Symbol Invariant of Partition and the Construction

The symbol is used to describe the Springer correspondence for the classical groups. We propose equivalent definitions of symbols for rigid partitions in the $B_n$, $C_n$, and $D_n$ theories uniformly. Analysing the new definition of symbol in detail, we give rules to construct symbol of a partition, which are easy to remember and to operate on. We introduce formal operations of a partition, which reduce the difficulties in the proof of the construction rules. According these rules, we give a closed formula of symbols for different theories uniformly. As applications, previous results can be illustrated more clearly by the construction rules of symbol.Comment: 31 pages,typo corrected,english improve

Rigid Surface Operators and Symbol Invariant of Partitions

The symbol is used to describe the Springer correspondence for the classical groups by Lusztig. We refine the explanation that the $S$ duality maps of the rigid surface operators are symbol preserving maps. We find that the maps $X_S$ and $Y_S$ are essentially the same. We clear up cause of the mismatch problem of the total number of the rigid surface operators between the $B_n$ and $C_n$ theories. We construct all the $B_n/C_n$ rigid surface operators which can not have a dual. A classification of the problematic surface operators is made.Comment: 23 pages, 26 figures,typo corrected, english improve

Singularities of non-Q\mathbb{Q}-Gorenstein varieties admitting a polarized endomorphism

In this paper, we discuss a generalization of log canonical singularities in the non-$\mathbb{Q}$-Gorenstein setting. We prove that if a normal complex projective variety has a non-invertible polarized endomorphism, then it has log canonical singularities in our sense. As a corollary, we give an affirmative answer to a conjecture of Broustet and H\"{o}ring.Comment: 21 pages. This paper is revised about the following points that the assumption in Theorem 1.6 is removed, and Theorem 6.7, Definition 6.8 and Theorem 6.9 are added. Furthermore Section 7 is also added in version

Invariants of partitions

The symbol invariant is used to describe the Springer correspondence for the classical groups by Lusztig. And the fingerprint invariant can be used to describe the Kazhdan-Lusztig map. They are invariants of rigid semisimple operators labeled by pairs of partitions $(\lambda^{'}, \lambda^{"})$. It is conjectured that the symbol invariant is equivalent to the fingerprint invariant. We prove that the former imply the latter one. We make a classification of the maps preserving symbol, and then prove these maps preserve fingerprint. We also discuss the classification of the maps preserving fingerprint, which is found related to the conditions of the definition of the fingerprint. The constructions of the symbol and the fingerprint invariants in previous works play significant roles in the proof.Comment: 30 pages, 60 figures. arXiv admin note: text overlap with arXiv:1711.0988

Complete next-to-leading order QCD corrections to charged Higgs boson associated production with top quark at the CERN Large Hadron Collider

The complete next-to-leading order (NLO) QCD corrections to charged Higgs boson associated production with top quark through $b g \to tH^{-}$ at the CERN Large Hadron Collider are calculated in the minimal supersymmetric standard model (MSSM) and two-Higgs-doublet model in the $\bar{MS}$ scheme. The NLO QCD corrections can reduce the scale dependence of the leading order (LO) cross section. The K-factor (defined as the ratio of the NLO cross section to the LO one) does not depend on $\tan\beta$ if the same quark running masses are used in the NLO and LO cross sections, and varies roughly from $\sim 1.6$ to $\sim 1.8$ when charged Higgs boson mass increases from 200 GeV to 1000 GeV.Comment: 31 pages, discussions, figs and refs added, conclusion unchanged, final PRD versio

Dark Matter Signature from the Sky and at Colliders

In this talk, we briefly review our recent investigations on the properties of dark matter (DM) particle.Comment: 4 pages, talk at ICHEP201

Inferring dissipation from the violation of Fluctuation-Dissipation Theorem

The Harada-Sasa equality elegantly connects the energy dissipation rate of a moving object with its measurable violation of the Fluctuation-Dissipation Theorem (FDT). Although proven for Langevin processes, its validity remains unclear for discrete Markov systems whose forward and backward transition rates respond asymmetrically to external perturbation. A typical example is a motor protein called kinesin. Here we show generally that the FDT violation persists surprisingly in the high-frequency limit due to the asymmetry, resulting in a divergent FDT violation integral and thus a complete breakdown of the Harada-Sasa equality. A renormalized FDT violation integral still well predicts the dissipation rate when each discrete transition produces a small entropy in the environment. Our study also suggests a new way to infer this perturbation asymmetry based on the measurable high-frequency-limit FDT violation.Comment: 10 pages, 4 figure

Exact microscopic wave function for a topological quantum membrane

The higher dimensional quantum Hall liquid constructed recently supports stable topological membrane excitations. Here we introduce a microscopic interacting Hamiltonian and present its exact ground state wave function. We show that this microscopic ground state wave function describes a topological quantum membrane. We also construct variational wave functions for excited states using the non-commutative algebra on the four sphere. Our approach introduces a non-perturbative method to quantize topological membranes

SO(5) Quantum Nonlinear sigma Model Theory of the High Tc Superconductivity

We show that the complex phase diagram of high $T_c$ superconductors can be deduced from a simple symmetry principle, a $SO(5)$ symmetry which unifies antiferromagnetism with $d$ wave superconductivity. We derive the approximate $SO(5)$ symmetry from the microscopic Hamiltonian and show furthermore that this symmetry becomes exact under the renormalization group flow towards a bicritical point. With the help of this symmetry, we construct a $SO(5)$ quantum nonlinear $\sigma$ model to describe the effective low energy degrees of freedom of the high $T_c$ superconductors, and use it to deduce the phase diagram and the nature of the low lying collective excitations of the system. We argue that this model naturally explains the basic phenomenology of the high $T_c$ superconductors from the insulating to the underdoped and the optimally doped region.Comment: 36 pages, 1 Postscript figur

W−→τνˉτW^- \to \tau \bar \nu_\tau 3-sigma anomaly in new physics beyond the standard model

Among so-called three 3-sigma anomalies in high energy physics, the excess of the branching ratio $W^- \to \tau \bar \nu_\tau$ with respect to the electrons and muons is especially interesting because (1) in the standard model (SM), $W^-\ell\bar \nu_\ell$ is the pure left-handed charge-current which has been tested precisely already, at least for the first two generation fermions, and (2) the $W^\pm$ two-body leptonic decay is the cleanest one among three anomalies due to its simpler kinematics and less hadronic uncertainties. In this paper, we explore the possibilities to account for the anomaly in type II two-Higgs-doublet model (2HDM) and minimal supersymmetric model (MSSM), as well as effective lagrangian approach by introducing anomalous left- and right-handed $W^-\tau \bar\nu_\tau$ couplings. Our results show that 2HDM and MSSM can hardly accommodate $W^- \to \tau \nu_\tau$ anomaly, and the anomaly is only marginally consistent to the measurements of $\tau \to \nu_\tau \ell \bar \nu_\ell$ at 95% confidence level with the presence of anomalous couplings. In the allowed regions, the right-handed coupling of $W^-\tau \nu_\tau$ shifts from 0 in SM to $\sim 0.12$ while the left-handed one from 1 to $\sim 1.005$.Comment: 9 page