6,715 research outputs found
On highest-energy state in the su(1|1) sector of N=4 super Yang-Mills theory
We consider the highest-energy state in the su(1|1) sector of N=4 super
Yang-Mills theory containing operators of the form tr(Z^{L-M} \psi^M) where Z
is a complex scalar and \psi is a component of gaugino. We show that this state
corresponds to the operator tr(\psi^L) and can be viewed as an analogue of the
antiferromagnetic state in the su(2) sector. We find perturbative expansions of
the energy of this state in both weak and strong 't Hooft coupling regimes
using asymptotic gauge theory Bethe ansatz equations. We also discuss a
possible analog of this state in the conjectured string Bethe ansatz equations.Comment: 23 pages, Late
Two-loop AdS_5 x S^5 superstring: testing asymptotic Bethe ansatz and finite size corrections
We continue the investigation of two-loop string corrections to the energy of
a folded string with a spin S in AdS_5 and an angular momentum J in S^5, in the
scaling limit of large J and S with ell=pi J/(lambda^(1/2) ln S)=fixed. We
compute the generalized scaling function at two-loop order f_2(ell) both for
small and large values of ell matching the predictions based on the asymptotic
Bethe ansatz. In particular, in the small ell expansion, we derive an exact
integral form for the ell-dependent coefficient of the Catalan's constant term
in f_2(ell). Also, by resumming a certain subclass of multi-loop Feynman
diagrams we obtain an exact expression for the leading (ln ell) part of
f(lambda^(1/2), ell) which is valid to any order in the alpha'~1/lambda^(1/2)
expansion. At large ell the string energy has a BMN-like expansion and the
first few leading coefficients are expected to be the same at weak and at
strong coupling. We provide a new example of this non-renormalization for the
term which is generated at two loops in string theory and at one-loop in gauge
theory (sub-sub-leading in 1/J). We also derive a simple algebraic formula for
the term of maximal transcendentality in f_2(ell) expanded at large ell. In the
second part of the paper we initiate the study of 2-loop finite size
corrections to the string energy by formally compactifying the spatial
world-sheet direction in the string action expanded near long fast-spinning
string. We observe that the leading finite-size corrections are of "Casimir"
type coming from terms containing at least one massless propagator. We consider
in detail the one-loop order (reproducing the leading Landau-Lifshitz model
prediction) and then focus on the two-loop contributions to the (1/ln S) term
(for J=0). We find that in a certain regularization scheme used to discard
power divergences the two-loop coefficient of the (1/ln S) term appears to
vanish.Comment: 50 pages, 4 figures v2: typos corrected, references adde
5d superconformal field theories and graphs
We propose graphs, the Combined Fiber Diagrams (CFD), to characterize all 5d superconformal field theories (SCFTs) that arise as S1-reductions of 6d SCFTs. Transitions between CFDs encode mass deformations that trigger RG-flows between SCFTs. They provide a combinatorial classification of all such 5d SCFTs and encode physical information about the strongly coupled theories, like the superconformal flavor symmetry and BPS states. We consistently reproduce known results, but more importantly predict new theories and strong coupling effects in 5d SCFTs
Comparison of techniques for handling missing covariate data within prognostic modelling studies: a simulation study
Background: There is no consensus on the most appropriate approach to handle missing covariate data within prognostic modelling studies. Therefore a simulation study was performed to assess the effects of different missing data techniques on the performance of a prognostic model.
Methods: Datasets were generated to resemble the skewed distributions seen in a motivating breast cancer example. Multivariate missing data were imposed on four covariates using four different mechanisms; missing completely at random (MCAR), missing at random (MAR), missing not at random (MNAR) and a combination of all three mechanisms. Five amounts of incomplete cases from 5% to 75% were considered. Complete case analysis (CC), single imputation (SI) and five multiple imputation (MI) techniques available within the R statistical software were investigated: a) data augmentation (DA) approach assuming a multivariate normal distribution, b) DA assuming a general location model, c) regression switching imputation, d) regression switching with predictive mean matching (MICE-PMM) and e) flexible additive imputation models. A Cox proportional hazards model was fitted and appropriate estimates for the regression coefficients and model performance measures were obtained.
Results: Performing a CC analysis produced unbiased regression estimates, but inflated standard errors, which affected the significance of the covariates in the model with 25% or more missingness. Using SI, underestimated the variability; resulting in poor coverage even with 10% missingness. Of the MI approaches, applying MICE-PMM produced, in general, the least biased estimates and better coverage for the incomplete covariates and better model performance for all mechanisms. However, this MI approach still produced biased regression coefficient estimates for the incomplete skewed continuous covariates when 50% or more cases had missing data imposed with a MCAR, MAR or combined mechanism. When the missingness depended on the incomplete covariates, i.e. MNAR, estimates were biased with more than 10% incomplete cases for all MI approaches.
