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Mikhailov has constructed an infinite family of 1 8 BPS D3-branes in AdS 5 × S 5 . We regulate Mikhailov's solution space by focussing on finite dimensional submanifolds. Our submanifolds are topologically complex projective spaces with symplectic form cohomologically equal to 2πN times the Fubini-Study Kähler class. Upon quantization and removing the regulator we find the Hilbert Space of N noninteracting Bose particles in a 3d Harmonic oscillator, a result previously conjectured by Beasley.This Hilbert Space is isomorphic to the classical chiral ring of 1 8 BPS states in N = 4 Yang-Mills theory. We view our result as evidence that the spectrum of 1 8 BPS states in N = 4 Yang Mills theory, which is known to jump discontinuously from zero to infinitesimal coupling, receives no further renormalization at finite values of the 't Hooft coupling.

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Abstract. We study the spaces of stable real and quaternionic vector bundles on a real algebraic curve. The basic relationship is established with unitary representations of an extension of Z/2 by the fundamental group. By comparison with the space of real or quaternionic connections, some of the basic topological invariants of these spaces are calculated.

Given a compact Kähler manifold M and a connected reductive algebraic group G over [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /], a prinlcipal G -bundle over M admits an Einstein-Hermitian connection if and only if the principal bundle is polystable. If M is a projective manifold, a Higgs G -bundle over M admits an Einstein-Hermitian connection if and only if the Higgs bundle is polystable.