138 research outputs found
-identities and affinized projective varieties, I. Quadratic monomial ideals
We define the concept of an affinized projective variety and show how one
can, in principle, obtain q-identities by different ways of computing the
Hilbert series of such a variety. We carry out this program for projective
varieties associated to quadratic monomial ideals. The resulting identities
have applications in describing systems of quasi-particles containing
null-states and can be interpreted as alternating sums of quasi-particle Fock
space characters.Comment: AMSTeX, 22 page
q-Identities and affinized projective varieties, II. Flag varieties
In a previous paper we defined the concept of an affinized projective variety
and its associated Hilbert series. We computed the Hilbert series for varieties
associated to quadratic monomial ideals. In this paper we show how to apply
these results to affinized flag varieties. We discuss various examples and
conjecture a correspondence between the Hilbert series of an affinized flag
variety and a modified Hall-Littlewood polynomial. We briefly discuss the
application of these results to quasi-particle character formulas for affine
Lie algebra modules.Comment: AMSTeX, 25 pages, 3 figure
Spherical T-Duality and the spherical Fourier-Mukai transform
In earlier papers, we introduced spherical T-duality, which relates pairs of
the form consisting of an oriented -bundle and a
7-cocycle on called the 7-flux. Intuitively, the spherical T-dual is
another such pair and spherical T-duality exchanges the
7-flux with the Euler class, upon fixing the Pontryagin class and the second
Stiefel-Whitney class. Unless , not all pairs admit
spherical T-duals and the spherical T-duals are not always unique. In this
paper, we define a canonical Poincar\'e virtual line bundle on
(actually also for ) and the spherical
Fourier-Mukai transform, which implements a degree shifting isomorphism in
K-theory on the trivial -bundle. This is then used to prove that all
spherical T-dualities induce natural degree-shifting isomorphisms between the
7-twisted K-theories of the pairs and when
, improving our earlier results.Comment: 19 pages, clarifications added, typos correcte
Nonassociative tori and applications to T-duality
In this paper, we initiate the study of C*-algebras endowed with a twisted
action of a locally compact Abelian Lie group, and we construct a twisted
crossed product, which is in general a nonassociative, noncommutative, algebra.
The properties of this twisted crossed product algebra are studied in detail,
and are applied to T-duality in Type II string theory to obtain the T-dual of a
general principal torus bundle with general H-flux, which we will argue to be a
bundle of noncommutative, nonassociative tori. We also show that this
construction of the T-dual includes all of the special cases that were
previously analysed.Comment: 32 pages, latex2e, uses xypic; added more details on the
nonassociative toru
T-duality for principal torus bundles and dimensionally reduced Gysin sequences
We reexamine the results on the global properties of T-duality for principal
circle bundles in the context of a dimensionally reduced Gysin sequence. We
will then construct a Gysin sequence for principal torus bundles and examine
the consequences. In particular, we will argue that the T-dual of a principal
torus bundle with nontrivial H-flux is, in general, a continuous field of
noncommutative, nonassociative tori.Comment: 21 pages, typos correcte
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