469 research outputs found
Massless particles on supergroups and AdS3 x S3 supergravity
Firstly, we study the state space of a massless particle on a supergroup with
a reparameterization invariant action. After gauge fixing the
reparameterization invariance, we compute the physical state space through the
BRST cohomology and show that the quadratic Casimir Hamiltonian becomes
diagonalizable in cohomology. We illustrate the general mechanism in detail in
the example of a supergroup target GL(1|1). The space of physical states
remains an indecomposable infinite dimensional representation of the space-time
supersymmetry algebra. Secondly, we show how the full string BRST cohomology in
the particle limit of string theory on AdS3 x S3 renders the quadratic Casimir
diagonalizable, and reduces the Hilbert space to finite dimensional
representations of the space-time supersymmetry algebra (after analytic
continuation). Our analysis provides an efficient way to calculate the
Kaluza-Klein spectrum for supergravity on AdS3 x S3. It may also be a step
towards the identification of an interesting and simpler subsector of
logarithmic supergroup conformal field theories, relevant to string theory.Comment: 16 pages, 10 figure
Conformal Current Algebra in Two Dimensions
We construct a non-chiral current algebra in two dimensions consistent with
conformal invariance. We show that the conformal current algebra is realized in
non-linear sigma-models on supergroup manifolds with vanishing dual Coxeter
number, with or without a Wess-Zumino term. The current algebra is computed
using two distinct methods. First we exploit special algebraic properties of
supergroups to compute the exact two- and three-point functions of the currents
and from them we infer the current algebra. The algebra is also calculated by
using conformal perturbation theory about the Wess-Zumino-Witten point and
resumming the perturbation series. We also prove that these models realize a
non-chiral Kac-Moody algebra and construct an infinite set of commuting
operators that is closed under the action of the Kac-Moody generators. The
supergroup models that we consider include models with applications to
statistical mechanics, condensed matter and string theory. In particular, our
results may help to systematically solve and clarify the quantum integrability
of PSU(n|n) models and their cosets, which appear prominently in string
worldsheet models on anti-deSitter spaces.Comment: 33 pages, minor correction
Non-chiral current algebras for deformed supergroup WZW models
We study deformed WZW models on supergroups with vanishing Killing form. The
deformation is generated by the isotropic current-current perturbation which is
exactly marginal under these assumptions. It breaks half of the global
isometries of the original supergroup. The current corresponding to the
remaining symmetry is conserved but its components are neither holomorphic nor
anti-holomorphic. We obtain the exact two- and three-point functions of this
current and a four-point function in the first two leading orders of a 1/k
expansion but to all orders in the deformation parameter. We further study the
operator product algebra of the currents, the equal time commutators and the
quantum equations of motion. The form of the equations of motion suggests the
existence of non-local charges which generate a Yangian. Possible applications
to string theory on Anti-de Sitter spaces and to condensed matter problems are
briefly discussed.Comment: 43 pages, Latex, one eps figure; v.2: minor corrections, a reference
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Modelling the unfolding pathway of biomolecules: theoretical approach and experimental prospect
We analyse the unfolding pathway of biomolecules comprising several
independent modules in pulling experiments. In a recently proposed model, a
critical velocity has been predicted, such that for pulling speeds
it is the module at the pulled end that opens first, whereas for
it is the weakest. Here, we introduce a variant of the model that is
closer to the experimental setup, and discuss the robustness of the emergence
of the critical velocity and of its dependence on the model parameters. We also
propose a possible experiment to test the theoretical predictions of the model,
which seems feasible with state-of-art molecular engineering techniques.Comment: Accepted contribution for the Springer Book "Coupled Mathematical
Models for Physical and Biological Nanoscale Systems and Their Applications"
(proceedings of the BIRS CMM16 Workshop held in Banff, Canada, August 2016),
16 pages, 6 figure
Random walks on finite lattice tubes
Exact results are obtained for random walks on finite lattice tubes with a
single source and absorbing lattice sites at the ends. Explicit formulae are
derived for the absorption probabilities at the ends and for the expectations
that a random walk will visit a particular lattice site before being absorbed.
