223 research outputs found
Ribbon graphs and mirror symmetry
Given a ribbon graph \u393 with some extra structure, we define, using constructible sheaves, a dg category CPM(\u393) meant to model the Fukaya category of a Riemann surface in the cell of Teichm\ufcller space described by \u393. When \u393 is appropriately decorated and admits a combinatorial \u201ctorus fibration with section,\u201d we construct from \u393 a one-dimensional algebraic stack X\u393 with toric components. We prove that our model is equivalent to Perf(X\u393), the dg category of perfect complexes on X\u393
Stokes matrices for the quantum differential equations of some Fano varieties
The classical Stokes matrices for the quantum differential equation of
projective n-space are computed, using multisummation and the so-called
monodromy identity. Thus, we recover the results of D. Guzzetti that confirm
Dubrovin's conjecture for projective spaces. The same method yields explicit
formulas for the Stokes matrices of the quantum differential equations of
smooth Fano hypersurfaces in projective n-space and for weighted projective
spaces.Comment: 20 pages. Introduction has been changed. Small corrections in the
tex
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
Constraints on Low-Dimensional String Compactifications
We study the restrictions imposed by cancellation of the tadpoles for two,
three, and four-form gauge fields in string theory, M-theory and F-theory
compactified to two, three and four dimensions, respectively. For a large class
of supersymmetric vacua, turning on a sufficient number of strings, membranes
and three-branes, respectively, can cancel the tadpoles, and preserve
supersymmetry. However, there are cases where the tadpole cannot be removed in
this way, either because the tadpole is fractional, or because of its sign. For
M-theory and F-theory compactifications, we also explore the relation of the
membranes and three-branes to the nonperturbative space-time superpotential.Comment: 16 pages, harvma
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
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
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
Topological Orbifold Models and Quantum Cohomology Rings
We discuss the toplogical sigma model on an orbifold target space. We
describe the moduli space of classical minima for computing correlation
functions involving twisted operators, and show, through a detailed computation
of an orbifold of by the dihedral group how to compute
the complete ring of observables. Through this procedure, we compute all the
rings from dihedral orbifolds; we note a similarity with rings
derived from perturbed series superpotentials of the classification
of minimal models. We then consider and show how the
techniques of topological-anti-topological fusion might be used to compute
twist field correlation functions for nonabelian orbifolds.Comment: 48 pages, harvmac, HUTP-92/A06
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-
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