Chern-Simons flows on Aloff-Wallach spaces and spin(7) instantons

Alexander S. Haupt, Tatiana A. Ivanova, Olaf Lechtenfeld, and Alexander D. Popov
Phys. Rev. D 83, 105028 – Published 27 May 2011

Abstract

Because of their explicit construction, Aloff-Wallach spaces are prominent in flux compactifications. They carry G2 structures and admit the G2-instanton equations, which are natural Bogomol’nyi-Prasad-Sommerfeld equations for Yang-Mills instantons on seven-manifolds and extremize a Chern-Simons–type functional. We consider the Chern-Simons flow between different G2 instantons on Aloff-Wallach spaces, which is equivalent to spin(7) instantons on a cylinder over them. For a general SU(3)-equivariant gauge connection, the generalized instanton equations turn into gradient-flow equations on C3×R2, with a particular cubic superpotential. For the simplest member of the Aloff-Wallach family (with 3-Sasakian structure) we present an explicit instanton solution of tanh-like shape.

  • Figure
  • Received 4 May 2011

DOI:https://doi.org/10.1103/PhysRevD.83.105028

© 2011 American Physical Society

Authors & Affiliations

Alexander S. Haupt1,*, Tatiana A. Ivanova2,†, Olaf Lechtenfeld1,3,‡, and Alexander D. Popov2,§

  • 1Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany
  • 2Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Moscow Region, Russia
  • 3Centre for Quantum Engineering and Space-Time Research, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany

  • *Alexander.Haupt@itp.uni-hannover.de
  • ita@theor.jinr.ru
  • Olaf.Lechtenfeld@itp.uni-hannover.de
  • §popov@theor.jinr.ru

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Vol. 83, Iss. 10 — 15 May 2011

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