55 research outputs found
Branes at \C^4/\Ga Singularity from Toric Geometry
We study toric singularities of the form of \C^4/\Ga for finite abelian
groups \Ga \subset SU(4). In particular, we consider the simplest case
\Ga=\Z_2 \times \Z_2 \times \Z_2 and find explicitly charge matrices for
partial resolutions of this orbifold by extending the method by Morrison and
Plesser. We obtain three kinds of algebraic equations, and where 's parametrize
\C^5. When we put D1 branes at this singularity, it is known that the
field theory on the worldvolume of D1 branes is T-dual to brane cub model. We analyze geometric interpretation for field
theory parameters and moduli space.Comment: 1 figure, 4 tables, latex file and 26 pages:v1 added mathematical
results on projective crepant resolutions by Dais et al and refs added:v2
typos corrected and the beginning paragrphs in section 3 clarifie
Symmetry of Quantum Torus with Crossed Product Algebra
In this paper, we study the symmetry of quantum torus with the concept of
crossed product algebra. As a classical counterpart, we consider the orbifold
of classical torus with complex structure and investigate the transformation
property of classical theta function. An invariant function under the group
action is constructed as a variant of the classical theta function. Then our
main issue, the crossed product algebra representation of quantum torus with
complex structure under the symplectic group is analyzed as a quantum version
of orbifolding.
We perform this analysis with Manin's so-called model II quantum theta
function approach. The symplectic group Sp(2n,Z) satisfies the consistency
condition of crossed product algebra representation. However, only a subgroup
of Sp(2n,Z) satisfies the consistency condition for orbifolding of quantum
torus.Comment: LaTeX 17pages, changes in section 3 on crossed product algebr
Morita Equivalence of Noncommutative Supertori
In this paper we study the extension of Morita equivalence of noncommutative
tori to the supersymmetric case. The structure of the symmetry group yielding
Morita equivalence appears to be intact but its parameter field becomes
supersymmetrized having both body and soul parts. Our result is mainly in the
two dimensional case in which noncommutative supertori have been constructed
recently: The group , where denotes Grassmann even
number whose body part belongs to , yields Morita equivalent
noncommutative supertori in two dimensions.Comment: LaTeX 18 pages, the version appeared in JM
Quantum Thetas on Noncommutative T^4 from Embeddings into Lattice
In this paper we investigate the theta vector and quantum theta function over
noncommutative T^4 from the embedding of R x Z^2. Manin has constructed the
quantum theta functions from the lattice embedding into vector space (x finite
group). We extend Manin's construction of the quantum theta function to the
embedding of vector space x lattice case. We find that the holomorphic theta
vector exists only over the vector space part of the embedding, and over the
lattice part we can only impose the condition for Schwartz function. The
quantum theta function built on this partial theta vector satisfies the
requirement of the quantum theta function. However, two subsequent quantum
translations from the embedding into the lattice part are non-additive,
contrary to the additivity of those from the vector space part.Comment: 20 pages, LaTeX, version to appear in J. Phys.
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