A note on the geometry of hypermultiplets in the field theory of intersecting D3-branes

Abstract

We study the Kähler geometry of the hypermultiplet moduli space in the effective field theory of two intersecting D3-branes from the viewpoint of the classical RG flow equation governing the running of the Kähler potential defining the theory. We analyze this equation as a nonlinear PDE of first order and construct a general class of its solutions compatible with the symmetries in the problem. These solutions involve an arbitrary function of two independent variables and generically break the N=2 supersymmetry of the system to N=1 in 4 dimensions. Restricting this general class by the constraints of N=2 supersymmetry and periodicity for magnetic charge quantization, we recover the Gibbons-Hawking geometry previously proposed for this system in ref. [5]. This provides a systematic derivation and a uniqueness proof for the geometry of the moduli space in this problem. We also give an independent proof of the preservation of the N=2 supersymmetry by the RG flow and a reinterpretation of the periodicity in terms of a symmetry of the RG flow equation in appendices.