-2374-0

View in:

pdf

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Abstract: (Springer)

Using canonical 1-parameter family of Hermitian connections on the tangent bundle, we provide invariant solutions to the Strominger system on certain complex Lie groups and their quotients. Both flat and non-flat cases are discussed in detail. This paper answers a question proposed by Andreas and Garcia-Fernandez in Comm Math Phys 332(3):1381–1383, 2014.

Note:

11 pages, comments are welcome. Updates in v2: minor typos are corrected. Updates in v3: small revisions, to be consistent with published version

group: Lie
fibre bundle
fibre bundle: vector
SL(2,C)
solution

References(19)

Figures(0)

[AG86]

Hermitian left invariant metrics on complex Lie groups and cosymplectic Hermitian manifolds

E. Abbena
,
A. Grassi

- Boll.Union.Mat.Ital.A 5 (1986) 371-379

[AGF12]

Solutions of the Strominger System via Stable Bundles on Calabi-Yau Threefolds

- Commun.Math.Phys. 315 (2012) 153-168
•
e-Print:
- 1008.1018
•
DOI:
- 10.1007/s00220-012-1509-9

[AGF14]

Note on Solutions of the Strominger System from Unitary Representations of Cocompact Lattices of ${SL(2,\mathbb{C})}$

- Commun.Math.Phys. 332 (2014) 3, 1381-1383
•
DOI:
- 10.1007/s00220-014-1920-5

[BM13]

Solutions of Strominger system from unitary representations of cocompact lattices of SL(2,C)

Indranil Biswas
(
- Tata Inst.
)
,
Avijit Mukherjee
(
- Jadavpur U.
)

- Commun.Math.Phys. 322 (2013) 373-384
•
e-Print:
- 1301.0375
•
DOI:
- 10.1007/s00220-013-1765-3

[FIUV09]

Non-Kaehler Heterotic String Compactifications with non-zero fluxes and constant dilaton

Marisa Fernandez
(
- Basque U., Bilbao
)
,
Stefan Ivanov
(
- Sofiya U., Math. Comp. Sci. Dept.
)
,
Luis Ugarte
(
- Zaragoza U.
)
,
Raquel Villacampa
(
- Zaragoza U.
)

- Commun.Math.Phys. 288 (2009) 677-697
•
e-Print:
- 0804.1648
•
DOI:
- 10.1007/s00220-008-0714-z

[FTY09]

Local Heterotic Torsional Models

Ji-Xiang Fu
(
- Fudan U.
)
,
Li-Sheng Tseng
(
- Harvard U., Dept. Math. and
- Harvard U., Phys. Dept.
)
,
Shing-Tung Yau
(
- Harvard U., Dept. Math.
)

- Commun.Math.Phys. 289 (2009) 1151-1169
•
e-Print:
- 0806.2392
•
DOI:
- 10.1007/s00220-009-0789-1

[FY08]

The Theory of superstring with flux on non-Kahler manifolds and the complex Monge-Ampere equation

Ji-Xiang Fu
(
- Fudan U. and
- Fudan U., Surf. Phys. Lab.
)
,
Shing-Tung Yau
(
- Harvard U., Dept. Math.
)

- J.Diff.Geom. 78 (2008) 3, 369-428
•
e-Print:
- hep-th/0604063

[Gau97]

Hermitian connections and Dirac operators. Bollettino della Unione Matematica ItalianaB, 11(2, Suppl.):257-288

P. Gauduchon

[GP04]

Geometric model for complex nonKahler manifolds with SU(3) structure

- Commun.Math.Phys. 251 (2004) 65-78
•
e-Print:
- hep-th/0212307
•
DOI:
- 10.1007/s00220-004-1167-7

[Gra11]

Geometry of compact complex homogeneous spaces with vanishing first Chern class

Gueo Grantcharov
(
- FIU, Miami
)

- Adv.Math. 226 (2011) 3136-3159
•
e-Print:
- 0905.0040
•
DOI:
- 10.1016/j.aim.2010.10.005

[Kna02]

Lie Groups beyond an Introduction 2nd Edition. Progress in Mathematics Vol. 140. Birkhäuser

A.W. Knapp

[LY87]

Hermitian-Yang-Mills connection on non-Kähler manifolds. In Mathematical Aspects of String Theory, Advanced Series in Mathematical Physics Vol. 1, pages 560-573

J. Li
,
S.-T. Yau

[LY05]

The Existence of supersymmetric string theory with torsion

- J.Diff.Geom. 70 (2005) 1, 143-181
•
e-Print:
- hep-th/0411136

[Mic82]

On the existence of special metrics in complex geometry. Acta Mathematica, 149(1):261-295

M.L. Michelsohn

[Rei87]

The moduli space of 3-folds with K = 0 may nevertheless be irreducible

M. Reid

- Math.Ann. 278 (1987) 329-334

[Str86]

Superstrings with Torsion

Andrew Strominger
(
- Santa Barbara, KITP and
- Princeton, Inst. Advanced Study
)

- Nucl.Phys.B 274 (1986) 253,
- Nucl. Phys. B274 ( 1986) 253-284 and Calif. Univ. Santa Barbara - NSF-ITP-86-016 (86,REC.MAR.) 32 P. (604232)
•
DOI:
- 10.1016/0550-3213(86)90286-5

[UY86]

On the existence of Hermitian-Yang-Mills connections in stable vector bundles. Communications on Pure and Applied Mathematics, 39(S1):257-293

K. Uhlenbeck
,
S.-T. Yau

[Wan54]

Complex parallisable manifolds

H.-C. Wang

- Proc.Am.Math.Soc. 5 (1954) 771-776

[Yau78]

On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I

Shing-Tung Yau

- Commun.Pure Appl.Math. 31 (1978) 3, 339-411
•
DOI:
- 10.1002/cpa.3160310304