1,229 research outputs found
Lifting 1/4-BPS States on K3 and Mathieu Moonshine
The elliptic genus of K3 is an index for the 1/4-BPS states of its sigma
model. At the torus orbifold point there is an accidental degeneracy of such
states. We blow up the orbifold fixed points using conformal perturbation
theory, and find that this fully lifts the accidental degeneracy of the 1/4-BPS
states with h=1. At a generic point near the Kummer surface the elliptic genus
thus measures not just their index, but counts the actual number of these BPS
states. We comment on the implication of this for symmetry surfing and Mathieu
moonshine.Comment: 29+5 pp, a sign mistake corrected in eqs. (3.14) and (4.20), footnote
6 added to clarify this point, references adde
Genus Two Partition Functions and Renyi Entropies of Large c CFTs
We compute genus two partition functions in two dimensional conformal field
theories at large central charge, focusing on surfaces that give the third
Renyi entropy of two intervals. We compute this for generalized free theories
and for symmetric orbifolds, and compare it to the result in pure gravity. We
find a new phase transition if the theory contains a light operator of
dimension . This means in particular that unlike the second
Renyi entropy, the third one is no longer universal.Comment: 28 pages + Appendice
Conformal Perturbation Theory for Twisted Fields
We investigate second order conformal perturbation theory for
orbifolds of conformal field theories in two dimensions. To evaluate the
necessary twisted sector correlation functions and their integrals, we map them
from the sphere to its torus double cover. We discuss how this relates crossing
symmetry to the modular group, and introduce a regularization scheme on the
cover that allows to evaluate the integrals numerically. These methods do not
require supersymmetry. As an application, we show that in the torus orbifold of
8 and 16 free bosons, twist fields are marginal at first order,
but stop being marginal at second order.Comment: 29pp, v2: minor corrections + references adde
The coronagraphic Modal Wavefront Sensor: a hybrid focal-plane sensor for the high-contrast imaging of circumstellar environments
The raw coronagraphic performance of current high-contrast imaging
instruments is limited by the presence of a quasi-static speckle (QSS)
background, resulting from instrumental non-common path errors (NCPEs). Rapid
development of efficient speckle subtraction techniques in data reduction has
enabled final contrasts of up to 10-6 to be obtained, however it remains
preferable to eliminate the underlying NCPEs at the source. In this work we
introduce the coronagraphic Modal Wavefront Sensor (cMWS), a new wavefront
sensor suitable for real-time NCPE correction. This pupil-plane optic combines
the apodizing phase plate coronagraph with a holographic modal wavefront
sensor, to provide simultaneous coronagraphic imaging and focal-plane wavefront
sensing using the science point spread function. We first characterise the
baseline performance of the cMWS via idealised closed-loop simulations, showing
that the sensor successfully recovers diffraction-limited coronagraph
performance over an effective dynamic range of +/-2.5 radians root-mean-square
(RMS) wavefront error within 2-10 iterations. We then present the results of
initial on-sky testing at the William Herschel Telescope, and demonstrate that
the sensor is able to retrieve injected wavefront aberrations to an accuracy of
10nm RMS under realistic seeing conditions. We also find that the cMWS is
capable of real-time broadband measurement of atmospheric wavefront variance at
a cadence of 50Hz across an uncorrected telescope sub-aperture. When combined
with a suitable closed-loop adaptive optics system, the cMWS holds the
potential to deliver an improvement in raw contrast of up to two orders of
magnitude over the uncorrected QSS floor. Such a sensor would be eminently
suitable for the direct imaging and spectroscopy of exoplanets with both
existing and future instruments, including EPICS and METIS for the E-ELT.Comment: 14 pages, 12 figures: accepted for publication in Astronomy &
Astrophysic
Continuity of the four-point function of massive -theory above threshold
In this paper we prove that the four-point function of massive
\vp_4^4-theory is continuous as a function of its independent external
momenta when posing the renormalization condition for the (physical) mass
on-shell. The proof is based on integral representations derived inductively
from the perturbative flow equations of the renormalization group. It closes a
longstanding loophole in rigorous renormalization theory in so far as it shows
the feasibility of a physical definition of the renormalized coupling.Comment: 23 pages; to appear in Rev. Math. Physics few corrections, two
explanatory paragraphs adde
Narain to Narnia
We generalize the holographic correspondence between topological gravity coupled to an abelian Chern-Simons theory in three dimensions and an ensemble average of Narain's family of massless free bosons in two dimensions, discovered by Afkhami-Jeddi et al. and by Maloney and Witten. We find that the correspondence also works for toroidal orbifolds but not for K3 or Calabi-Yau sigma-models and not always for the minimal models. We conjecture that the correspondence requires that the central charge is equal to the critical central charge defined by the asymptotic density of states of the chiral algebra. For toroidal orbifolds, we extend the holographic correspondence to correlation functions of twist operators by using topological properties of rational tangles in the three-dimensional ball, which represent configurations of vortices associated to a discrete gauge symmetry
On rational points in CFT moduli spaces
Motivated by the search for rational points in moduli spaces of two-dimensional conformal field theories, we investigate how points with enhanced symmetry algebras are distributed there. We first study the bosonic sigma-model with S1 target space in detail and uncover hitherto unknown features. We find for instance that the vanishing of the twist gap, though true for the S1 example, does not automatically follow from enhanced symmetry points being dense in the moduli space. We then explore the supersymmetric sigma-model on K3 by perturbing away from the torus orbifold locus. Though we do not reach a definite conclusion on the distribution of enhanced symmetry points in the K3 moduli space, we make several observations on how chiral currents can emerge and disappear under conformal perturbation theory
Evaluation of phase-diversity techniques for solar-image restoration
Phase-diversity techniques provide a novel observational method for overcomming the effects of turbulence and instrument-induced aberrations in ground-based astronomy. Two implementations of phase-diversity techniques that differ with regard to noise model, estimator, optimization algorithm, method of regularization, and treatment of edge effects are described. Reconstructions of solar granulation derived by applying these two implementations to common data sets are shown to yield nearly identical images. For both implementations, reconstructions from phase-diverse speckle data (involving multiple realizations of turbulence) are shown to be superior to those derived from conventional phase-diversity data (involving a single realization). Phase-diverse speckle reconstructions are shown to achieve near diffraction-limited resolution and are validated by internal and external consistency tests, including a comparison with a reconstruction using a well-accepted speckle-imaging method
Towards a 4d/2d correspondence for Sicilian quivers
We study the 4d/2d AGT correspondence between four-dimensional instanton
counting and two-dimensional conformal blocks for generalized SU(2) quiver
gauge theories coming from punctured Gaiotto curves of arbitrary genus. We
propose a conformal block description that corresponds to the elementary SU(2)
trifundamental half-hypermultiplet, and check it against Sp(1)-SO(4) instanton
counting.Comment: 39 pages, 11 figure
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