Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-04-19
Nucl.Phys. B731 (2005) 45-84
Physics
High Energy Physics
High Energy Physics - Theory
Latex, 50 pages, 2 figures ; v2 : a systematic typographical error corrected + minor changes
Scientific paper
10.1016/j.nuclphysb.2005.09.044
We consider space and time dependent fuzzy spheres $S^{2p}$ arising in $D1-D(2p+1)$ intersections in IIB string theory and collapsing D(2p)-branes in IIA string theory. In the case of $S^2$, where the periodic space and time-dependent solutions can be described by Jacobi elliptic functions, there is a duality of the form $r$ to ${1 \over r}$ which relates the space and time dependent solutions. This duality is related to complex multiplication properties of the Jacobi elliptic functions. For $S^4$ funnels, the description of the periodic space and time dependent solutions involves the Jacobi Inversion problem on a hyper-elliptic Riemann surface of genus 3. Special symmetries of the Riemann surface allow the reduction of the problem to one involving a product of genus one surfaces. The symmetries also allow a generalisation of the $r$ to ${1 \over r} $ duality. Some of these considerations extend to the case of the fuzzy $S^6$.
Papageorgakis Constantinos
Ramgoolam Sanjaye
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