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

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Abstract

This note is motivated by a recently published paper (Biswas and Mukherjee in Commun Math Phys 322(2):373–384, 2013). We prove a no-go result for the existence of suitable solutions of the Strominger system in a compact complex parallelizable manifold \({M = G/\Gamma}\). For this, we assume G to be non-abelian, the Hermitian metric to be induced from a right invariant metric on G, the Bianchi identity to be satisfied using the Chern connection and furthermore the gauge field to be flat. In Biswas and Mukherjee (Commun Math Phys 322(2):373–384, 2013) it is claimed that one such solution exists on \({SL(2, \mathbb{C})/\Gamma}\). Our result contradicts the main result in Biswas and Mukherjee (Commun Math Phys 322(2):373–384, 2013).

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Authors and Affiliations

  1. Department of Mathematics, Free University Berlin, Arnimallee 4, 14195, Berlin, Germany

    Bjorn Andreas

  2. EPFL SB MATHGEOM GEOM, École Polytechnique Fédéral de Lausanne, MA B1 437, Station 8, 1015, Lausanne, Switzerland

    Mario Garcia-Fernandez

Authors
  1. Bjorn Andreas
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  2. Mario Garcia-Fernandez
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Correspondence to Bjorn Andreas.

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Communicated by N. A. Nekrasov

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Andreas, B., Garcia-Fernandez, M. Note on Solutions of the Strominger System from Unitary Representations of Cocompact Lattices of \({SL(2,\mathbb{C})}\) . Commun. Math. Phys. 332, 1381–1383 (2014). https://doi.org/10.1007/s00220-014-1920-5

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  • DOI: https://doi.org/10.1007/s00220-014-1920-5

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