2,261 research outputs found
Modular properties of two-loop maximal supergravity and connections with string theory
The low-momentum expansion of the two-loop four-graviton scattering amplitude
in eleven-dimensional supergravity compactified on a circle and a two-torus is
considered up to terms of order S^6R^4 (where S is a Mandelstam invariant and R
is the linearized Weyl curvature). In the case of the toroidal compactification
the coefficient of each term in the low energy expansion is generically a sum
of a number of SL(2,Z)-invariant functions of the complex structure of the
torus. Each such function satisfies a separate Poisson equation on moduli space
with particular source terms that are bilinear in coefficients of lower order
terms, consistent with qualitative arguments based on supersymmetry. Comparison
is made with the low-energy expansion of type II string theories in ten and
nine dimensions. Although the detailed behaviour of the string amplitude is not
generally expected to be reproduced by supergravity perturbation theory to all
orders, for the terms considered here we find agreement with direct results
from string perturbation theory. These results point to a fascinating pattern
of interrelated Poisson equations for the IIB coefficients at higher orders in
the momentum expansion which may have a significance beyond the particular
methods by which they were motivated.Comment: 79 pages, 4 figures. Latex format. v2: Small corrections made,
version to appear in JHE
Eisenstein series for higher-rank groups and string theory amplitudes
Scattering amplitudes of superstring theory are strongly constrained by the
requirement that they be invariant under dualities generated by discrete
subgroups, E_n(Z), of simply-laced Lie groups in the E_n series (n<= 8). In
particular, expanding the four-supergraviton amplitude at low energy gives a
series of higher derivative corrections to Einstein's theory, with coefficients
that are automorphic functions with a rich dependence on the moduli. Boundary
conditions supplied by string and supergravity perturbation theory, together
with a chain of relations between successive groups in the E_n series,
constrain the constant terms of these coefficients in three distinct parabolic
subgroups. Using this information we are able to determine the expressions for
the first two higher derivative interactions (which are BPS-protected) in terms
of specific Eisenstein series. Further, we determine key features of the
coefficient of the third term in the low energy expansion of the
four-supergraviton amplitude (which is also BPS-protected) in the E_8 case.
This is an automorphic function that satisfies an inhomogeneous Laplace
equation and has constant terms in certain parabolic subgroups that contain
information about all the preceding terms.Comment: Latex. 38 pages. 1 figure. v2: minor changes and clarifications. v3:
minor corrections, version to appear in Communications in Number Theory and
Physics. v4: corrections to table
Generalized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index H>=1/4
Given a locally bounded real function g, we examine the existence of a 4-covariation , where is a fractional Brownian motion with a Hurst index . We provide two essential applications. First, we relate the 4-covariation to one expression involving the derivative of local time, in the case , generalizing an identity of Bouleau--Yor type, well known for the classical Brownian motion. A second application is an Itô formula of Stratonovich type for . The main difficulty comes from the fact has only a finite 4-variation
The Lorentz force between D0 and D6 branes in string and M(atrix) theory
We use different techniques to analyze the system formed by a D0 brane and a
D6 brane (with background gauge fields) in relative motion. In particular,
using the closed string formalism of boosted boundary states, we show the
presence of a term linear in the velocity, corresponding to the Lorentz force
experienced by the D0 brane moving in the magnetic background produced by the
D6 brane. This term, that was missed in previous analyses of this system, comes
entirely from the R-R odd spin structure and is also reproduced by a M(atrix)
theory calculation.Comment: 13 pages, plain LaTeX; some clarifying comments and a reference adde
Automorphic properties of low energy string amplitudes in various dimensions
This paper explores the moduli-dependent coefficients of higher derivative
interactions that appear in the low-energy expansion of the four-graviton
amplitude of maximally supersymmetric string theory compactified on a d-torus.
These automorphic functions are determined for terms up to order D^6R^4 and
various values of d by imposing a variety of consistency conditions. They
satisfy Laplace eigenvalue equations with or without source terms, whose
solutions are given in terms of Eisenstein series, or more general automorphic
functions, for certain parabolic subgroups of the relevant U-duality groups.
