We present a quasiperiodic self-dual metric of the Gibbons-Hawking type with one gravitational instanton per spacetime cell. The solution, based on an adaptation of Weierstrassian ζ and σ functions to three dimensions, conforms to a definition of spacetime foam given by Hawking.

The commutator of the Virasoro operator Lm and general vertex operator V for the mass level L is explicitly calculated. By demanding that a physical vertex operator must be of conformal dimension J=1, a set of algebraic equations for determining the vertex operators corresponding to all physical states of bosonic strings is obtained. Explicit expressions for the first three mass levels are given.

The Seiberg-Witten equations, when dimensionally reduced to R 2 , naturally yield the Liouville equation, whose solutions are parametrized by an arbitrary analytic function g(z). The magnetic flux Φ is the integral of a singular Kaehler form involving g(z); for an appropriate choice of g(z) , N coaxial or separated vortex configurations with Φ = 2πN e are obtained when the integral is regularized. The regularized connection in the R 1 case coincides with the kink solution of ϕ 4 theory.

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