26 research outputs found
Quantum Mechanics of the Doubled Torus
We investigate the quantum mechanics of the doubled torus system, introduced
by Hull [1] to describe T-folds in a more geometric way. Classically, this
system consists of a world-sheet Lagrangian together with some constraints,
which reduce the number of degrees of freedom to the correct physical number.
We consider this system from the point of view of constrained Hamiltonian
dynamics. In this case the constraints are second class, and we can quantize on
the constrained surface using Dirac brackets. We perform the quantization for a
simple T-fold background and compare to results for the conventional
non-doubled torus system. Finally, we formulate a consistent supersymmetric
version of the doubled torus system, including supersymmetric constraints.Comment: 31 pages, 1 figure; v2: references added, minor corrections to final
sectio
D-branes in T-fold conformal field theory
We investigate boundary dynamics of orbifold conformal field theory involving
T-duality twists. Such models typically appear in contexts of non-geometric
string compactifications that are called monodrofolds or T-folds in recent
literature. We use the framework of boundary conformal field theory to analyse
the models from a microscopic world-sheet perspective. In these backgrounds
there are two kinds of D-branes that are analogous to bulk and fractional
branes in standard orbifold models. The bulk D-branes in T-folds allow
intuitive geometrical interpretations and are consistent with the classical
analysis based on the doubled torus formalism. The fractional branes, on the
other hand, are `non-geometric' at any point in the moduli space and their
geometric counterparts seem to be missing in the doubled torus analysis. We
compute cylinder amplitudes between the bulk and fractional branes, and find
that the lightest modes of the open string spectra show intriguing non-linear
dependence on the moduli (location of the brane or value of the Wilson line),
suggesting that the physics of T-folds, when D-branes are involved, could
deviate from geometric backgrounds even at low energies. We also extend our
analysis to the models with SU(2) WZW fibre at arbitrary levels.Comment: 38 pages, no figure, ams packages. Essentially the published versio
Superstring partition functions in the doubled formalism
Computation of superstring partition function for the non-linear sigma model
on the product of a two-torus and its dual within the scope of the doubled
formalism is presented. We verify that it reproduces the partition functions of
the toroidally compactified type--IIA and type--IIB theories for appropriate
choices of the GSO projection.Comment: 15 page
D-branes in Nongeometric Backgrounds
"T-fold" backgrounds are generically-nongeometric compactifications of string
theory, described by T^n fibrations over a base N with transition functions in
the perturbative T-duality group. We review Hull's doubled torus formalism,
which geometrizes these backgrounds, and use the formalism to constrain the
D-brane spectrum (to leading order in g_s and alpha') on T^n fibrations over
S^1 with O(n,n;Z) monodromy. We also discuss the (approximate) moduli space of
such branes and argue that it is always geometric. For a D-brane located at a
point on the base N, the classical ``D-geometry'' is a T^n fibration over a
multiple cover of N.Comment: 29 pages; uses harvmac.tex; v2: substantial revision throughou
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Generalised Geometry for M-Theory
Generalised geometry studies structures on a d-dimensional manifold with a
metric and 2-form gauge field on which there is a natural action of the group
SO(d,d). This is generalised to d-dimensional manifolds with a metric and
3-form gauge field on which there is a natural action of the group .
This provides a framework for the discussion of M-theory solutions with flux. A
different generalisation is to d-dimensional manifolds with a metric, 2-form
gauge field and a set of p-forms for either odd or even on which there is a
natural action of the group . This is useful for type IIA or IIB
string solutions with flux. Further generalisations give extended tangent
bundles and extended spin bundles relevant for non-geometric backgrounds.
Special structures that arise for supersymmetric backgrounds are discussed.Comment: 31 page
Generalized Flux Vacua
We consider type II string theory compactified on a symmetric T^6/Z_2
orientifold. We study a general class of discrete deformations of the resulting
four-dimensional supergravity theory, including gaugings arising from geometric
and "nongeometric'' fluxes, as well as the usual R-R and NS-NS fluxes. Solving
the equations of motion associated with the resulting N = 1 superpotential, we
find parametrically controllable infinite families of supersymmetric vacua with
all moduli stabilized. We also describe some aspects of the distribution of
generic solutions to the SUSY equations of motion for this model, and note in
particular the existence of an apparently infinite number of solutions in a
finite range of the parameter space of the four-dimensional effective theory.Comment: 30 pages, 4 .eps figures; v2, reference adde
Flux compactifications in string theory: a comprehensive review
We present a pedagogical overview of flux compactifications in string theory,
from the basic ideas to the most recent developments. We concentrate on closed
string fluxes in type II theories. We start by reviewing the supersymmetric
flux configurations with maximally symmetric four-dimensional spaces. We then
discuss the no-go theorems (and their evasion) for compactifications with
fluxes. We analyze the resulting four-dimensional effective theories, as well
as some of its perturbative and non-perturbative corrections, focusing on
moduli stabilization. Finally, we briefly review statistical studies of flux
backgrounds.Comment: 85 pages, 2 figures. v2, v3: minor changes, references adde
Mirrorfolds with K3 Fibrations
We study a class of non-geometric string vacua realized as completely soluble
superconformal field theory (SCFT). These models are defined as `interpolating
orbifolds' of by the mirror transformation acting on the
fiber combined with the half-shift on the -base. They are variants of the
T-folds, the interpolating orbifolds by T-duality transformations, and thus may
be called `mirrorfolds'. Starting with arbitrary (compact or non-compact)
Gepner models for the fiber, we construct modular invariant partition
functions of general mirrorfold models. In the case of compact fiber the
mirrorfolds only yield non-supersymmetric string vacua. They exhibit IR
instability due to winding tachyon condensation which is similar to the
Scherk-Schwarz type circle compactification. When the fiber SCFT is non-compact
(say, the ALE space in the simplest case), on the other hand, both
supersymmetric and non-supersymmetric vacua can be constructed. The non-compact
non-supersymmetric mirrorfolds can get stabilised at the level of string
perturbation theory. We also find that in the non-compact supersymmeric
mirrorfolds D-branes are {\em always} non-BPS. These D-branes can get
stabilized against both open- and closed-string marginal deformations.Comment: Eqns (2.61) and (3.17) correcte
Lectures on Nongeometric Flux Compactifications
These notes present a pedagogical review of nongeometric flux
compactifications. We begin by reviewing well-known geometric flux
compactifications in Type II string theory, and argue that one must include
nongeometric "fluxes" in order to have a superpotential which is invariant
under T-duality. Additionally, we discuss some elementary aspects of the
worldsheet description of nongeometric backgrounds. This review is based on
lectures given at the 2007 RTN Winter School at CERN.Comment: 31 pages, JHEP