808 research outputs found
Semiclassical Approach to Finite-N Matrix Models
We reformulate the zero-dimensional hermitean one-matrix model as a
(nonlocal) collective field theory, for finite~. The Jacobian arising by
changing variables from matrix eigenvalues to their density distribution is
treated {\it exactly\/}. The semiclassical loop expansion turns out {\it not\/}
to coincide with the (topological) ~expansion, because the
classical background has a non-trivial -dependence. We derive a simple
integral equation for the classical eigenvalue density, which displays strong
non-perturbative behavior around . This leads to IR singularities
in the large- expansion, but UV divergencies appear as well, despite
remarkable cancellations among the Feynman diagrams. We evaluate the free
energy at the two-loop level and discuss its regularization. A simple example
serves to illustrate the problems and admits explicit comparison with
orthogonal polynomial results.Comment: 27 pages / 3 figures (ps file fixed
Time-Space Noncommutative Abelian Solitons
We demonstrate the construction of solitons for a time-space Moyal-deformed
integrable U(n) sigma model (the Ward model) in 2+1 dimensions. These solitons
cannot travel parallel to the noncommutative spatial direction. For the U(1)
case, the rank-one single-soliton configuration is constructed explicitly and
is singular in the commutative limit. The projection to 1+1 dimensions reduces
it to a noncommutative instanton-like configuration. The latter is governed by
a new integrable equation, which describes a Moyal-deformed sigma model with a
particular Euclidean metric and a magnetic field.Comment: 1+10 page
From N=2 Fermionic Strings to Superstrings?
I review the covariant quantization of the critical fermionic string
with and without a global twist. The BRST analysis yields massless
bosonic and fermionic vertex operators in various ghost and picture number
sectors, as well as picture-changers and their inverses, depending on the field
basis chosen for bosonization. Two distinct GSO projections exist, one
(untwisted) retaining merely the known bosonic scalar and its spectral-flow
partner, the other (twisted) yielding two fermions and one boson, on the
massless level. The absence of interactions in the latter case rules out
standard spacetime supersymmetry. In the untwisted theory, the
-invariant three-point and vanishing four-point functions are confirmed
at tree level. I comment on the string field theory, the integration
over moduli and the realization of spectral flow.Comment: 15 pages, latex, no figures, macros included, 52 kb Talk at Symposium
in Wendisch-Rietz, 8/9
Supersymmetric noncommutative solitons
I consider a supersymmetric Bogomolny-type model in 2+1 dimensions
originating from topological string theory. By a gauge fixing this model is
reduced to a supersymmetric U(n) chiral model with a Wess-Zumino-Witten-type
term in 2+1 dimensions. After a noncommutative extension of the model, I employ
the dressing method to construct explicit multi-soliton configurations on
noncommutative R^{2,1|2N}.Comment: 13 pages, 2 figures; talk given during "Noncommutative Spacetime
Geometries" at Alessandria, March 2007, and "Noncommutative Geometry and
Physics" at Orsay, April 200
On the BRST Cohomology of N=2 Strings
We analyze the BRST cohomology of the critical N=2 NSR string using chiral
bosonization. Picture-changing and spectral flow is made explicit in a
holomorphic field basis. The integration of fermionic and U(1) moduli is
performed and yields picture- and U(1) ghost number-changing insertions into
the string measure for n-point amplitudes at arbitrary genus and U(1) instanton
number.Comment: Talk at ``Strings '95'', March 95; 2 page
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