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arXiv · hep-th/0504157

Large-small dualities between periodic collapsing/expanding branes and brane funnels

C. Papageorgakis·S. Ramgoolam
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Abstract

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 $S^6$.

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C. Papageorgakis, S. Ramgoolam. 2005-05-02. Large-small dualities between periodic collapsing/expanding branes and brane funnels. https://doi.org/10.1016/j.nuclphysb.2005.09.044

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