5,330 research outputs found
(2,0) Superconformal OPEs in D=6, Selection Rules and Non-renormalization Theorems
We analyse the OPE of any two 1/2 BPS operators of (2,0) SCFT by
constructing all possible three-point functions that they can form with
another, in general long operator. Such three-point functions are uniquely
determined by superconformal symmetry. Selection rules are derived, which allow
us to infer ``non-renormalization theorems'' for an abstract superconformal
field theory. The latter is supposedly related to the strong-coupling dynamics
of coincident M5 branes, dual, in the large- limit, to the bulk
M-theory compactified on AdSS. An interpretation of extremal and
next-to-extremal correlators in terms of exchange of operators with protected
conformal dimension is given.Comment: some details correcte
Four-point correlators of BPS operators in N=4 SYM at order g^4
We study the large N degeneracy in the structure of the four-point amplitudes
of 1/2-BPS operators of arbitrary weight k in perturbative N=4 SYM theory. At
one loop (order g^2) this degeneracy manifests itself in a smaller number of
independent conformal invariant functions describing the amplitude, compared to
AdS_5 supergravity results. To study this phenomenon at the two-loop level
(order g^4) we consider a particular N=2 hypermultiplet projection of the
general N=4 amplitude. Using the formalism of N=2 harmonic superspace we then
explicitly compute this four-point correlator at two loops and identify the
corresponding conformal invariant functions. In the cases of 1/2-BPS operators
of weight k=3 and k=4 the one-loop large N degeneracy is lifted by the two-loop
corrections. However, for weight k > 4 the degeneracy is still there at the
two-loop level. This behavior suggests that for a given weight k the degeneracy
will be removed if perturbative corrections of sufficiently high order are
taken into account. These results are in accord with the AdS/CFT duality
conjecture.Comment: 45 pages, latex, 14 figure
Stimulated Emission from a single excited atom in a waveguide
We study stimulated emission from an excited two-level atom coupled to a
waveguide containing an incident single-photon pulse. We show that the strong
photon correlation, as induced by the atom, plays a very important role in
stimulated emission. Additionally, the temporal duration of the incident photon
pulse is shown to have a marked effect on stimulated emission and atomic
lifetime.Comment: 6 pages, 3 figure
A common goodness-of-fit framework for neural population models using marked point process time-rescaling
A critical component of any statistical modeling procedure is the ability to assess the goodness-of-fit between a model and observed data. For spike train models of individual neurons, many goodness-of-fit measures rely on the time-rescaling theorem and assess model quality using rescaled spike times. Recently, there has been increasing interest in statistical models that describe the simultaneous spiking activity of neuron populations, either in a single brain region or across brain regions. Classically, such models have used spike sorted data to describe relationships between the identified neurons, but more recently clusterless modeling methods have been used to describe population activity using a single model. Here we develop a generalization of the time-rescaling theorem that enables comprehensive goodness-of-fit analysis for either of these classes of population models. We use the theory of marked point processes to model population spiking activity, and show that under the correct model, each spike can be rescaled individually to generate a uniformly distributed set of events in time and the space of spike marks. After rescaling, multiple well-established goodness-of-fit procedures and statistical tests are available. We demonstrate the application of these methods both to simulated data and real population spiking in rat hippocampus. We have made the MATLAB and Python code used for the analyses in this paper publicly available through our Github repository at https://github.com/Eden-Kramer-Lab/popTRT.This work was supported by grants from the NIH (MH105174, NS094288) and the Simons Foundation (542971). (MH105174 - NIH; NS094288 - NIH; 542971 - Simons Foundation)Published versio
Operator mixing in N=4 SYM: The Konishi anomaly revisited
In the context of the superconformal N=4 SYM theory the Konishi anomaly can
be viewed as the descendant of the Konishi multiplet in the 10 of
SU(4), carrying the anomalous dimension of the multiplet. Another descendant
with the same quantum numbers, but this time without anomalous
dimension, is obtained from the protected half-BPS operator (the
stress-tensor multiplet). Both and are renormalized mixtures
of the same two bare operators, one trilinear (coming from the superpotential),
the other bilinear (the so-called "quantum Konishi anomaly"). Only the operator
is allowed to appear in the right-hand side of the Konishi anomaly
equation, the protected one does not match the conformal properties of
the left-hand side. Thus, in a superconformal renormalization scheme the
separation into "classical" and "quantum" anomaly terms is not possible, and
the question whether the Konishi anomaly is one-loop exact is out of context.
The same treatment applies to the operators of the BMN family, for which no
analogy with the traditional axial anomaly exists. We illustrate our abstract
analysis of this mixing problem by an explicit calculation of the mixing matrix
at level g^4 ("two loops") in the supersymmetric dimensional reduction scheme.Comment: 28 pp LaTeX, 3 figure
Experiments to investigate particulate materials in reduced gravity fields
Study investigates agglomeration and macroscopic behavior in reduced gravity fields of particles of known properties by measuring and correlating thermal and acoustical properties of particulate materials. Experiment evaluations provide a basis for a particle behavior theory and measure bulk properties of particulate materials in reduced gravity
Exceptional non-renormalization properties and OPE analysis of chiral four-point functions in N=4 SYM_4
We show that certain classes of apparently unprotected operators in N=4 SYM_4
do not receive quantum corrections as a consequence of a partial
non-renormalization theorem for the 4-point function of chiral primary
operators. We develop techniques yielding the asymptotic expansion of the
4-point function of CPOs up to order O(\lambda^2) and we perform a detailed OPE
analysis. Our results reveal the existence of new non-renormalized operators of
approximate dimension 6.Comment: an error in Sect. 4 corrected; references adde
Nonlinear field theories during homogeneous spatial dilation
The effect of a uniform dilation of space on stochastically driven nonlinear
field theories is examined. This theoretical question serves as a model problem
for examining the properties of nonlinear field theories embedded in expanding
Euclidean Friedmann-Lema\^{\i}tre-Robertson-Walker metrics in the context of
cosmology, as well as different systems in the disciplines of statistical
mechanics and condensed matter physics. Field theories are characterized by the
speed at which they propagate correlations within themselves. We show that for
linear field theories correlations stop propagating if and only if the speed at
which the space dilates is higher than the speed at which correlations
propagate. The situation is in general different for nonlinear field theories.
In this case correlations might stop propagating even if the velocity at which
space dilates is lower than the velocity at which correlations propagate. In
particular, these results imply that it is not possible to characterize the
dynamics of a nonlinear field theory during homogeneous spatial dilation {\it a
priori}. We illustrate our findings with the nonlinear Kardar-Parisi-Zhang
equation
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