Entropy of Pairs of Dual Attractors in 6D/7D

We study the attractor mechanism of dual pairs of black brane bounds in N=2 supergravity in six and seven dimensions. First, we consider the effective potentials of the 6D and 7D black branes as well as their entropies. The contribution coming from the SO(1,1) factor of the moduli spaces M_{6D} and M_{7D} of these theories is carefully analyzed and it is used to motivate the study of the dual black branes bounds; which in turn allow to fix the critical value of the dilaton at horizon. The attractor eqs of the black branes and the bound pairs are derived by combining the criticality conditions of the corresponding effective potentials and the Lagrange multiplier method capturing constraints eqs on the fields moduli.Comment: 55 pages, 2 figures, To appear in JHE

HyperKhaler Metrics Building and Integrable Models

Methods developed for the analysis of integrable systems are used to study the problem of hyperK\"ahler metrics building as formulated in D=2 N=4 supersymmetric harmonic superspace. We show, in particular, that the constraint equation $\beta\partial^{++2}\omega -\xi^{++2}\exp 2\beta\omega =0$ and its Toda like generalizations are integrable. Explicit solutions together with the conserved currents generating the symmetry responsible of the integrability of these equations are given. Other features are also discussedComment: Latex file, 12 page