Superconducting symmetry of three-dimensional tt-JJ model on simple cubic lattice

Motivated by the finding of nearly isotropic superconductivity in $\mathrm{(Ba,K)Fe_2As_2}$, we use renormalized mean field theory to investigated the $t$-$J$ model on three-dimensional simple cubic lattice. A tunable anisotropic parameter is introduced to dictate the coupling on $z$ 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 ${2/3}\pi$ phase shift to each other. However, when the interaction on $z$ 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 $X$ 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 $\cal{W}_{g,\gamma,\bf{d}}$ together with a $\mathbb{C}^*$ action is constructed. Applying virtual localization to their virtual classes $[\cal{W}_{g,\gamma,\bf{d}}]^{vir}$, 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 $[(\cal{W}_{g,\gamma,\bf{d}})^{\mathbb{C}^*}]^{vir}$. This vanishing verifies that in Witten's GLSM only $r$-spin invariants of insertions $2/5$ 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

O(αsv2){\mathcal O}(\alpha_s v^2) correction to J/ψJ/\psi plus ηc\eta_c production in e+e−e^+e^- annihilation at $\sqrt{s}=10.6GeV

Based on the nonrelativistic QCD factorization approach, ${\mathcal O}(\alpha_s v^2)$ corrections to \jpsi plus $\eta_c$ production in $e^+e^-$ annihilation at \sqrt{s}=10.6 \gev is calculated in this work. The numerical results show that the correction at $\alpha_s v^2$ 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 $Res\frac{\psi}{s}$ to virtual cases, namely cases when the zero loci of the section $s$ 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 33-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