925 research outputs found

### A Hiker's Guide to K3 - Aspects of N=(4,4) Superconformal Field Theory with central charge c=6

We study the moduli space ${\cal M}$ of N=(4,4) superconformal field theories
with central charge c=6. After a slight emendation of its global description we
find the locations of various known models in the component of ${\cal M}$
associated to K3 surfaces. Among them are the Z_2 and Z_4 orbifold theories
obtained from the torus component of ${\cal M}$. Here, SO(4,4) triality is
found to play a dominant role. We obtain the B-field values in direction of the
exceptional divisors which arise from orbifolding. We prove T-duality for the
Z_2 orbifolds and use it to derive the form of ${\cal M}$ purely within
conformal field theory. For the Gepner model (2)^4 and some of its orbifolds we
find the locations in ${\cal M}$ and prove isomorphisms to nonlinear sigma
models. In particular we prove that the Gepner model (2)^4 has a geometric
interpretation with Fermat quartic target space.Comment: 58 pages, version submitted to Comm. Math. Phys; references added and
minor mistakes correcte

### Dilogarithm Identities in Conformal Field Theory

Dilogarithm identities for the central charges and conformal dimensions exist
for at least large classes of rational conformally invariant quantum field
theories in two dimensions. In many cases, proofs are not yet known but the
numerical and structural evidence is convincing. In particular, close relations
exist to fusion rules and partition identities. We describe some examples and
ideas, and present some conjectures useful for the classification of conformal
theories. The mathematical structures seem to be dual to Thurston's program for
the classification of 3-manifolds.Comment: 14 pages, BONN-preprint. (a few minor changes, two major corrections
in chapter 3, namely: (3.10) only holds in the case of the A series,
Goncharovs conjecture is not an equivalence but rather an implication and a
theorem

### An evaluation of image feature detectors based on spatial density and temporal robustness in microsurgical image processing

Optical image processing is part of many applications used for brain surgeries. Microscope camera, or patient movement, like brain-movement through the pulse or a change in the liquor, can cause the image processing to fail. One option to compensate movement is feature detection and spatial allocation. This allocation is based on image features. The frame wise matched features are used to calculate the transformation matrix. The goal of this project was to evaluate different feature detectors based on spatial density and temporal robustness to reveal the most appropriate feature. The feature detectors included corner-, and blob-detectors and were applied on nine videos. These videos were taken during brain surgery with surgical microscopes and include the RGB channels. The evaluation showed that each detector detected up to 10 features for nine frames. The feature detector KAZE resulted in being the best feature detector in both density and robustness

### Radiative corrections to the pressure and the one-loop polarization tensor of massless modes in SU(2) Yang-Mills thermodynamics

We compute the one-loop polarization tensor $\Pi$ for the on-shell, massless
mode in a thermalized SU(2) Yang-Mills theory being in its deconfining phase.
Postulating that SU(2)$_{\tiny{CMB}}\stackrel{\tiny{today}}=U(1)_Y$, we discuss
$\Pi$'s effect on the low-momentum part of the black-body spectrum at
temperatures $\sim 2... 4$ $T_{\tiny{CMB}}$ where $T_{\tiny{CMB}}\sim 2.73$K.
A table-top experiment is proposed to test the above postulate. As an
application, we point out a possible connection with the stability of dilute,
cold, and old innergalactic atomic hydrogen clouds. We also compute the
two-loop correction to the pressure arising from the instantaneous massless
mode in unitary-Coulomb gauge, which formerly was neglected, and present
improved estimates for subdominant corrections.Comment: 25 pages, 17 figs, v4: consequences of a modification of the
evolution equation for the effectice coupling implemented, no qualitative
change of the physic

### Orbifold resolutions with general profile

A very general class of resolved versions of the C/Z_N, T^2/Z_N and S^1/Z_2
orbifolds is considered and the free theory of 6D chiral fermions studied on
it. As the orbifold limit is taken, localized 4D chiral massless fermions are
seen to arise at the fixed points. Their number, location and chirality is
found to be independent on the detailed profile of the resolving space and to
agree with the result of hep-th/0409229, in which a particular resolution was
employed. As a consistency check of the resolution procedure, the massive
equation is numerically studied. In particular, for S^1/Z_2, the "resolved"
mass--spectrum and wave functions in the internal space are seen to correctly
reproduce the usual orbifold ones, as the orbifold limit is taken.Comment: 28 pages, 3 figures, typos corrected, references adde

### Laplacian modes probing gauge fields

We show that low-lying eigenmodes of the Laplace operator are suitable to
represent properties of the underlying SU(2) lattice configurations. We study
this for the case of finite temperature background fields, yet in the
confinement phase. For calorons as classical solutions put on the lattice, the
lowest mode localizes one of the constituent monopoles by a maximum and the
other one by a minimum, respectively. We introduce adjustable phase boundary
conditions in the time direction, under which the role of the monopoles in the
mode localization is interchanged. Similar hopping phenomena are observed for
thermalized configurations. We also investigate periodic and antiperiodic modes
of the adjoint Laplacian for comparison.
In the second part we introduce a new Fourier-like low-pass filter method. It
provides link variables by truncating a sum involving the Laplacian eigenmodes.
The filter not only reproduces classical structures, but also preserves the
confining potential for thermalized ensembles. We give a first characterization
of the structures emerging from this procedure.Comment: 43 pages, 26 figure

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