11,790 research outputs found
Non-associative Deformations of Geometry in Double Field Theory
Non-geometric string backgrounds were proposed to be related to a
non-associative deformation of the space-time geometry. In the flux formulation
of double field theory (DFT), the structure of mathematically possible
non-associative deformations is analyzed in detail. It is argued that on-shell
there should not be any violation of associativity in the effective DFT action.
For imposing either the strong or the weaker closure constraint we discuss two
possible non-associative deformations of DFT featuring two different ways how
on-shell associativity can still be kept.Comment: 29 pages, 1 figure, v2: major revision of section 4, discussion of
closure constraint change
The standard mean-field treatment of inter-particle attraction in classical DFT is better than one might expect
In classical density functional theory (DFT) the part of the Helmholtz free
energy functional arising from attractive inter-particle interactions is often
treated in a mean-field or van der Waals approximation. On the face of it, this
is a somewhat crude treatment as the resulting functional generates the simple
random phase approximation (RPA) for the bulk fluid pair direct correlation
function. We explain why using standard mean-field DFT to describe
inhomogeneous fluid structure and thermodynamics is more accurate than one
might expect based on this observation. By considering the pair correlation
function and structure factor of a one-dimensional model fluid,
for which exact results are available, we show that the mean-field DFT,
employed within the test-particle procedure, yields results much superior to
those from the RPA closure of the bulk Ornstein-Zernike equation. We argue that
one should not judge the quality of a DFT based solely on the approximation it
generates for the bulk pair direct correlation function.Comment: 9 pages, 3 figure
Gauged Double Field Theory
We find necessary and sufficient conditions for gauge invariance of the
action of Double Field Theory (DFT) as well as closure of the algebra of gauge
symmetries. The so-called weak and strong constraints are sufficient to satisfy
them, but not necessary. We then analyze compactifications of DFT on twisted
double tori satisfying the consistency conditions. The effective theory is a
Gauged DFT where the gaugings come from the duality twists. The action,
bracket, global symmetries, gauge symmetries and their closure are computed by
twisting their analogs in the higher dimensional DFT. The non-Abelian heterotic
string and lower dimensional gauged supergravities are particular examples of
Gauged DFT.Comment: Minor changes, references adde
Geometric Low-Energy Effective Action in a Doubled Spacetime
The ten-dimensional supergravity theory is a geometric low-energy effective
theory and the equations of motion for its fields can be obtained from string
theory by computing functions. With compact dimensions, we can add
to it an geometric structure and construct the
supergravity theory inspired by double field theory through the use of a
suitable commutative star product. The latter implements the weak constraint of
the double field theory on its fields and gauge parameters in order to have a
closed gauge symmetry algebra. The consistency of the action here proposed is
based on the orthogonality of the momenta associated with fields in their
triple star products in the cubic terms defined for . This orthogonality
holds also for an arbitrary number of star products of fields for .
