1,106 research outputs found
Chern-Simons Theory on Seifert 3-Manifolds
We study Chern-Simons theory on 3-manifolds M that are circle-bundles over
2-dimensional orbifolds S by the method of Abelianisation. This method, which
completely sidesteps the issue of having to integrate over the moduli space of
non-Abelian flat connections, reduces the complete partition function of the
non-Abelian theory on M to a 2-dimensional Abelian theory on the orbifold S
which is easily evaluated.Comment: 27 page
Equivariant Kaehler Geometry and Localization in the G/G Model
We analyze in detail the equivariant supersymmetry of the model. In
spite of the fact that this supersymmetry does not model the infinitesimal
action of the group of gauge transformations, localization can be established
by standard arguments. The theory localizes onto reducible connections and a
careful evaluation of the fixed point contributions leads to an alternative
derivation of the Verlinde formula for the WZW model. We show that the
supersymmetry of the model can be regarded as an infinite dimensional
realization of Bismut's theory of equivariant Bott-Chern currents on K\"ahler
manifolds, thus providing a convenient cohomological setting for understanding
the Verlinde formula. We also show that the supersymmetry is related to a
non-linear generalization (q-deformation) of the ordinary moment map of
symplectic geometry in which a representation of the Lie algebra of a group
is replaced by a representation of its group algebra with commutator . In the large limit it reduces to the ordinary moment map of
two-dimensional gauge theories.Comment: LaTex file, 40 A4 pages, IC/94/108 and ENSLAPP-L-469/9
The Universality of Penrose Limits near Space-Time Singularities
We prove that Penrose limits of metrics with arbitrary singularities of
power-law type show a universal leading u^{-2}-behaviour near the singularity
provided that the dominant energy condition is satisfied and not saturated. For
generic power-law singularities of this type the oscillator frequencies of the
resulting homogeneous singular plane wave turn out to lie in a range which is
known to allow for an analytic extension of string modes through the
singularity. The discussion is phrased in terms of the recently obtained
covariant characterisation of the Penrose limit; the relation with null
geodesic deviation is explained in detail.Comment: 36 pages, LaTeX2e, 4 figure
Penrose limits and maximal supersymmetry
We show that the maximally supersymmetric pp-waves of IIB superstring and
M-theories can be obtained as a Penrose limit of the supersymmetric AdS x S
solutions. In addition we find that in a certain large tension limit, the
geometry seen by a brane probe in an AdS x S background is either Minkowski
space or a maximally supersymmetric pp-wave.Comment: 12 pages, v2: references adde
Euclidean SYM Theories by Time Reduction and Special Holonomy Manifolds
Euclidean supersymmetric theories are obtained from Minkowskian theories by
performing a reduction in the time direction. This procedure elucidates certain
mysterious features of Zumino's N=2 model in four dimensions, provides
manifestly hermitian Euclidean counterparts of all non-mimimal SYM theories,
and is also applicable to supergravity theories. We reanalyse the twists of the
4d N=2 and N=4 models from this point of view. Other applications include SYM
theories on special holonomy manifolds. In particular, we construct a twisted
SYM theory on Kaehler 3-folds and clarify the structure of SYM theory on
hyper-Kaehler 4-folds.Comment: 21 pages, LaTeX fil
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