Brane Resolution Through Transgression
  Modifications to the singularity structure of D3-branes that result from turning on a flux for the R-R and NS-NS 3-forms (fractional D3-branes) provide important gravity duals of four-dimensional N=1 super-Yang-Mills theories. We construct generalisations of these modified p-brane solutions in a variety of other cases, including heterotic 5-branes, dyonic strings, M2-branes, D2-branes, D4-branes and type IIA and type IIB strings, by replacing the flat transverse space with a Ricci-flat manifold M_n that admits covariantly constant spinors, and turning on a flux built from a harmonic form in M_n, thus deforming the original solution and introducing fractional branes. The construction makes essential use of the Chern-Simons or ``transgression'' terms in the Bianchi-identity or equation of motion of the field strength that supports the original undeformed solution. If the harmonic form is L^2 normalisable, this can result in a deformation of the brane solution that is free of singularities, thus providing viable gravity duals of field theories in diverse dimensions that have less than maximal supersymmetry. We obtain examples of non-singular heterotic 5-branes, dyonic strings, M2-branes, type IIA strings, and D2-branes. 
M. Cvetic, H. Lu and C.N. Pope