Reduced Moduli Space Research Articles

Almost-isometry between the Teichmüller metric and the length-spectrum metric on reduced moduli space for surfaces with boundary

We show that the Teichmüller metric and the length-spectrum metric are almost-isometric on moduli space of hyperbolic surfaces with geodesic boundaries whose lengths are bounded above.

The single-state supermultiplet in (1 + 1) dimensions

We consider multiplet shortening forBogomol'nyi-Prasad-Sommerfield solitons in \U0001d4a9 = 1 two-dimensional models. Examples of single-statemultiplets were established previously in \U0001d4a9 = 1Landau-Ginzburg models. The shortening comes at the price oflosing the fermion parity (-1)F due to boundary effects. Thisimplies the disappearance of the boson-fermion classificationresulting in abnormal statistics. We discuss an appropriateindex that counts such short multiplets.A broad class of hybrid models which extend the Landau-Ginzburgmodels to include a nonflat metric on the target space areconsidered. Our index turns out to be related to the index ofthe Dirac operator on the soliton reduced moduli space (themoduli space is reduced by factoring out the translationalmodulus). The index vanishes in most cases, implying the absenceof shortening. In particular, it vanishes when there are onlytwo critical points on the compact target space and the reducedmoduli space has nonvanishing dimension.We also generalize the anomaly in the central charge totake into account the target space metric.

Lump Dynamics in the ℂ P 1 Model on the Torus

The topology and geometry of the moduli space, M 2, of degree 2 static solutions of the ℂP 1 model on a torus (spacetime T 2×ℝ) are studied. It is proved that M 2 is homeomorphic to the left coset space G/G 0, where G is a certain eight-dimensional noncompact Lie group and G 0 is a discrete subgroup of order 4. Low energy two-lump dynamics is approximated by geodesic motion on M 2 with respect to a metric g defined by the restriction to M 2 of the kinetic energy functional of the model. This lump dynamics decouples into a trivial “centre of mass” motion and nontrivial relative motion on a reduced moduli space. It is proved that (M 2,g) is geodesically incomplete and has only finite diameter. A low dimensional geodesic submanifold is identified and a full description of its geodesics obtained.