Non-Collapsing Membrane Instantons in Higher Dimensions

Details Non-Collapsing Membrane Instantons in Higher Dimensions Non-Collapsing Membrane Instantons in Higher Dimensions

2002-08-21

arxiv.org/abs/hep-th/0208151v1

Phys.Lett. B545 (2002) 190-196

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, 2 figures

Scientific paper

10.1016/S0370-2693(02)02550-9

We introduce a particular embedding of seven dimensional self-duality membrane equations in C^3\times R which breaks G_2 invariance down to SU(3). The world-volume membrane instantons define SU(3) special lagrangian submanifolds of C^3. We discuss in detail solutions for spherical and toroidal topologies assuming factorization of time. We show that the extra dimensions manifest themselves in the solutions through the appearance of a non-zero conserved charge which prevents the collapse of the membrane. We find non-collapsing rotating membrane instantons which contract from infinite size to a finite one and then they bounce to infinity in finite time. Their motion is periodic. These generalized complex Nahm equations, in the axially symmetric case, lead to extensions of the continuous Toda equation to complex space.

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