The ultraviolet divergences of the corresponding supergravity field theory
limits are encoded in various logarithms, although the string theory
expressions are finite. This analysis includes intriguing representations of
SL(d) and SO(d,d) Eisenstein series in terms of toroidally compactified one and
two-loop string and supergravity amplitudes.Comment: 80 pages. 1 figure. v2:Typos corrected, footnotes amended and small
clarifications. v3: minor corrections. Version to appear in Phys Rev
Ultraviolet properties of maximal supergravity
We argue that recent results in string perturbation theory indicate that the four-graviton amplitude of four-dimensional
N
=
8
supergravity might be ultraviolet finite up to eight loops. We similarly argue that the
h
-loop
M
-graviton amplitude might be finite for
h
<
7
+
M
/
2
Exciton Footprint of Self-assembled AlGaAs Quantum Dots in Core-Shell Nanowires
Quantum-dot-in-nanowire systems constitute building blocks for advanced
photonics and sensing applications. The electronic symmetry of the emitters
impacts their function capabilities. Here, we study the fine structure of
gallium-rich quantum dots nested in the shell of GaAs-AlGaAs core-shell
nanowires. We used optical spectroscopy to resolve the splitting resulting from
the exchange terms and extract the main parameters of the emitters. Our results
indicate that the quantum dots can host neutral as well as charges excitonic
complexes and that the excitons exhibit a slightly elongated footprint, with
the main axis tilted with respect to the growth axis. GaAs-AlGaAs emitters in a
nanowire are particularly promising for overcoming the limitations set by
strain in other systems, with the benefit of being integrated in a versatile
photonic structure
Non-renormalization conditions for four-gluon scattering in supersymmetric string and field theory
The constraints imposed by maximal supersymmetry on multi-loop contributions
to the scattering of four open superstrings in the U(N) theory are examined by
use of the pure spinor formalism. The double-trace term k^2 t_8(tr F^2)^2
(where k represents an external momentum and F the Yang--Mills field strength)
only receives contributions from L<=2 (where L is the loop number) while the
single-trace term k^2 t_8(tr F^4) receives contributions from all L. We
verified these statements up to L=5, but arguments based on supersymmetry
suggest they extend to all L. This explains why the single-trace contributions
to low energy maximally supersymmetric Yang--Mills field theory are more
divergent in the ultraviolet than the double-trace contributions. We also
comment further on the constraints on closed string amplitudes and their
implications for ultraviolet divergences in N=8 supergravity.Comment: 25 pages. 2 eps figures. Harvmac format. v2 qualifications regarding
comments on closed strings. References adde
Feature based volumes for implicit intersections.
The automatic generation of volumes bounding the intersection of two implicit surfaces (isosurfaces of real functions of 3D point coordinates) or feature based volumes (FBV) is presented. Such FBVs are defined by constructive operations, function normalization and offsetting. By applying various offset operations to the intersection of two surfaces, we can obtain variations in the shape of an FBV. The resulting volume can be used as a boundary for blending operations applied to two corresponding volumes, and also for visualization of feature curves and modeling of surface based structures including microstructures
Non-renormalisation Conditions in Type II String Theory and Maximal Supergravity
This paper considers general features of the derivative expansion of Feynman
diagram contributions to the four-graviton scattering amplitude in
eleven-dimensional supergravity compactified on a two-torus. These are
translated into statements about interactions of the form D^2k R^4 in type II
superstring theories, assuming the standard M-theory/string theory duality
relationships, which provide powerful constraints on the effective
interactions. In the ten-dimensional IIA limit we find that there can be no
perturbative contributions beyond k string loops (for k>0). Furthermore, the
genus h=k contributions are determined exactly by the one-loop
eleven-dimensional supergravity amplitude for all values of k. A plausible
interpretation of these observations is that the sum of h-loop Feynman diagrams
of maximally extended supergravity is less divergent than might be expected and
could be ultraviolet finite in dimensions d < 4 + 6/h -- the same bound as for
N=4 Yang--Mills.Comment: 30 pages, 4 figures. v3 Some rewording, typos corrected and some
references added. v4: Abstract rephrased. More typos corrected. Version to be
publishe
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