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BPS D3-branes on smooth ALE manifolds

Pietro Fré
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Abstract

In this talk I review the recent construction of a new family of classical BPS solutions of type IIB supergravity describing 3-branes transverse to a 6-dimensional space with topology $\mathbb{R}^{2}\times$ALE. They are characterized by a non-trivial flux of the supergravity 2-forms through the homology 2-cycles of a generic smooth ALE manifold. These solutions have two Killing spinors and thus preserve $\mathcal{N}=2$ supersymmetry. They are expressed in terms of a quasi harmonic function $H$ (the ``warp factor''), whose properties was studied in detail in the case of the simplest ALE, namely the Eguchi-Hanson manifold. The equation for $H$ was identified as an instance of the confluent Heun equation.

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Pietro Fré. 2001-10-30. BPS D3-branes on smooth ALE manifolds. https://arxiv.org/abs/hep-th/0110281

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