Making manifest the symmetry enhancement for coinciding BPS branes

We consider g = N − 1 coinciding M-5-branes on top of each other, in the multiple KK monopole background Q. The worldvolume of an M-5-brane is the local product of the four-dimensional spacetime R and an elliptic curve. Taken together, these genus-one Riemann surfaces are supposed to give a single (SeibergWitten) hyperelliptic curve Σg in the coincidence limit, where the gauge symmetry is known to be enhanced to SU(N). We make this gauge symmetry enhancement manifest by analyzing the corresponding hypermultiplet LEEA which is given by the N=2 non-linear sigma-model having Q as the target space. The hyper-Kähler manifold Q is known to be given by the multicentre Taub-NUT space, which in the coincidence limit amounts to the multiple Eguchi-Hanson (ALE) space QmEH. The latter is most naturally described by using the hyper-Kähler coset construction in harmonic superspace, in terms of the auxiliary N=2 vector superfields as Lagrange multipliers in the presence of FI terms. The Maldacena limit, in which the LEEA is given by the N=4 SYM with the gauge group SU(N), corresponds to sending all the FI terms to zero at large N , when all the auxiliary N=2 vector superfields