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

Color Prompting for Data-Free Continual Unsupervised Domain Adaptive Person Re-Identification

Unsupervised domain adaptive person re-identification (Re-ID) methods alleviate the burden of data annotation through generating pseudo supervision messages. However, real-world Re-ID systems, with continuously accumulating data streams, simultaneously demand more robust adaptation and anti-forgetting capabilities. Methods based on image rehearsal addresses the forgetting issue with limited extra storage but carry the risk of privacy leakage. In this work, we propose a Color Prompting (CoP) method for data-free continual unsupervised domain adaptive person Re-ID. Specifically, we employ a light-weighted prompter network to fit the color distribution of the current task together with Re-ID training. Then for the incoming new tasks, the learned color distribution serves as color style transfer guidance to transfer the images into past styles. CoP achieves accurate color style recovery for past tasks with adequate data diversity, leading to superior anti-forgetting effects compared with image rehearsal methods. Moreover, CoP demonstrates strong generalization performance for fast adaptation into new domains, given only a small amount of unlabeled images. Extensive experiments demonstrate that after the continual training pipeline the proposed CoP achieves 6.7% and 8.1% average rank-1 improvements over the replay method on seen and unseen domains, respectively. The source code for this work is publicly available in https://github.com/vimar-gu/ColorPromptReID