3,426 research outputs found
Superconducting symmetry of three-dimensional - model on simple cubic lattice
Motivated by the finding of nearly isotropic superconductivity in
, we use renormalized mean field theory to
investigated the - model on three-dimensional simple cubic lattice. A
tunable anisotropic parameter is introduced to dictate the coupling on
direction. The symmetry of the superconducting order is studied in detail.
Calculation shows that for the isotropic case, pairing parameters on the three
perpendicular directions have phase shift to each other. However,
when the interaction on direction is suppressed, the corresponding
amplitude of the pairing parameter decreases rapidly, furthermore,
two-dimensional d-wave state pairing is favored when the anisotropic rate less
than 0.75.Comment: 4 pages, 4 figure
Semi-Perfect Obstruction theory and DT Invariants of Derived Objects
We introduce semi-perfect obstruction theory of a Deligne-Mumford stack
consisting of local perfect obstruction theories with weak comparisons on
overlaps. We show that semi-perfect obstruction theory shares similar
properties with perfect obstruction theory. We use semi-perfect obstruction
theory to construct virtual cycles of moduli of derived objects on Calabi-Yau
threefolds.
In the revision, we assume the existence of obstruction sheaf and put the
(coarse moduli of the) intrinsic normal cone inside the obstruction sheaf. This
avoids the issue of descent of bundle stacks of the local obstruction
complexes.Comment: 18 page
A vanishing associated with irregular MSP fields
In previous work, Mixed-Spin-P field has been introduced and their moduli
space together with a action is
constructed. Applying virtual localization to their virtual classes
, polynomial relations among GW and FJRW
invariants of Fermat quintics are derived.
In this paper, we prove a vanishing of a class of terms in
. This vanishing verifies
that in Witten's GLSM only -spin invariants of insertions contribute
to the phase transition between GW and FJRW invariants of Fermat quintics.Comment: 35page
Invariants of stable quasimaps with fields
For an arbitrary smooth hypersurface X in a projective space, we construct
its LG moduli of quasimaps with P fields. Apply Kiem-Li's cosection
localization we obtain a virtual fundamental class. We show the class
coincides, up to sign, with that of moduli of quasimaps to X. This generalizes
Chang-Li's numerical identity to the cycle level, and from Gromov Witten
invariants to quasimap invariants
Canonical Entropy of charged black hole
Recently, Hawking radiation of the black hole has been studied by using the
tunnel effect method. It is found that the radiation spectrum of the black hole
is not a strictly pure thermal spectrum. How does the departure from pure
thermal spectrum affect the entropy? This is a very interesting problem. In
this paper, we calculate the partition function through energy spectrum
obtained by using the tunnel effect. From the relation between the partition
function and canonical entropy, we can derive the entropy of charged black
hole. In our calculation, we consider not only the correction to the black hole
entropy due to fluctuation of energy, but also the effect of the change in the
black hole charges on entropy. There is not any assumption. This makes our
result more reliable.Comment: 9 page
correction to plus production in annihilation at $\sqrt{s}=10.6GeV
Based on the nonrelativistic QCD factorization approach, corrections to \jpsi plus production in
annihilation at \sqrt{s}=10.6 \gev is calculated in this work. The numerical
results show that the correction at order is only about a few
percent for the total theoretical result. It indicates that the perturbative
expansions for the theoretical prediction become convergence and higher order
correction will be smaller. The uncertainties from the long-distance matrix
elements, renormalization scale and the measurement in experiment are also
discussed. Our result is in agreement with previous result in ref [1]
Virtual Residue and an integral formalism
We generalize Grothendieck's residues to virtual cases,
namely cases when the zero loci of the section has dimension larger than
the expected dimension(zero). We also provide an exponential type integral
formalism for the virtual residue, which can be viewed as an analogue of the
Mathai-Quillen formalism for localized Euler classes
The theory of N-Mixed-Spin-P fields
This is the first part of the project toward proving the BCOV's Feymann graph
sum formula of all genera Gromov-Witten invariants of quintic Calabi-Yau
threefolds. In this paper, we introduce the notion of N-Mixed-Spin-P fields,
construct their moduli spaces, their virtual cycles, their virtual localization
formulas, and a vanishing result associated with irregular graphs
BCOV's Feynman rule of quintic -folds
We prove the BCOV Feynman rule by identifying the Feynman graph sum to the
graph sum of an R-matrix action extracted from the NMSP theory. As direct
consequences, (i) we obtain the genus one and genus two potentials, and (ii) we
prove the two Yamaguchi-Yau equations.Comment: We add to the original version (i) a full argument obtaining the
genus two potential, (ii) a short proof that BCOV Feynman rules imply
Yamaguchi-Yau equations, and (iii) explicit formulae for R-matrices in
appendix. All supplementary material, and additional information related to
the NMSP theory, are available at https://sites.google.com/site/guoshuaimath
Torus localization and wall crossing for cosection localized virtual cycles
Since its introduction in 1995 by Li-Tian and Behrend-Fantechi, the theory of
virtual fundamental class has played a key role in algebraic geometry, defining
important invariants such as the Gromov-Witten invariant and the
Donaldson-Thomas invariant. Quite a few methods for handling the virtual
fundamental classes were discovered such as torus localization, degeneration,
virtual pullback and cosection localization. Often combining these methods
turns out to be quite effective. In this paper, we prove virtual pullback,
torus localization and wall crossing formulas for cosection localized virtual
cycles.Comment: 18 page
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