The geometry of the moduli space of $P^1$ vortex-antivortex pairs

Martin Speight (University of Leeds)

Friday 27th March, 2015 15:00-16:00 Maths 214

Abstract

Vortices are topological solitons in (2+1) dimensions which carry quantized magnetic flux. There is an interesting version of Ginzburg-Landau theory, where the field takes values in ${\mathbb C}P^1$, which supports stable vortex-antivortex pairs in any relative positions. The space of such pairs carries a natural Riemannian metric whose geodesics model low energy vortex-antivortex dynamics. I will describe this metric, deriving conjectural asymptotic formulae for it in the regimes of large and small vortex-antivortex separation. (Joint work with Nuno Romao.)

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