Monopoles, Curves and Ramanujan

Research paper by H. W. Braden, V. Z. Enolski

Indexed on: 30 Apr '07Published on: 30 Apr '07Published in: Mathematical Physics


We develop the Ercolani-Sinha construction of SU(2) monopoles and make this effective for (a five parameter family of centred) charge 3 monopoles. In particular we show how to solve the transcendental constraints arising on the spectral curve. For a class of symmetric curves the transcendental constraints become a number theoretic problem and a recently proven identity of Ramanujan provides a solution.