Conclusion: The results from this simulation study suggest that performing MICE-PMM may be the preferred MI approach provided that less than 50% of the cases have missing data and the missing data are not MNAR
Integrability and Transcendentality
We derive the two-loop Bethe ansatz for the sl(2) twist operator sector of
N=4 gauge theory directly from the field theory. We then analyze a recently
proposed perturbative asymptotic all-loop Bethe ansatz in the limit of large
spacetime spin at large but finite twist, and find a novel all-loop scaling
function. This function obeys the Kotikov-Lipatov transcendentality principle
and does not depend on the twist. Under the assumption that one may extrapolate
back to leading twist, our result yields an all-loop prediction for the
large-spin anomalous dimensions of twist-two operators. The latter also appears
as an undetermined function in a recent conjecture of Bern, Dixon and Smirnov
for the all-loop structure of the maximally helicity violating (MHV) n-point
gluon amplitudes of N=4 gauge theory. This potentially establishes a direct
link between the worldsheet and the spacetime S-matrix approach. A further
assumption for the validity of our prediction is that perturbative BMN
(Berenstein-Maldacena-Nastase) scaling does not break down at four loops, or
beyond. We also discuss how the result gets modified if BMN scaling does break
down. Finally, we show that our result qualitatively agrees at strong coupling
with a prediction of string theory.Comment: 45 pages LaTeX, 3 postscript figures. v2: Chapter on BMN scaling and
transcendentality added. v3: version accepted for publication in JSTA
On the Fermionic Frequencies of Circular Strings
We revisit the semiclassical computation of the fluctuation spectrum around
different circular string solutions in AdS_5xS^5 and AdS_4xCP^3, starting from
the Green-Schwarz action. It has been known that the results for these
frequencies obtained from the algebraic curve and from the worldsheet
computations sometimes do not agree. In particular, different methods give
different results for the half-integer shifts in the mode numbers of the
frequencies. We find that these discrepancies can be removed if one carefully
takes into account the transition matrices in the spin bundle over the target
space.Comment: 13 pages, 1 figur
Foundations of the AdS_5 x S^5 Superstring. Part I
We review the recent advances towards finding the spectrum of the AdS_5 x S^5
superstring. We thoroughly explain the theoretical techniques which should be
useful for the ultimate solution of the spectral problem. In certain cases our
exposition is original and cannot be found in the existing literature. The
present Part I deals with foundations of classical string theory in AdS_5 x
S^5, light-cone perturbative quantization and derivation of the exact
light-cone world-sheet scattering matrix.Comment: 161 page
Black holes admitting a Freudenthal dual
The quantised charges x of four dimensional stringy black holes may be
assigned to elements of an integral Freudenthal triple system whose
automorphism group is the corresponding U-duality and whose U-invariant quartic
norm Delta(x) determines the lowest order entropy. Here we introduce a
Freudenthal duality x -> \tilde{x}, for which \tilde{\tilde{x}}=-x. Although
distinct from U-duality it nevertheless leaves Delta(x) invariant. However, the
requirement that \tilde{x} be integer restricts us to the subset of black holes
for which Delta(x) is necessarily a perfect square. The issue of higher-order
corrections remains open as some, but not all, of the discrete U-duality
invariants are Freudenthal invariant. Similarly, the quantised charges A of
five dimensional black holes and strings may be assigned to elements of an
integral Jordan algebra, whose cubic norm N(A) determines the lowest order
entropy. We introduce an analogous Jordan dual A*, with N(A) necessarily a
perfect cube, for which A**=A and which leaves N(A) invariant. The two
dualities are related by a 4D/5D lift.Comment: 32 pages revtex, 10 tables; minor corrections, references adde
The Role of Nonequilibrium Dynamical Screening in Carrier Thermalization
We investigate the role played by nonequilibrium dynamical screening in the
thermalization of carriers in a simplified two-component two-band model of a
semiconductor. The main feature of our approach is the theoretically sound
treatment of collisions. We abandon Fermi's Golden rule in favor of a
nonequilibrium field theoretic formalism as the former is applicable only in
the long-time regime. We also introduce the concept of nonequilibrium dynamical
screening. The dephasing of excitonic quantum beats as a result of
carrier-carrier scattering is brought out. At low densities it is found that
the dephasing times due to carrier-carrier scattering is in picoseconds and not
femtoseconds, in agreement with experiments. The polarization dephasing rates
are computed as a function of the excited carrier density and it is found that
the dephasing rate for carrier-carrier scattering is proportional to the
carrier density at ultralow densities. The scaling relation is sublinear at
higher densities, which enables a comparison with experiment.Comment: Revised version with additional refs. 12 pages, figs. available upon
request; Submitted to Phys. Rev.
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