Results are obtained for lattice tubes of arbitrary size and each of the
regular lattice types; square, triangular and honeycomb. The results include an
adjustable parameter to model the effects of strain, such as surface curvature,
on the surface diffusion. Results for the triangular lattice tubes and the
honeycomb lattice tubes model diffusion of adatoms on single walled zig-zag
carbon nano-tubes with open ends.Comment: 22 pages, 4 figure
The conformal current algebra on supergroups with applications to the spectrum and integrability
We compute the algebra of left and right currents for a principal chiral
model with arbitrary Wess-Zumino term on supergroups with zero Killing form. We
define primary fields for the current algebra that match the affine primaries
at the Wess-Zumino-Witten points. The Maurer-Cartan equation together with
current conservation tightly constrain the current-current and current-primary
operator product expansions. The Hilbert space of the theory is generated by
acting with the currents on primary fields. We compute the conformal dimensions
of a subset of these states in the large radius limit. The current algebra is
shown to be consistent with the quantum integrability of these models to
several orders in perturbation theory.Comment: 45 pages. Minor correction
Asymptotic Symmetries of String Theory on AdS3 X S3 with Ramond-Ramond Fluxes
String theory on AdS3 space-times with boundary conditions that allow for
black hole states has global asymptotic symmetries which include an infinite
dimensional conformal algebra. Using the conformal current algebra for
sigma-models on PSU(1,1|2), we explicitly construct the R-symmetry and Virasoro
charges in the worldsheet theory describing string theory on AdS3 X S3 with
Ramond-Ramond fluxes. We also indicate how to construct the full boundary
superconformal algebra. The boundary superconformal algebra plays an important
role in classifying the full spectrum of string theory on AdS3 with
Ramond-Ramond fluxes, and in the microscopic entropy counting in D1-D5 systems.Comment: 30 page
The non-compact elliptic genus: mock or modular
We analyze various perspectives on the elliptic genus of non-compact
supersymmetric coset conformal field theories with central charge larger than
three. We calculate the holomorphic part of the elliptic genus via a free field
description of the model, and show that it agrees with algebraic expectations.
The holomorphic part of the elliptic genus is directly related to an
Appell-Lerch sum and behaves anomalously under modular transformation
properties. We analyze the origin of the anomaly by calculating the elliptic
genus through a path integral in a coset conformal field theory. The path
integral codes both the holomorphic part of the elliptic genus, and a
non-holomorphic remainder that finds its origin in the continuous spectrum of
the non-compact model. The remainder term can be shown to agree with a function
that mathematicians introduced to parameterize the difference between mock
theta functions and Jacobi forms. The holomorphic part of the elliptic genus
thus has a path integral completion which renders it non-holomorphic and
modular.Comment: 13 page
Relationship between knee pain and the presence, location, size and phenotype of femorotibial denuded areas of subchondral bone as visualized by MRI
Objective: Conflicting associations between imaging biomarkers and pain in knee osteoarthritis (OA) have been reported. A relation between pain and denuded areas of subchondral bone (dABs) has been suggested and this study explores this relationship further by relating the presence, phenotype, location and size of dABs to different measures of knee pain. Methods: 633 right knees from the Osteoarthritis Initiative (OAI) (250 men, age 61.7 +/- 9.6 yrs, BMI 29.4 +/- 4.7 kg/m(2)) were included. Manual segmentation of the femorotibial cartilage plates was performed on 3 T coronal fast low angle shot with water excitation (FLASHwe) images. dABs were defined as areas where the subchondral bone was uncovered by cartilage. The following measures of pain were used: weightbearing-, non-weightbearing-, moderate-to-severe-, infrequent- and frequent knee pain. Results: Using pain measures from subjects without dABs as a reference, those with at least one dAB had a 1.64-fold higher prevalence ratio [PR, 95% confidence interval (CI) 1.24-2.18] to have frequent and 1.45-fold higher for moderate-to-severe knee pain (95% CI 1.13-1.85). Subjects with dABs in central subregions had a 1.53-fold increased prevalence of having weightbearing pain (95% Cl 1.20-1.97), especially when the central subregion was moderately (>10%) denuded (PR 1.81, 95% CI 135-2.42). Individuals with cartilage-loss-type dABs had a slightly higher prevalence (PR 1.13, 95% CI 1.00-1.27) of having frequent knee pain compared to individuals with intra-chondral-osteophyte-type dABs. Conclusion: This study supports a positive relation between femorotibial dABs and knee pain, especially when the dABs are located centrally (i.e., in weightbearing regions) or when the respective central subregion is moderately denuded. (C) 2013 Osteoarthritis Research Society International. Published by Elsevier Ltd. All rights reserved
Kinetics of active surface-mediated diffusion in spherically symmetric domains
We present an exact calculation of the mean first-passage time to a target on
the surface of a 2D or 3D spherical domain, for a molecule alternating phases
of surface diffusion on the domain boundary and phases of bulk diffusion. We
generalize the results of [J. Stat. Phys. {\bf 142}, 657 (2011)] and consider a
biased diffusion in a general annulus with an arbitrary number of regularly
spaced targets on a partially reflecting surface. The presented approach is
based on an integral equation which can be solved analytically. Numerically
validated approximation schemes, which provide more tractable expressions of
the mean first-passage time are also proposed. In the framework of this minimal
model of surface-mediated reactions, we show analytically that the mean
reaction time can be minimized as a function of the desorption rate from the
surface.Comment: Published online in J. Stat. Phy
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