Defect (p,q)(p,q) five-branes

We study a local description of composite five-branes of codimension two. The formulation is constructed by virtue of SL(2,Z)×SL(2,Z)SL(2,Z)×SL(2,Z) monodromy associated with two-torus. Applying conjugate monodromy transformations to the complex structures of the two-torus, we obtain a field configuration of a defect (p,q)(p,q) five-brane. This is a composite state of p defect NS5-branes and q   exotic 522-branes. We also obtain a new example of hyper-Kähler geometry. This is an ALG space, a generalization of an ALF space which asymptotically has a tri-holomorphic two-torus action. This geometry appears in the conjugate configuration of a single defect KK5-brane.