307 research outputs found
Orientifolds, RR Torsion, and K-theory
We analyze the role of RR fluxes in orientifold backgrounds from the point of
view of K-theory, and demonstrate some physical implications of describing
these fluxes in K-theory rather than cohomology. In particular, we show that
certain fractional shifts in RR charge quantization due to discrete RR fluxes
are naturally explained in K-theory. We also show that some orientifold
backgrounds, which are considered distinct in the cohomology classification,
become equivalent in the K-theory description, while others become unphysical.Comment: 30 pages, 5 figures; typos corrected and references adde
Projective Group Algebras
In this paper we apply a recently proposed algebraic theory of integration to
projective group algebras. These structures have received some attention in
connection with the compactification of the theory on noncommutative tori.
This turns out to be an interesting field of applications, since the space
of the equivalence classes of the vector unitary irreducible
representations of the group under examination becomes, in the projective case,
a prototype of noncommuting spaces. For vector representations the algebraic
integration is equivalent to integrate over . However, its very
definition is related only at the structural properties of the group algebra,
therefore it is well defined also in the projective case, where the space has no classical meaning. This allows a generalization of the usual group
harmonic analysis. A particular attention is given to abelian groups, which are
the relevant ones in the compactification problem, since it is possible, from
the previous results, to establish a simple generalization of the ordinary
calculus to the associated noncommutative spaces.Comment: 24 pages, Late
Geometry of Orientifolds with NS-NS B-flux
We discuss geometry underlying orientifolds with non-trivial NS-NS B-flux. If
D-branes wrap a torus with B-flux the rank of the gauge group is reduced due to
non-commuting Wilson lines whose presence is implied by the B-flux. In the case
of D-branes transverse to a torus with B-flux the rank reduction is due to a
smaller number of D-branes required by tadpole cancellation conditions in the
presence of B-flux as some of the orientifold planes now have the opposite
orientifold projection. We point out that T-duality in the presence of B-flux
is more subtle than in the case with trivial B-flux, and it is precisely
consistent with the qualitative difference between the aforementioned two
setups. In the case where both types of branes are present, the states in the
mixed (e.g., 59) open string sectors come with a non-trivial multiplicity,
which we relate to a discrete gauge symmetry due to non-zero B-flux, and
construct vertex operators for the the mixed sector states. Using these results
we revisit K3 orientifolds with B-flux (where K3 is a T^4/Z_M orbifold) and
point out various subtleties arising in some of these models. For instance, in
the Z_2 case the conformal field theory orbifold does not appear to be the
consistent background for the corresponding orientifolds with B-flux. This is
related to the fact that non-zero B-flux requires the presence of both O5^- as
well as O5^+ planes at various Z_2 orbifold fixed points, which appears to be
inconsistent with the presence of the twisted B-flux in the conformal field
theory orbifold. We also consider four dimensional N=2 and N=1 supersymmetric
orientifolds. We construct consistent four dimensional models with B-flux which
do not suffer from difficulties encountered in the K3 cases.Comment: 79 pages, revte
D=6, N=1 String Vacua and Duality
We review the structure string vacua with emphasis on the
different connections due to T-dualities and S-dualities. The topics discussed
include: Anomaly cancellation; K3 and orbifold heterotic
compactifications; T-dualities between and
heterotic vacua; non-perturbative heterotic vacua and small instantons; N=2
Type-II/Heterotic duality in D=4 ; F-theory/heterotic duality in D=6; and
heterotic/heterotic duality in six and four dimensions.Comment: 52 pages, plain Latex. To appear in the proceedings of the APCTP
Winter School on Duality, Mt. Sorak (Korea), February 199
Tensors from K3 Orientifolds
Recently Gimon and Johnson (hep-th/9604129) and Dabholkar and Park
(hep-th/9604178) have constructed Type I theories on K3 orbifolds. The spectra
differ from that of Type I on a smooth K3, having extra tensors. We show that
the orbifold theories cannot be blown up to smooth K3's, but rather
