284 research outputs found
Coisotropic Branes, Noncommutativity, and the Mirror Correspondence
We study coisotropic A-branes in the sigma model on a four-torus by
explicitly constructing examples. We find that morphisms between coisotropic
branes can be equated with a fundamental representation of the noncommutatively
deformed algebra of functions on the intersection. The noncommutativity
parameter is expressed in terms of the bundles on the branes. We conjecture
these findings hold in general. To check mirror symmetry, we verify that the
dimensions of morphism spaces are equal to the corresponding dimensions of
morphisms between mirror objects.Comment: 13 page
Monopole and Dyon Bound States in N=2 Supersymmetric Yang-Mills Theories
We study the existence of monopole bound states saturating the BPS bound in
N=2 supersymmetric Yang-Mills theories. We describe how the existence of such
bound states relates to the topology of index bundles over the moduli space of
BPS solutions. Using an index theorem, we prove the existence of certain
BPS states predicted by Seiberg and Witten based on their study of the vacuum
structure of N=2 Yang-Mills theories.Comment: 34 pages, harvma
A categorification of Morelli's theorem
We prove a theorem relating torus-equivariant coherent sheaves on toric
varieties to polyhedrally-constructible sheaves on a vector space. At the level
of K-theory, the theorem recovers Morelli's description of the K-theory of a
smooth projective toric variety. Specifically, let be a proper toric
variety of dimension and let M_\bR = \mathrm{Lie}(T_\bR^\vee)\cong \bR^n
be the Lie algebra of the compact dual (real) torus T_\bR^\vee\cong U(1)^n.
Then there is a corresponding conical Lagrangian \Lambda \subset T^*M_\bR and
an equivalence of triangulated dg categories \Perf_T(X) \cong
\Sh_{cc}(M_\bR;\Lambda), where \Perf_T(X) is the triangulated dg category of
perfect complexes of torus-equivariant coherent sheaves on and
\Sh_{cc}(M_\bR;\Lambda) is the triangulated dg category of complex of sheaves
on M_\bR with compactly supported, constructible cohomology whose singular
support lies in . This equivalence is monoidal---it intertwines the
tensor product of coherent sheaves on with the convolution product of
constructible sheaves on M_\bR.Comment: 20 pages. This is a strengthened version of the first half of
arXiv:0811.1228v3, with new results; the second half becomes
arXiv:0811.1228v
On Duality Walls in String Theory
Following the RG flow of an N=1 quiver gauge theory and applying Seiberg
duality whenever necessary defines a duality cascade, that in simple cases has
been understood holographically. It has been argued that in certain cases, the
dualities will pile up at a certain energy scale called the duality wall,
accompanied by a dramatic rise in the number of degrees of freedom. In string
theory, this phenomenon is expected to occur for branes at a generic threefold
singularity, for which the associated quiver has Lorentzian signature. We here
study sequences of Seiberg dualities on branes at the C_3/Z_3 orbifold
singularity. We use the naive beta functions to define an (unphysical) scale
along the cascade. We determine, as a function of initial conditions, the scale
of the wall as well as the critical exponent governing the approach to it. The
position of the wall is piecewise linear, while the exponent appears to be
constant. We comment on the possible implications of these results for physical
walls.Comment: 22 pages, 2 figures. v2: physical interpretation rectified, reference
adde
Minimal Family Unification
Absract It is proposed that there exist, within a new , a gauged
discrete group (the order 12 double dihedral group) acting as a family
symmetry. This nonabelian finite group can explain hierarchical features of
families, using an assignment for quarks and leptons dictated by the
requirements of anomaly cancellation and of no additional quarks.Comment: 10 pages, IFP-701-UNC;VAND-TH-94-
Quantum symmetries and exceptional collections
We study the interplay between discrete quantum symmetries at certain points
in the moduli space of Calabi-Yau compactifications, and the associated
identities that the geometric realization of D-brane monodromies must satisfy.
We show that in a wide class of examples, both local and compact, the monodromy
identities in question always follow from a single mathematical statement. One
of the simplest examples is the Z_5 symmetry at the Gepner point of the
quintic, and the associated D-brane monodromy identity
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
Quantum-mechanical model for particles carrying electric charge and magnetic flux in two dimensions
We propose a simple quantum mechanical equation for particles in two
dimensions, each particle carrying electric charge and magnetic flux. Such
particles appear in (2+1)-dimensional Chern-Simons field theories as charged
vortex soliton solutions, where the ratio of charge to flux is a constant
independent of the specific solution. As an approximation, the charge-flux
interaction is described here by the Aharonov-Bohm potential, and the
charge-charge interaction by the Coulomb one. The equation for two particles,
one with charge and flux () and the other with () where
is a pure number is studied in detail. The bound state problem is solved
exactly for arbitrary and when . The scattering problem is
exactly solved in parabolic coordinates in special cases when takes integers or half integers. In both cases the cross sections obtained
are rather different from that for pure Coulomb scattering.Comment: 12 pages, REVTeX, no figur
NC Calabi-Yau Orbifolds in Toric Varieties with Discrete Torsion
Using the algebraic geometric approach of Berenstein et {\it al}
(hep-th/005087 and hep-th/009209) and methods of toric geometry, we study non
commutative (NC) orbifolds of Calabi-Yau hypersurfaces in toric varieties with
discrete torsion. We first develop a new way of getting complex mirror
Calabi-Yau hypersurfaces in toric manifolds with a action and analyze the general group of the
discrete isometries of . Then we build a general class of
complex dimension NC mirror Calabi-Yau orbifolds where the non
commutativity parameters are solved in terms of discrete
torsion and toric geometry data of in which the original
Calabi-Yau hypersurfaces is embedded. Next we work out a generalization of the
NC algebra for generic dimensions NC Calabi-Yau manifolds and give various
representations depending on different choices of the Calabi-Yau toric geometry
data. We also study fractional D-branes at orbifold points. We refine and
extend the result for NC to higher dimensional torii orbifolds
in terms of Clifford algebra.Comment: 38 pages, Late
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