Finally, we extend our analysis to the double sigma model, non-commutative
geometry and open string theory.Comment: 27 pages, minor changes, references adde
BRST symmetry of doubled membrane sigma-models
Courant sigma-models encode the geometric and non-geometric fluxes of
compactified closed string theory as generalized Wess-Zumino terms and exhibit
their relation to Courant algebroids. In recent work, we proposed a doubled
membrane sigma-model that establishes the corresponding connection to double
field theory and its algebroid structure. The strategy is to consider a "large"
Courant sigma-model over a doubled target spacetime and identify a suitable
projection that leads to a sigma-model for doubled fields. In this note, we
provide further details for this construction. Starting from the BRST symmetry
of the BV action that satisfies the classical master equation, we consistently
project the BRST transformations of the superfields of the "large" Courant
sigma-model to obtain the gauge transformations of the doubled membrane
sigma-model. We show that demanding gauge invariance and the closure of gauge
transformations of the worldvolume theory, leads to a condition that is in
direct correspondence to the strong constraint of the target space double field
theory.Comment: 13 pages; proceedings of "Dualities and Generalized Geometries",
Corfu Summer Institute 2018. v2: typos correcte
Crystallization of magnetic dipolar monolayers: a density functional approach
We employ density functional theory to study in detail the crystallization of
super-paramagnetic particles in two dimensions under the influence of an
external magnetic field that lies perpendicular to the confining plane. The
field induces non-fluctuating magnetic dipoles on the particles, resulting into
an interparticle interaction that scales as the inverse cube of the distance
separating them. In line with previous findings for long-range interactions in
three spatial dimensions, we find that explicit inclusion of liquid-state
structural information on the {\it triplet} correlations is crucial to yield
theoretical predictions that agree quantitatively with experiment. A
non-perturbative treatment is superior to the oft-employed functional Taylor
expansions, truncated at second or third order. We go beyond the usual Gaussian
parametrization of the density site-orbitals by performing free minimizations
with respect to both the shape and the normalization of the profiles, allowing
for finite defect concentrations.Comment: 23 pages, 18 figure
A fundamental measure theory for the sticky hard sphere fluid
We construct a density functional theory (DFT) for the sticky hard sphere
(SHS) fluid which, like Rosenfeld's fundamental measure theory (FMT) for the
hard sphere fluid [Phys. Rev. Lett. {\bf 63}, 980 (1989)], is based on a set of
weighted densities and an exact result from scaled particle theory (SPT). It is
demonstrated that the excess free energy density of the inhomogeneous SHS fluid
is uniquely defined when (a) it is solely a function of the
weighted densities from Kierlik and Rosinberg's version of FMT [Phys. Rev. A
{\bf 42}, 3382 (1990)], (b) it satisfies the SPT differential equation, and (c)
it yields any given direct correlation function (DCF) from the class of
generalized Percus-Yevick closures introduced by Gazzillo and Giacometti [J.
Chem. Phys. {\bf 120}, 4742 (2004)]. The resulting DFT is shown to be in very
good agreement with simulation data. In particular, this FMT yields the correct
contact value of the density profiles with no adjustable parameters. Rather
than requiring higher order DCFs, such as perturbative DFTs, our SHS FMT
produces them. Interestingly, although equivalent to Kierlik and Rosinberg's
FMT in the case of hard spheres, the set of weighted densities used for
Rosenfeld's original FMT is insufficient for constructing a DFT which yields
the SHS DCF.Comment: 11 pages, 3 figure
Double Field Theory on Group Manifolds in a Nutshell
We give a brief overview of the current status of Double Field Theory on
Group Manifolds (DFTWZW). Therefore, we start by reviewing some basic notions
known from Double Field Theory (DFT) and show how they extend/generalize into
the framework of Double Field Theory on Group Manifolds. In this context, we
discuss the relationship between both theories and the transition from DFTWZW
to DFT. Furthermore, we address some open questions and present an outlook into
our current research.Comment: Proceedings prepared for the "Workshop on Geometry and Physics",
November 2016, Ringberg Castle, Germany; v2: references adde
The gauge structure of Exceptional Field Theories and the tensor hierarchy
We address the construction of manifest U-duality invariant generalized
diffeomorphisms. The closure of the algebra requires an extension of the
tangent space to include a tensor hierarchy indicating the existence of an
underlying unifying structure, compatible with E_{11} and Borcherds algebras
constructions. We begin with four-dimensional gauged maximal supergravity, and
build a generalized Lie derivative that encodes all the gauge transformations
of the theory. A generalized frame is introduced, which accommodates for all
the degrees of freedom, including the tensor hierarchy. The generalized Lie
derivative defines generalized field-dependent fluxes containing all the
covariant quantities in the theory, and the closure conditions give rise to
their corresponding Bianchi Identities. We then move towards the construction
of a full generalized Lie derivative defined on an extended space, analyze the
closure conditions, and explore the connection with that of maximal gauged
supergravity via a generalized Scherk-Schwarz reduction, and with
11-dimensional supergravity.Comment: 53 page
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