42,091 research outputs found
Conformal Symmetry on the Instanton Moduli Space
The conformal symmetry on the instanton moduli space is discussed using the
ADHM construction, where a viewpoint of "homogeneous coordinates" for both the
spacetime and the moduli space turns out to be useful. It is shown that the
conformal algebra closes only up to global gauge transformations, which
generalizes the earlier discussion by Jackiw et al. An interesting
5-dimensional interpretation of the SU(2) single-instanton is also mentioned.Comment: 7 pages, LaTeX, version to appear in J. Phys. A: Math. Ge
Poset-free Families and Lubell-boundedness
Given a finite poset , we consider the largest size \lanp of a family
\F of subsets of that contains no subposet . This
continues the study of the asymptotic growth of \lanp; it has been
conjectured that for all , \pi(P):= \lim_{n\rightarrow\infty} \lanp/\nchn
exists and equals a certain integer, . While this is known to be true for
paths, and several more general families of posets, for the simple diamond
poset \D_2, the existence of frustratingly remains open. Here we
develop theory to show that exists and equals the conjectured value
for many new posets . We introduce a hierarchy of properties for
posets, each of which implies , and some implying more precise
information about \lanp. The properties relate to the Lubell function of a
family \F of subsets, which is the average number of times a random full
chain meets \F. We present an array of examples and constructions that
possess the properties
D3-branes on partial resolutions of abelian quotient singularities of Calabi-Yau threefolds
We investigate field theories on the worldvolume of a D3-brane transverse to
partial resolutions of a Calabi-Yau threefold quotient
singularity. We deduce the field content and lagrangian of such theories and
present a systematic method for mapping the moment map levels characterizing
the partial resolutions of the singularity to the Fayet-Iliopoulos parameters
of the D-brane worldvolume theory. As opposed to the simpler cases studied
before, we find a complex web of partial resolutions and associated
field-theoretic Fayet-Iliopoulos deformations. The analysis is performed by
toric methods, leading to a structure which can be efficiently described in the
language of convex geometry. For the worldvolume theory, the analysis of the
moduli space has an elegant description in terms of quivers. As a by-product,
we present a systematic way of extracting the birational geometry of the
classical moduli spaces, thus generalizing previous work on resolution of
singularities by D-branes.Comment: 52 pages, 9 figure
Can an observer really catch up with light
Given a null geodesic with a point in
conjugate to along , there will be a variation of
which will give a time-like curve from to . This is
a well-known theory proved in the famous book\cite{2}. In the paper we prove
that the time-like curves coming from the above-mentioned variation have a
proper acceleration which approaches infinity as the time-like curve approaches
the null geodesic. This means no observer can be infinitesimally near the light
and begin at the same point with the light and finally catch the light. Only
separated from the light path finitely, does the observer can begin at the same
point with the light and finally catch the light.Comment: 6 pages, no figures, submited to Physical Review
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