تقرير
Quantum K theory of Grassmannians, Wilson line operators, and Schur bundles
| العنوان: | Quantum K theory of Grassmannians, Wilson line operators, and Schur bundles |
|---|---|
| المؤلفون: | Gu, Wei, Mihalcea, Leonardo C., Sharpe, Eric, Zou, Hao |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics High Energy Physics - Theory |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, High Energy Physics - Theory, Mathematics - Combinatorics, Primary 14M15, 14N35, 81T60, Secondary 05E05 |
| الوصف: | 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 arise 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 pages; v2: rewrote Appendix A by utilizing the hypothesis that R is complete in the I-adic topology. This corrects a missing hypothesis in the Appendix from v1 of the paper. Fixed several minor typos |
| نوع الوثيقة: | Working Paper |
| الوصول الحر: | http://arxiv.org/abs/2208.01091Test |
| رقم الانضمام: | edsarx.2208.01091 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |