Logarithmic tensor category theory, VIII: Braided tensor category structure on categories of generalized modules for a conformal vertex algebra

This is the eighth part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part VIII), we construct the braided tensor category structure, using the previously developed results.Comment: Part VIII of a series of 8 papers generalizing the results in and collectively replacing arXiv:0710:2687, with new titles. 36 pages. Minor change

Logarithmic tensor product theory for generalized modules for a conformal vertex algebra, Part I

We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ``conformal vertex algebra'' or even more generally, for a "M\"obius vertex algebra.'' We do not require the module categories to be semisimple, and we accommodate modules with generalized weight spaces. As in the earlier series of papers, our tensor product functors depend on a complex variable, but in the present generality, the logarithm of the complex variable is involved. This first part is devoted to the study of logarithmic intertwining operators and their role in the construction of the tensor product functors. Part II of this work will be devoted to the construction of the appropriate natural associativity isomorphisms between triple tensor product functors, to the proof of their fundamental properties, and to the construction of the resulting braided tensor category structure. This work includes the complete proofs in the present generality and can be read independently of the earlier series of papers.Comment: 205 page

Logarithmic tensor category theory, III: Intertwining maps and tensor product bifunctors

This is the third part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part III), we introduce and study intertwining maps and tensor product bifunctors.Comment: Part III of a series of 8 papers generalizing the results in and collectively replacing arXiv:0710:2687, with new titles. 38 pages. Right exactness result added; minor change

Logarithmic tensor product theory for generalized modules for a conformal vertex algebra

We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ''conformal vertex algebra'' or even more generally, for a "M\"obius vertex algebra.'' We do not require the module categories to be semisimple, and we accommodate modules with generalized weight spaces. As in the earlier series of papers, our tensor product functors depend on a complex variable, but in the present generality, the logarithm of the complex variable is required; the general representation theory of vertex operator algebras requires logarithmic structure. The first part of this work is devoted to the study of logarithmic intertwining operators and their role in the construction of the tensor product functors. The remainder of this work is devoted to the construction of the appropriate natural associativity isomorphisms between triple tensor product functors, to the proof of their fundamental properties, and to the construction of the resulting braided tensor category structure. This work includes the complete proofs in the present generality and can be read independently of the earlier series of papers.Comment: 319 pages. Material added and minor change

Logarithmic tensor category theory, IV: Constructions of tensor product bifunctors and the compatibility conditions

This is the fourth part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part IV), we give constructions of the P(z)- and Q(z)-tensor product bifunctors using what we call "compatibility conditions" and certain other conditions.Comment: Part IV of a series of 8 papers generalizing the results in and collectively replacing arXiv:0710:2687, with new titles. 94 pages. Minor change

Role of the orbital degree of freedom in iron-based superconductors

Almost a decade has passed since the serendipitous discovery of the iron-based high temperature superconductors (FeSCs) in 2008. The question of how much similarity the FeSCs have with the copper oxide high temperature superconductors emerged since the initial discovery of long-range antiferromagnetism in the FeSCs in proximity to superconductivity. Despite the great resemblance in their phase diagrams, there exist important disparities between FeSCs and cuprates that need to be considered in order to paint a full picture of these two families of high temperature superconductors. One of the key differences lies in the multi-orbital multi-band nature of FeSCs, in contrast to the effective single-band model for cuprates. Due to the complexity of multi-orbital band structures, the orbital degree of freedom is often neglected in formulating the theoretical models for FeSCs. On the experimental side, systematic studies of the orbital related phenomena in FeSCs have been largely lacking. In this review, we summarize angle-resolved photoemission spectroscopy (ARPES) measurements across various FeSC families in literature, focusing on the systematic trend of orbital dependent electron correlations and the role of different Fe 3d orbitals in driving the nematic transition, the spin-density-wave transition, and implications for superconductivity.Comment: final published versio

On the concepts of intertwining operator and tensor product module in vertex operator algebra theory

We produce counterexamples to show that in the definition of the notion of intertwining operator for modules for a vertex operator algebra, the commutator formula cannot in general be used as a replacement axiom for the Jacobi identity. We further give a sufficient condition for the commutator formula to imply the Jacobi identity in this definition. Using these results we illuminate the crucial role of the condition called the ``compatibility condition'' in the construction of the tensor product module in vertex operator algebra theory, as carried out in work of Huang and Lepowsky. In particular, we prove by means of suitable counterexamples that the compatibility condition was indeed needed in this theory.Comment: 30 page

Detection of a Majorana-fermion zero mode by a T-shaped quantum-dot structure

Electron transport through the T-shaped quantum-dot (QD) structure is theoretically investigated, by considering a Majorana zero mode coupled to the terminal QD. It is found that in the double-QD case, the presence of the Majorana zero mode can efficiently dissolve the antiresonance point in the conductance spectrum and induce a conductance peak to appear at the same energy position whose value is equal to $e^2/2h$. This antiresonance-resonance change will be suitable to detect the Majorana bound states. Next in the multi-QD case, we observe that in the zero-bias limit, the conductances are always the same as the double-QD result, independent of the parity of the QD number. We believe that all these results can be helpful for understanding the properties of Majorana bound states

An X-ray periodicity of ∼\sim1.8 hours in a narrow-line Seyfert 1 galaxy Mrk 766

In the narrow-line Seyfert 1 galaxy Mrk 766, a Quasi-Periodic Oscillation (QPO) signal with a period of $\sim6450$ s is detected in the \emph{XMM-Newton} data collected on 2005 May 31. This QPO signal is highly statistical significant at the confidence level at $\sim5\sigma$ with the quality factor of $Q=f/\Delta f>13.6$. The X-ray intensity changed by a factor of 3 with root mean square fractional variability of $14.3\%$. Furthermore, this QPO signal presents in the data of all three EPIC detectors and two RGS cameras and its frequency follows the $f_{\rm QPO}$-$M_{\rm BH}$ relation spanning from stellar-mass to supermassive black holes. Interestingly, a possible QPO signal with a period of $\sim4200$ s had been reported in the literature. The frequency ratio of these two QPO signals is $\sim$ 3:2. Our result is also in support of the hypothesis that the QPO signals can be just transient. The spectral analysis reveals that the contribution of the soft excess component below $\sim$ 1 keV is different between epochs with and without QPO, this property as well as the former frequency-ratio are well detected in X-ray BH binaries, which may have shed some lights on the physical origin of our event.Comment: 7 pages, 5 figures, 1 table. Accepted for publication in Ap

WRFRFT-based Coherent Detection and Parameter Estimation of Radar Moving Target With Unknown Entry/Departure Time

A moving target may enter a radar coverage area unannounced and leave after an unspecified period, which implies that the target's entry time and departure time are unknown. In the absence of these time information, target detection and parameter estimation (DAPE) will be severely impacted. In this paper, we consider the coherent detection and parameters estimation problem for a radar moving target with unknown entry time and departure time (that is, the time when the target appears-in/leaves the radar detection field is unknown), involving across range cell (ARC) and Doppler spread (DS) effects within the observation period. A new algorithm, known as window Radon Fractional Fourier transform (WRFRFT) is proposed to detect and estimate the target's time parameters (i.e., entry time and departure time) and motion parameters (i.e., range, velocity and acceleration). The observation values of a maneuvering target are first intercepted and extracted by the window function and searching along the motion trajectory. Then these values are fractional Fourier transformed and well accumulated in the WRFRFT domain, where the DAPE of target could be accomplished thereafter. Experiments with simulated and real radar data sets prove its effectiveness.Comment: 30 pages, 10 figure