12,944 research outputs found
Symmetry Reduction by Lifting for Maps
We study diffeomorphisms that have one-parameter families of continuous
symmetries. For general maps, in contrast to the symplectic case, existence of
a symmetry no longer implies existence of an invariant. Conversely, a map with
an invariant need not have a symmetry. We show that when a symmetry flow has a
global Poincar\'{e} section there are coordinates in which the map takes a
reduced, skew-product form, and hence allows for reduction of dimensionality.
We show that the reduction of a volume-preserving map again is volume
preserving. Finally we sharpen the Noether theorem for symplectic maps. A
number of illustrative examples are discussed and the method is compared with
traditional reduction techniques.Comment: laTeX, 31 pages, 5 figure
ADE string vacua with discrete torsion
We complete the classification of (2,2) string vacua that can be constructed
by diagonal twists of tensor products of minimal models with ADE invariants.
Using the \LG\ framework, we compute all spectra from inequivalent models of
this type. The completeness of our results is only possible by systematically
avoiding the huge redundancies coming from permutation symmetries of tensor
products. We recover the results for (2,2) vacua of an extensive computation of
simple current invariants by Schellekens and Yankielowitz, and find 4
additional mirror pairs of spectra that were missed by their stochastic method.
For the model we observe a relation between redundant spectra and
groups that are related in a particular way.Comment: 13 pages (LaTeX), preprint CERN-TH.6931/93 and ITP-UH-20/93
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