22,776 research outputs found
D-Branes, Derived Categories, and Grothendieck Groups
In this paper we describe how Grothendieck groups of coherent sheaves and
locally free sheaves can be used to describe type II D-branes, in the case that
all D-branes are wrapped on complex varieties and all connections are
holomorphic. Our proposal is in the same spirit as recent discussions of
K-theory and D-branes; within the restricted class mentioned, Grothendieck
groups encode a choice of connection on each D-brane worldvolume, in addition
to information about the smooth bundles. We also point out that derived
categories can also be used to give insight into D-brane constructions, and
analyze how a Z_2 subset of the T-duality group acting on D-branes on tori can
be understood in terms of a Fourier-Mukai transformation.Comment: LaTeX, 21 page
Exact duality and dual Monte-Carlo simulation for the Bosonic Hubbard model
We derive the exact dual to the Bosonic Hubbard model. The dual variables
take the form of conserved current loops (local and global). Previously this
has been done only for the very soft core model at very high density. No such
approximations are made here. In particular, the dual of the hard core model is
shown to have a very simple form which is then used to construct an efficient
Monte Carlo algorithm which is quite similar to the World Line algorithm but
with some important differences. For example, with this algorithm we can
measure easily the correlation function of the order parameter (Green
function), a quantity which is extremely difficult to measure with the standard
World Line algorithm. We demonstrate the algorithm for the one and two
dimensional hardcore Bosonic Hubbard models. We present new results especially
for the Green function and zero mode filling fraction in the two dimensional
hardcore model.Comment: 14 pages, 15 figures include
Holographic coherent states from random tensor networks
Random tensor networks provide useful models that incorporate various
important features of holographic duality. A tensor network is usually defined
for a fixed graph geometry specified by the connection of tensors. In this
paper, we generalize the random tensor network approach to allow quantum
superposition of different spatial geometries. We set up a framework in which
all possible bulk spatial geometries, characterized by weighted adjacent
matrices of all possible graphs, are mapped to the boundary Hilbert space and
form an overcomplete basis of the boundary. We name such an overcomplete basis
as holographic coherent states. A generic boundary state can be expanded on
this basis, which describes the state as a superposition of different spatial
geometries in the bulk. We discuss how to define distinct classical geometries
and small fluctuations around them. We show that small fluctuations around
classical geometries define "code subspaces" which are mapped to the boundary
Hilbert space isometrically with quantum error correction properties. In
addition, we also show that the overlap between different geometries is
suppressed exponentially as a function of the geometrical difference between
the two geometries. The geometrical difference is measured in an area law
fashion, which is a manifestation of the holographic nature of the states
considered.Comment: 33 pages, 8 figures. An error corrected on page 14. Reference update
D-Branes and Bundles on Elliptic Fibrations
We study the D-brane spectrum on a two-parameter Calabi-Yau model. The
analysis is based on different tools in distinct regions of the moduli space:
wrapped brane configurations on elliptic fibrations near the large radius
limit, and SCFT boundary states at the Gepner point. We develop an explicit
correspondence between these two classes of objects, suggesting that boundary
states are natural quantum generalizations of bundles. We also find interesting
D-brane dynamics in deep stringy regimes. The most striking example is,
perhaps, that nonsupersymmetric D6-D0 and D4-D2 large radius configurations
become stable BPS states at the Gepner point.Comment: 22 page
Seiberg Duality is an Exceptional Mutation
The low energy gauge theory living on D-branes probing a del Pezzo
singularity of a non-compact Calabi-Yau manifold is not unique. In fact there
is a large equivalence class of such gauge theories related by Seiberg duality.
As a step toward characterizing this class, we show that Seiberg duality can be
defined consistently as an admissible mutation of a strongly exceptional
collection of coherent sheaves.Comment: 32 pages, 4 figures; v2 refs added, "orbifold point" discussion
refined; v3 version to appear in JHEP, discussion of torsion sheaves improve
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