Quantum K theory rings of partial flag manifolds
W. Gu, L. Mihalcea, E. Sharpe, W. Xu, H. Zhang, H. Zou
TL;DR
This paper uses 3D gauged linear sigma models to predict the structure of equivariant quantum K theory rings of partial flag manifolds, extending previous work on Grassmannians and linking to Wilson line OPEs.
Contribution
It introduces a physical approach to compute quantum K theory rings of partial flag manifolds, generalizing prior results for Grassmannians and providing a simplified Chern-Simons level computation method.
Findings
Predictions for quantum K theory ring structures of partial flag manifolds.
Extension of previous Grassmannian results to more general flag varieties.
A simplified method for computing relevant Chern-Simons levels.
Abstract
In this paper we use three-dimensional gauged linear sigma models to make physical predictions for Whitney-type presentations of equivariant quantum K theory rings of partial flag manifolds, as quantum products of universal subbundles and various ratios, extending previous work for Grassmannians. Physically, these arise as OPEs of Wilson lines for certain Chern-Simons levels. We also include a simplified method for computing Chern-Simons levels pertinent to standard quantum K theory.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology