109 research outputs found
D-branes, B fields, and Ext groups
In this paper we extend previous work on calculating massless boundary Ramond
sector spectra of open strings to include cases with nonzero flat B fields. In
such cases, D-branes are no longer well-modelled precisely by sheaves, but
rather they are replaced by `twisted' sheaves, reflecting the fact that gauge
transformations of the B field act as affine translations of the Chan-Paton
factors. As in previous work, we find that the massless boundary Ramond sector
states are counted by Ext groups -- this time, Ext groups of twisted sheaves.
As before, the computation of BRST cohomology relies on physically realizing
some spectral sequences. Subtleties that cropped up in previous work also
appear here.Comment: 23 pages, LaTeX; v2: typos fixed; v3: reference adde
GLSM realizations of maps and intersections of Grassmannians and Pfaffians
In this paper we give gauged linear sigma model (GLSM) realizations of a
number of geometries not previously presented in GLSMs. We begin by describing
GLSM realizations of maps including Veronese and Segre embeddings, which can be
applied to give GLSMs explicitly describing constructions such as the
intersection of one hypersurface with the image under some map of another. We
also discuss GLSMs for intersections of Grassmannians and Pfaffians with one
another, and with their images under various maps, which sometimes form exotic
constructions of Calabi-Yaus, as well as GLSMs for other exotic Calabi-Yau
constructions of Kanazawa. Much of this paper focuses on a specific set of
examples of GLSMs for intersections of Grassmannians G(2,N) with themselves
after a linear rotation, including the Calabi-Yau case N=5. One phase of the
GLSM realizes an intersection of two Grassmannians, the other phase realizes an
intersection of two Pfaffians. The GLSM has two nonabelian factors in its gauge
group, and we consider dualities in those factors. In both the original GLSM
and a double-dual, one geometric phase is realized perturbatively (as the
critical locus of a superpotential), and the other via quantum effects.
Dualizing on a single gauge group factor yields a model in which each geometry
is realized through a simultaneous combination of perturbative and quantum
effects.Comment: LaTeX, 50 pages; v2: typos fixed and a few comments on other
dualities adde
On the full, strongly exceptional collections on toric varieties with Picard number three
We investigate full strongly exceptional collections on smooth, com- plete
toric varieties. We obtain explicit results for a large family of varieties
with Picard number three, containing many of the families already known. We
also describe the relations between the collections and the split of the push
forward of the trivial line bundle by the toric Frobenius morphism
A variant of the Mukai pairing via deformation quantization
We give a new method to prove a formula computing a variant of Caldararu's
Mukai pairing \cite{Cal1}. Our method is based on some important results in the
area of deformation quantization. In particular, part of the work of Kashiwara
and Schapira in \cite{KS} as well as an algebraic index theorem of Bressler,
Nest and Tsygan in \cite{BNT},\cite{BNT1} and \cite{BNT2} are used. It is hoped
that our method is useful for generalization to settings involving certain
singular varieties.Comment: 8 pages. Comments and suggestions welcom
Decompactifications and Massless D-Branes in Hybrid Models
A method of determining the mass spectrum of BPS D-branes in any phase limit
of a gauged linear sigma model is introduced. A ring associated to monodromy is
defined and one considers K-theory to be a module over this ring. A simple but
interesting class of hybrid models with Landau-Ginzburg fibres over CPn are
analyzed using special Kaehler geometry and D-brane probes. In some cases the
hybrid limit is an infinite distance in moduli space and corresponds to a
decompactification. In other cases the hybrid limit is at a finite distance and
acquires massless D-branes. An example studied appears to correspond to a novel
theory of supergravity with an SU(2) gauge symmetry where the gauge and
gravitational couplings are necessarily tied to each other.Comment: PDF-LaTeX, 34 pages, 2 mps figure
Modifying the Sum Over Topological Sectors and Constraints on Supergravity
The standard lore about the sum over topological sectors in quantum field
theory is that locality and cluster decomposition uniquely determine the sum
over such sectors, thus leading to the usual theta-vacua. We show that without
changing the local degrees of freedom, a theory can be modified such that the
sum over instantons should be restricted; e.g. one should include only
instanton numbers which are divisible by some integer p. This conclusion about
the configuration space of quantum field theory allows us to carefully
reconsider the quantization of parameters in supergravity. In particular, we
show that FI-terms and nontrivial Kahler forms are quantized. This analysis
also leads to a new derivation of recent results about linearized supergravity.Comment: 17 pages, minor change
Rigidly Supersymmetric Gauge Theories on Curved Superspace
In this note we construct rigidly supersymmetric gauged sigma models and
gauge theories on certain Einstein four-manifolds, and discuss constraints on
these theories. In work elsewhere, it was recently shown that on some
nontrivial Einstein four-manifolds such as AdS, N=1 rigidly supersymmetric
sigma models are constrained to have target spaces with exact K\"ahler forms.
Similarly, in gauged sigma models and gauge theories, we find that
supersymmetry imposes constraints on Fayet-Iliopoulos parameters, which have
the effect of enforcing that K\"ahler forms on quotient spaces be exact. We
also discuss general aspects of universality classes of gauged sigma models, as
encoded by stacks, and also discuss affine bundle structures implicit in these
constructions.Comment: 23 pages; references added; more discussion added; v4: typos fixe
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