3,574 research outputs found
Chiral anomalies in noncommutative gauge theories
Using cohomological methods we discuss several issues related to chiral
anomalies in noncommutative U(N) YM theories in any even dimension. We show
that for each dimension there is only one solution of the WZ consistency
condition and that there cannot be any reducible anomaly, nor any mixed anomaly
when the gauge group is a product group. We also clarify some puzzling aspects
of the issue of the anomaly when chiral fermions are in the adjoint
representation.Comment: 12 pages, Latex, typos and semantic ambiguities correcte
Conifold geometries, matrix models and quantum solutions
This paper is a continuation of hepth/0507224 where open topological B-models
describing D-branes on 2-cycles of local Calabi--Yau geometries with conical
singularities were studied. After a short review, the paper expands in
particular on two aspects: the gauge fixing problem in the reduction to two
dimensions and the quantum matrix model solutions.Comment: 17 p. To appear in proc. Symposium QTS-4, Varna (Bulgaria), August
200
Generalized q-deformed Correlation Functions as Spectral Functions of Hyperbolic Geometry
We analyse the role of vertex operator algebra and 2d amplitudes from the
point of view of the representation theory of infinite dimensional Lie
algebras, MacMahon and Ruelle functions. A p-dimensional MacMahon function is
the generating function of p-dimensional partitions of integers. These
functions can be represented as amplitudes of a two-dimensional c=1 CFT. In
this paper we show that p-dimensional MacMahon functions can be rewritten in
terms of Ruelle spectral functions, whose spectrum is encoded in the
Patterson-Selberg function of three dimensional hyperbolic geometry.Comment: 12 pages, no figure
Heterotic Matrix String Theory and Riemann Surfaces
We extend the results found for Matrix String Theory to Heterotic Matrix
String Theory, i.e. to a 2d O(N) SYM theory with chiral (anomaly free) matter
and N=(8,0) supersymmetry. We write down the instanton equations for this
theory and solve them explicitly. The solutions are characterized by branched
coverings of the basis cylinder, i.e. by compact Riemann surfaces with
punctures. We show that in the strong coupling limit the action becomes the
heterotic string action plus a free Maxwell action. Moreover the amplitude
based on a Riemann surface with p punctures and h handles is proportional to
g^{2-2h-p}, as expected for the heterotic string interaction theory with string
coupling g_s=1/g.Comment: 17 pages, JHEP LaTeX style, sentence delete
Fermionic flows and tau function of the N=(1|1) superconformal Toda lattice hierarchy
An infinite class of fermionic flows of the N=(1|1) superconformal Toda
lattice hierarchy is constructed and their algebraic structure is studied. We
completely solve the semi-infinite N=(1|1) Toda lattice and chain hierarchies
and derive their tau functions, which may be relevant for building
supersymmetric matrix models. Their bosonic limit is also discussed.Comment: 11 pages, no figures, revised version published in Nucl. Phys.
N=2 local and N=4 nonlocal reductions of supersymmetric KP hierarchy in N=2 superspace
A N=4 supersymmetric matrix KP hierarchy is proposed and a wide class of its
reductions which are characterized by a finite number of fields are described.
This class includes the one-dimensional reduction of the two-dimensional
N=(2|2) superconformal Toda lattice hierarchy possessing the N=4 supersymmetry
-- the N=4 Toda chain hierarchy -- which may be relevant in the construction of
supersymmetric matrix models. The Lax pair representations of the bosonic and
fermionic flows, corresponding local and nonlocal Hamiltonians, finite and
infinite discrete symmetries, the first two Hamiltonian structures and the
recursion operator connecting all evolution equations and the Hamiltonian
structures of the N=4 Toda chain hierarchy are constructed in explicit form.
Its secondary reduction to the N=2 supersymmetric alpha=-2 KdV hierarchy is
discussed.Comment: 26 pages, LaTeX, a few misprints correcte
Supersymmetrization of horizontality condition: nilpotent symmetries for a free spinning relativistic particle
We derive the off-shell nilpotent and absolutely anticommuting
Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for a
supersymmetric system of a free spinning relativistic particle within the
framework of superfield approach to BRST formalism. A novel feature of our
present investigation is the consistent and clear supersymmetric modification
of the celebrated horizontality condition for the precise determination of the
proper (anti-)BRST symmetry transformations for all the bosonic and fermionic
dynamical variables of our theory which is considered on a (1, 2)-dimensional
supermanifold parameterized by an even (bosonic) variable (\tau) and a pair of
odd (fermionic) variables \theta and \bar\theta (with \theta^2 = \bar\theta^2 =
0,\; \theta \bar\theta + \bar\theta \theta = 0) of the Grassmann algebra. One
of the most important features of our present investigation is the derivation
of (anti-)BRST invariant Curci-Ferrari type restriction which turns out to be
responsible for the absolute anticommutativity of the (anti-)BRST symmetry
transformations and existence of the coupled (but equivalent) Lagrangians for
the present theory of a supersymmetric system.Comment: LaTeX file, 24 pages, version to appear in EPJ
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