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arXiv · 1702.08063

On the Octonionic Self Duality equations of 3-brane Instantons

Emmanuel Floratos·George K. Leontaris
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Abstract

We study the octonionic selfduality equations for $p=3$-branes in the light cone gauge and we construct explicitly, instanton solutions for spherical and toroidal topologies in various flat spacetime dimensions $(D=5+1,7+1,8+1,9+1)$, extending previous results for $p=2$ membranes. Assuming factorization of time we reduce the self-duality equations to integrable systems and we determine explicitly periodic, in Euclidean time, solutions in terms of the elliptic functions. These solutions describe 4d associative and non-associative calibrations in $D=7,8$ dimensions. It turns out that for spherical topology the calibration is non compact while for the toroidal topology is compact. We discuss possible applications of our results to the problem of 3-brane topology change and its implications for a non-perturbative definition of the 3-brane interactions.

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Emmanuel Floratos, George K. Leontaris. 2017-02-26. On the Octonionic Self Duality equations of 3-brane Instantons. https://arxiv.org/abs/1702.08063

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