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We consider deformations of torsion-free G2 structures, defined by the G2-invariant 3-form $phi$ and compute the expansion of the Hodge star of $phi$ to fourth order in the deformations of $phi$. By considering M-theory compactified on a G2 manifold, the G2 moduli space is naturally complexified, and we get a Kahler metric on it. Using the expansion of the Hodge star of $phi$ we work out the full curvature of this metric and relate it to the Yukawa coupling.
We study the moduli space volume of BPS vortices in quiver gauge theories on compact Riemann surfaces. The existence of BPS vortices imposes constraints on the quiver gauge theories. We show that the moduli space volume is given by a vev of a suitabl
In this paper we show that the homology of a certain natural compactification of the moduli space, introduced by Kontsevich in his study of Wittens conjectures, can be described completely algebraically as the homology of a certain differential grade
We show that the moduli space of regular affine vortices, which are solutions of the symplectic vortex equation over the complex plane, has the structure of a smooth manifold. The construction uses Zilteners Fredholm theory results [31]. We also exte
Harmonic maps that minimise the Dirichlet energy in their homotopy classes are known as lumps. Lump solutions on real projective space are explicitly given by rational maps subject to a certain symmetry requirement. This has consequences for the beha
We investigate the distribution of field theories that arise from the low energy limit of flux vacua built on type IIB string theory compactified on the mirror quintic. For a large collection of these models, we numerically determine the distribution