631 research outputs found
Resolution requirements for numerical simulations of transition
The resolution requirements for direct numerical simulations of transition to turbulence are investigated. A reliable resolution criterion is determined from the results of several detailed simulations of channel and boundary-layer transition
On duality symmetries of supergravity invariants
The role of duality symmetries in the construction of counterterms for
maximal supergravity theories is discussed in a field-theoretic context from
different points of view. These are: dimensional reduction, the question of
whether appropriate superspace measures exist and information about non-linear
invariants that can be gleaned from linearised ones. The former allows us to
prove that F-term counterterms cannot be E7(7)-invariant in D=4, N=8
supergravity or E6(6)-invariant in D=5 maximal supergravity. This is confirmed
by the two other methods which can also be applied to D=4 theories with fewer
supersymmetries and allow us to prove that N=6 supergravity is finite at three
and four loops and that N=5 supergravity is three-loop finite.Comment: Clarification of arguments and their consistency with higher
dimensional divergences added, e.g. we prove the 5D 4L non-renormalisation
theorem. The 4L N=6 divergence is also ruled out. References adde
U(N|M) quantum mechanics on Kaehler manifolds
We study the extended supersymmetric quantum mechanics, with supercharges
transforming in the fundamental representation of U(N|M), as realized in
certain one-dimensional nonlinear sigma models with Kaehler manifolds as target
space. We discuss the symmetry algebra characterizing these models and, using
operatorial methods, compute the heat kernel in the limit of short propagation
time. These models are relevant for studying the quantum properties of a
certain class of higher spin field equations in first quantization.Comment: 21 pages, a reference adde
A simple approach to counterterms in N=8 supergravity
We present a simple systematic method to study candidate counterterms in N=8
supergravity. Complicated details of the counterterm operators are avoided
because we work with the on-shell matrix elements they produce. All n-point
matrix elements of an independent SUSY invariant operator of the form D^{2k}
R^n +... must be local and satisfy SUSY Ward identities. These are strong
constraints, and we test directly whether or not matrix elements with these
properties can be constructed. If not, then the operator does not have a
supersymmetrization, and it is excluded as a potential counterterm. For n>4, we
find that R^n, D^2 R^n, D^4 R^n, and D^6 R^n are excluded as counterterms of
MHV amplitudes, while only R^n and D^2 R^n are excluded at the NMHV level. As a
consequence, for loop order L<7, there are no independent D^{2k}R^n
counterterms with n>4. If an operator is not ruled out, our method constructs
an explicit superamplitude for its matrix elements. This is done for the 7-loop
D^4 R^6 operator at the NMHV level and in other cases. We also initiate the
study of counterterms without leading pure-graviton matrix elements, which can
occur beyond the MHV level. The landscape of excluded/allowed candidate
counterterms is summarized in a colorful chart.Comment: 25 pages, 1 figure, published versio
R^4 counterterm and E7(7) symmetry in maximal supergravity
The coefficient of a potential R^4 counterterm in N=8 supergravity has been
shown previously to vanish in an explicit three-loop calculation. The R^4 term
respects N=8 supersymmetry; hence this result poses the question of whether
another symmetry could be responsible for the cancellation of the three-loop
divergence. In this article we investigate possible restrictions from the coset
symmetry E7(7)/SU(8), exploring the limits as a single scalar becomes soft, as
well as a double-soft scalar limit relation derived recently by Arkani-Hamed et
al. We implement these relations for the matrix elements of the R^4 term that
occurs in the low-energy expansion of closed-string tree-level amplitudes. We
find that the matrix elements of R^4 that we investigated all obey the
double-soft scalar limit relation, including certain
non-maximally-helicity-violating six-point amplitudes. However, the single-soft
limit does not vanish for this latter set of amplitudes, which suggests that
the E7(7) symmetry is broken by the R^4 term.Comment: 33 pages, typos corrected, published versio
Constraints on Automorphic Forms of Higher Derivative Terms from Compactification
By dimensionally reducing the higher derivative corrections of
ten-dimensional IIB theory on a torus we deduce constraints on the E_{n+1}
automorphic forms that occur in d=10-n dimensions. In particular we argue that
these automorphic forms involve the representation of E_{n+1} with fundamental
weight \lambda^{n+1}, which is also the representation to which the string
charges in d dimensions belong. We also consider a similar calculation for the
reduction of higher derivative terms in eleven-dimensional M-theory.Comment: Minor corrections, to appear in JHE
Superconformal symmetry and maximal supergravity in various dimensions
In this paper we explore the relation between conformal superalgebras with 64
supercharges and maximal supergravity theories in three, four and six
dimensions using twistorial oscillator techniques. The massless fields of N=8
supergravity in four dimensions were shown to fit into a CPT-self-conjugate
doubleton supermultiplet of the conformal superalgebra SU(2,2|8) a long time
ago. We show that the fields of maximal supergravity in three dimensions can
similarly be fitted into the super singleton multiplet of the conformal
superalgebra OSp(16|4,R), which is related to the doubleton supermultiplet of
SU(2,2|8) by dimensional reduction. Moreover, we construct the ultra-short
supermultiplet of the six-dimensional conformal superalgebra OSp(8*|8) and show
that its component fields can be organized in an on-shell superfield. The
ultra-short OSp(8*|8) multiplet reduces to the doubleton supermultiplet of
SU(2,2|8) upon dimensional reduction. We discuss the possibility of a chiral
maximal (4,0) six-dimensional supergravity theory with USp(8) R-symmetry that
reduces to maximal supergravity in four dimensions and is different from
six-dimensional (2,2) maximal supergravity, whose fields cannot be fitted into
a unitary supermultiplet of a simple conformal superalgebra. Such an
interacting theory would be the gravitational analog of the (2,0) theory.Comment: 54 pages, PDFLaTeX, Section 5 and several references added. Version
accepted for publication in JHE
Higher derivative type II string effective actions, automorphic forms and E11
By dimensionally reducing the ten-dimensional higher derivative type IIA
string theory effective action we place constraints on the automorphic forms
that appear in the effective action in lower dimensions. We propose a number of
properties of such automorphic forms and consider the prospects that E11 can
play a role in the formulation of the higher derivative string theory effective
action.Comment: 34 page
Phosphorylation of LCRMP-1 by GSK3β Promotes Filopoda Formation, Migration and Invasion Abilities in Lung Cancer Cells
LCRMP-1, a novel isoform of CRMP-1, can promote cancer cell migration, invasion and associate with poor clinical outcome in patients with non-small-cell lung cancer (NSCLC). However, the underlying regulatory mechanisms of LCRMP-1 in cancer cell invasiveness still remain obscure. Here, we report that GSK3β can phosphorylate LCRMP-1 at Thr-628 in consensus sequences and this phosphorylation is crucial for function of LCRMP-1 to promote filopodia formation, migration and invasion in cancer cells. Impediment of Thr-628 phosphorylation attenuates the stimulatory effects of LCRMP-1 on filopodia forming, migration and invasion abilities in cancer cells; simultaneously, kinase-dead GSK3β diminishes regulation of LCRMP-1 on cancer cell invasion. Furthermore, we also found that patients with low-level Ser-9-phosphorylated GSK3β expression and high-level LCRMP-1 expression have worse overall survival than those with high-level inactive GSK3β expressions and low-level LCRMP-1 expressions (P<0.0001). Collectively, these results demonstrate that GSK3β-dependent phosphorylation of LCRMP-1 provides an important mechanism for regulation of LCRMP-1 on cancer cell invasiveness and clinical outcome
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