Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-12-28
Mod.Phys.Lett.A11:827-834,1996
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX file, 8 pages, a reference corrected
Scientific paper
10.1142/S0217732396000837
We investigate possible existence of duality symmetries which exchange the Kaluza-Klein modes with the wrapping modes of a BPS saturated $p$-brane on a torus. Assuming the validity of the conjectured $U$-duality symmetries of type II and heterotic string theories and $M$-theory, we show that for a BPS saturated $p$-brane there is an SL(2,Z) symmetry that mixes the Kaluza-Klein modes on a $(p+1)$ dimensional torus $T^{(p+1)}$ with the wrapping modes of the $p$-brane on $T^{(p+1)}$. The field that transforms as a modular parameter under this SL(2,Z) transformation has as its real part the component of the $(p+1)$-form gauge field on $T^{(p+1)}$, and as its imaginary part the volume of $T^{(p+1)}$, measured in the metric that couples naturally to the $p$-brane.
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