orbifold singularities always remain. Douglas's recent proposal to use D-branes
as probes is useful in understanding the geometry. The singularities are
of a new type, with a different orientifold projection from those previously
considered. We also find a new world-sheet consistency condition that must be
satisfied by orientifold models.Comment: References added. 16 pages, LaTe
Type IIB orientifolds with discrete torsion
We consider compact four-dimensional type IIB
orientifolds, for certain values of and . We allow the additional
feature of discrete torsion and discuss the modification of the consistency
conditions arising from tadpole cancellation. We point out the differences
between the cases with and without discrete torsion.Comment: 4 pages LaTeX. Write-up of talk at DPF2000, Columbus, OH, August 10,
2000. References adde
Gravitational couplings of orientifold planes
We reanalyse the gravitational couplings of the perturbative orientifold
planes , (and D-branes). We first compute their
instantonic corrections for . Then, by using U-dualities, we obtain the
Wess-Zumino terms of orientifolds with RR flux for . The expressions
for the effective actions can be partially checked via M-theory. We point out a
previous oversimplification and we show in fact that the difficulty still
stands in the way of the full computation of 7 Brane instanton corrections.Comment: 13 pages, 1 figure, 2 tables. 3 references adde
A Chiral N=1 Type I Vacuum in Four Dimensions and Its Heterotic Dual
In this paper we consider Type I string theory compactified on a Z_7
orbifold. The model has N=1 supersymmetry, a U(4) \otimes U(4) \otimes U(4)
\otimes SO(8) gauge group, and chiral matter. There are only D9-branes (for
which we discuss tadpole cancellation conditions) in this model corresponding
to a perturbative heterotic description in a certain region of the moduli
space. We construct the heterotic dual, match the perturbative type I and
heterotic tree-level massless spectra via giving certain scalars appropriate
vevs, and point out the crucial role of the perturbative superpotential (on the
heterotic side) for this matching. The relevant couplings in this
superpotential turn out to be non-renormalizable (unlike the Z-orbifold case
discussed in Ref [1], where Yukawa couplings sufficed for duality matching). We
also discuss the role of the anomalous U(1) gauge symmetry present in both type
I and heterotic models. In the perturbative regime we match the (tree-level)
moduli spaces of these models. We point out possible generalizations of the Z_3
and Z_7 cases to include D5-branes which would help in understanding
non-perturbative five-brane dynamics on the heterotic side.Comment: Revtex 3.0, 23 pages, 1 eps figure (to appear in Phys. Rev. D
Type I on (Generalized) Voisin-Borcea Orbifolds and Non-perturbative Orientifolds
We consider non-perturbative four dimensional N=1 space-time supersymmetric
orientifolds corresponding to Type I compactifications on (generalized)
Voisin-Borcea orbifolds. Some states in such compactifications arise in
``twisted'' open string sectors which lack world-sheet description in terms of
D-branes. Using Type I-heterotic duality as well as the map between Type IIB
orientifolds and F-theory we are able to obtain the massless spectra of such
orientifolds. The four dimensional compactifications we discuss in this context
are examples of chiral N=1 supersymmetric string vacua which are
non-perturbative from both orientifold and heterotic points of view. In
particular, they contain both D9- and D5-branes as well as non-perturbative
``twisted'' open string sector states. We also explain the origins of various
inconsistencies arising in such compactifications for certain choices of the
gauge bundle.Comment: 34 pages, revtex; minor misprints correcte
Stable non-BPS states in string theory: a pedagogical review
We present a pedagogical review of the stable non-BPS states in string theory
which have recently attracted some attention in the literature. In particular,
following the analysis of A. Sen, we discuss in detail the case of the stable
non-BPS D-particle of Type I theory whose existence is predicted (and required)
by the heterotic/Type I duality. We show that this D-particle originates from
an unstable bound state formed by a D1/anti-D1 pair of Type IIB in which the
tachyon field acquires a solitonic kink configuration. The mechanism of tachyon
condensation is discussed first at a qualitative level and then with an exact
conformal field theory analysis.Comment: 58 pages, 1 figure; minor correction
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