Supersymmetric Localization in GLSMs for Supermanifolds

In this paper we apply supersymmetric localization to study gauged linear sigma models (GLSMs) describing supermanifold target spaces. We use the localization method to show that A-twisted GLSM correlation functions for certain supermanifolds are equivalent to A-twisted GLSM correlation functions for hypersurfaces in ordinary spaces under certain conditions. We also argue that physical two-sphere partition functions are the same for these two types of target spaces. Therefore, we reproduce the claim of arXiv:hep-th/9404186, arXiv:hep-th/9506070. Furthermore, we explore elliptic genera and (0,2) deformations and find similar phenomena.Comment: 31 pages, no figure

Quantum K theory of Grassmannians, Wilson line operators, and Schur bundles

We prove a `Whitney' presentation, and a `Coulomb branch' presentation, for the torus equivariant quantum K theory of the Grassmann manifold $\mathrm{Gr}(k;n)$, inspired from physics, and stated in an earlier paper. The first presentation is obtained by quantum deforming the product of the Hirzebruch $\lambda_y$ classes of the tautological bundles. In physics, the $\lambda_y$ classes appeared as certain Wilson line operators. The second presentation is obtained from the Coulomb branch equations involving the partial derivatives of a twisted superpotential from supersymmetric gauge theory. This is closest to a presentation obtained by Gorbounov and Korff, utilizing integrable systems techniques. Algebraically, we relate the Coulomb and Whitney presentations utilizing transition matrices from the (equivariant) Grothendieck polynomials to the (equivariant) complete homogeneous symmetric polynomials. The calculations of K-theoretic Gromov-Witten invariants of wedge powers of the tautological subbundles on the Grassmannian utilize the `quantum=classical' statement.Comment: 39 page

Quantum K Whitney relations for partial flag varieties

In a recent paper, we stated conjectural presentations for the equivariant quantum K ring of partial flag varieties, motivated by physics considerations. In this companion paper, we analyze these presentations mathematically. We prove that if the conjectured relations hold, then they must form a complete set of relations. Our main result is a proof of the conjectured presentation in the case of the incidence varieties. We also show that if a quantum K divisor axiom holds (as conjectured by Buch and Mihalcea), then the conjectured presentation also holds for the complete flag variety.Comment: 25 pages; revised Remark 5.9 and added Example 5.1

One-off and Repeating Fast Radio Bursts: A Statistical Analysis

According to the number of detected bursts, fast radio bursts (FRBs) can be classified into two categories, i.e., one-off FRBs and repeating ones. We make a statistical comparison of these two categories based on the first FRB catalog of the Canadian Hydrogen Intensity Mapping Experiment Fast Radio Burst Project. Using the Anderson-Darling, Kolmogrov-Smirnov, and Energy statistic tests, we find significant statistical differences ($p$-value $<$ 0.001) of the burst properties between the one-off FRBs and the repeating ones. More specifically, after controlling for distance, we find that the peak luminosities of one-off FRBs are, on average, higher than the repeating ones; the pulse temporal widths of repeating FRBs are, on average, longer than the one-off ones. The differences indicate that these two categories could have distinct physical origins. Moreover, we discuss the sub-populations of FRBs and provide statistical evidence to support the existence of sub-populations in one-off FRBs and in repeating ones.Comment: 10 pages, 6 figures, accepted for publication in Ap

Research on sound radiation characteristics of the high-speed train wheel

Taking the standard wheel model as an example, the radiation noise of a single wheel under excitation force which is computed by multi-body dynamics model is computed by acoustic boundary element method (BEM). Then, the damped wheel is proposed, and the sound radiation characteristics of both wheels are analyzed and compared. The results show that sound field of a single wheel presents an obvious directivity with petaloid change and continuous decrease, and the wheel tread and web contribute the most rolling noise. Compared with the standard wheel, the acoustic radiation power of the damped wheel decreased significantly, especially at the peak frequency. After that, the radiation noise generated by the wheel in the train is researched. The results show that the radiation noise generated by the wheel in the train is a complex sound field after the superposition and interference of multiple wheel noises, which are mainly in the bogies at both ends and its vicinity region. Meanwhile, the basic directivity characteristics of the petaloid change and continuous reduction are remained. The radiation noise which is generated by the wheel in the train has obvious peak characteristic, whose corresponding peak noises are below 110 dB. The radiation noise of the damped wheel is significantly smaller than that of the standard wheel at most frequency bands, and the total SPL at the observation point has decreased by 14.5 dB with obvious noise reduction effect. In order to further research the radiation noise of the damping wheel, influence factors on the noise reduction are analyzed. Finally, these parameters such as thickness and material should be considered comprehensively during designing the damping wheel, in order to find the optimal combination of all parameters