4,585 research outputs found
Virasoro constraints and the Chern classes of the Hodge bundle
We analyse the consequences of the Virasoro conjecture of Eguchi, Hori and
Xiong for Gromov-Witten invariants, in the case of zero degree maps to the
manifolds CP^1 and CP^2 (or more generally, smooth projective curves and smooth
simply-connected projective surfaces). We obtain predictions involving
intersections of psi and lambda classes on the compactification of M_{g,n}. In
particular, we show that the Virasoro conjecture for CP^2 implies the numerical
part of Faber's conjecture on the tautological Chow ring of M_g.Comment: 12 pages, latex2
Study of tooling concepts for manufacturing operations in space Final report
Mechanical linkage device for manufacturing operations with orbital workshop
Computing top intersections in the tautological ring of
We derive effective recursion formulae of top intersections in the
tautological ring of the moduli space of curves of genus .
As an application, we prove a convolution-type tautological relation in
.Comment: 18 page
Is the energy density of the ground state of the sine-Gordon model unbounded from below for beta^2 > 8 pi ?
We discuss Coleman's theorem concerning the energy density of the ground
state of the sine-Gordon model proved in Phys. Rev. D 11, 2088 (1975).
According to this theorem the energy density of the ground state of the
sine-Gordon model should be unbounded from below for coupling constants beta^2
> 8 pi. The consequence of this theorem would be the non-existence of the
quantum ground state of the sine-Gordon model for beta^2 > 8 pi. We show that
the energy density of the ground state in the sine-Gordon model is bounded from
below even for beta^2 > 8 pi. This result is discussed in relation to Coleman's
theorem (Comm. Math. Phys. 31, 259 (1973)), particle mass spectra and
soliton-soliton scattering in the sine-Gordon model.Comment: 22 pages, Latex, no figures, revised according to the version
accepted for publication in Journal of Physics
Perturbative Chern-Simons Theory From The Penner Model
We show explicitly that the perturbative SU(N) Chern-Simons theory arises
naturally from two Penner models, with opposite coupling constants. As a result
computations in the perturbative Chern-Simons theory are carried out using the
Penner model, and it turns out to be simpler and transparent. It is also shown
that the connected correlators of the puncture operator in the Penner model,
are related to the connected correlators of the operator that gives the Wilson
loop operator in the conjugacy class.Comment: 7 Pages, Published Versio
Noncommutative resolutions of discriminants
We give an introduction to the McKay correspondence and its connection to
quotients of by finite reflection groups. This yields a natural
construction of noncommutative resolutions of the discriminants of these
reflection groups. This paper is an extended version of E.F.'s talk with the
same title delivered at the ICRA.Comment: 15 pages, 4 figures. Final version to appear in Contemporary
Mathematics 705, "Representations of Algebras
A McKay correspondence for reflection groups
We construct a noncommutative desingularization of the discriminant of a finite reflection group G as a quotient of the skew group ring A=S∗G. If G is generated by order 2 reflections, then this quotient identifies with the endomorphism ring of the reflection arrangement A(G) viewed as a module over the coordinate ring SG/(Δ) of the discriminant of G. This yields, in particular, a correspondence between the nontrivial irreducible representations of G to certain maximal Cohen–Macaulay modules over the coordinate ring SG/(Δ). These maximal Cohen–Macaulay modules are precisely the nonisomorphic direct summands of the coordinate ring of the reflection arrangement A(G) viewed as a module over SG/(Δ). We identify some of the corresponding matrix factorizations, namely, the so-called logarithmic (co-)residues of the discriminant
Directionally asymmetric self-assembly of cadmium sulfide nanotubes using porous alumina nanoreactors: Need for chemohydrodynamic instability at the nanoscale
We explore nanoscale hydrodynamical effects on synthesis and self-assembly of
cadmium sulfide nanotubes oriented along one direction. These nanotubes are
synthesized by horizontal capillary flow of two different chemical reagents
from opposite directions through nanochannels of porous anodic alumina which
are used primarily as nanoreactors. We show that uneven flow of different
chemical precursors is responsible for directionally asymmetric growth of these
nanotubes. On the basis of structural observations using scanning electron
microscopy, we argue that chemohydrodynamic convective interfacial instability
of multicomponent liquid-liquid reactive interface is necessary for sustained
nucleation of these CdS nanotubes at the edges of these porous nanochannels
over several hours. However, our estimates clearly suggest that classical
hydrodynamics cannot account for the occurrence of such instabilities at these
small length scales. Therefore, we present a case which necessitates further
investigation and understanding of chemohydrodynamic fluid flow through
nanoconfined channels in order to explain the occurrence of such interfacial
instabilities at nanometer length scales.Comment: 26 pages, 6 figures; http://www.iiserpune.ac.in/researchhighlight
Vibrational modes of circular free plates under tension
The vibrational frequencies of a plate under tension are given by the
eigenvalues of the equation . This
paper determines the eigenfunctions and eigenvalues of this bi-Laplace problem
on the ball under natural (free) boundary conditions. In particular, the
fundamental modes --- the eigenfunctions of the lowest nonzero eigenvalue ---
are identified and found to have simple angular dependence.Comment: 17 pages. To be submitted for publication shortly
Topological String Partition Functions as Polynomials
We investigate the structure of the higher genus topological string
amplitudes on the quintic hypersurface. It is shown that the partition
functions of the higher genus than one can be expressed as polynomials of five
generators. We also compute the explicit polynomial forms of the partition
functions for genus 2, 3, and 4. Moreover, some coefficients are written down
for all genus.Comment: 22 pages, 6 figures. v2:typos correcte
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