788 research outputs found
Non-Simply-Connected Gauge Groups and Rational Points on Elliptic Curves
We consider the F-theory description of non-simply-connected gauge groups
appearing in the E8 x E8 heterotic string. The analysis is closely tied to the
arithmetic of torsion points on an elliptic curve. The general form of the
corresponding elliptic fibration is given for all finite subgroups of E8 which
are applicable in this context. We also study the closely-related question of
point-like instantons on a K3 surface whose holonomy is a finite group. As an
example we consider the case of the heterotic string on a K3 surface having the
E8 gauge symmetry broken to (E6 x SU(3))/Z3 or SU(9)/Z3 by point-like
instantons with Z3 holonomy.Comment: 15 pages, 2 embedded figures, some spurious U(1)'s remove
Chiral Rings Do Not Suffice: N=(2,2) Theories with Nonzero Fundamental Group
The Kahler moduli space of a particular non-simply-connected Calabi-Yau
manifold is mapped out using mirror symmetry. It is found that, for the model
considered, the chiral ring may be identical for different associated conformal
field theories. This ambiguity is explained in terms of both A-model and
B-model language. It also provides an apparent counterexample to the global
Torelli problem for Calabi-Yau threefolds.Comment: 12 page
Mirror Symmetry and the Type II String
If and are a mirror pair of Calabi--Yau threefolds, mirror symmetry
should extend to an isomorphism between the type IIA string theory compactified
on and the type IIB string theory compactified on , with all
nonperturbative effects included. We study the implications which this proposal
has for the structure of the semiclassical moduli spaces of the compactified
type II theories. For the type IIB theory, the form taken by discrete shifts in
the Ramond-Ramond scalars exhibits an unexpected dependence on the -field.
(Based on a talk at the Trieste Workshop on S-Duality and Mirror Symmetry.)Comment: 8 pages, LaTeX using espcrc2.st
Mirror Symmetry for Two Parameter Models -- II
We describe in detail the space of the two K\"ahler parameters of the
Calabi--Yau manifold by exploiting mirror symmetry.
The large complex structure limit of the mirror, which corresponds to the
classical large radius limit, is found by studying the monodromy of the periods
about the discriminant locus, the boundary of the moduli space corresponding to
singular Calabi--Yau manifolds. A symplectic basis of periods is found and the
action of the generators of the modular group is determined. From
the mirror map we compute the instanton expansion of the Yukawa couplings and
the generalized index, arriving at the numbers of instantons of genus
zero and genus one of each degree. We also investigate an symmetry
that acts on a boundary of the moduli space.Comment: 57 pages + 9 figures using eps
U-Duality and Integral Structures
We analyze the U-duality group for the case of a type II superstring
compactified to four dimensions on a K3 surface times a torus. The various
limits of this theory are considered which have interpretations as type IIA and
IIB superstrings, the heterotic string, and eleven-dimensional supergravity,
allowing all these theories to be directly related to each other. The integral
structure which appears in the Ramond-Ramond sector of the type II superstring
is related to the quantum cohomology of general Calabi-Yau threefolds which
allows the moduli space of type II superstring compactifications on Calabi-Yau
manifolds to be analyzed.Comment: 14 pages, latex once only (Revision has minor changes and an added
reference
Orbifold Resolution by D-Branes
We study topological properties of the D-brane resolution of
three-dimensional orbifold singularities, C^3/Gamma, for finite abelian groups
Gamma. The D-brane vacuum moduli space is shown to fill out the background
spacetime with Fayet--Iliopoulos parameters controlling the size of the
blow-ups. This D-brane vacuum moduli space can be classically described by a
gauged linear sigma model, which is shown to be non-generic in a manner that
projects out non-geometric regions in its phase diagram, as anticipated from a
number of perspectives.Comment: 26 pages, 2 figures (TeX, harvmac big, epsf
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