arXiv subjects

L. Mihalcea

Publications and source records attributed to L. Mihalcea.

4 recordsLinked to original sources

arXiv2025

Quantum K-theory levels in physics and math

The purpose of this paper is to describe a dictionary between Chern-Simons levels in three-dimensional gauged linear sigma models (GLSMs) and twistings of quantum K-theory in mathematics, including as special cases the (coincidentally-named) Ruan-Zhang levels. Each defines a twisting of quantum K-theory, and our proposed dictionary identifies these two twistings, in the cases of projective spaces, smooth Fano toric varieties, Grassmannians, and flag manifolds. We verify the dictionary by realizing the Coulomb branch equations as symbols of certain difference operators annihilating a twisted version of the I function associated to the abelianized GLSM theory, and also by comparing the geometric window for Chern-Simons levels to an analogous window in mathematics. In the process, we interpret the geometric window for the Chern-Simons levels in terms of equalities of I and J functions. This provides a fuller mathematical understanding of some special cases in the physics literature. We also make conjectures for twisted quantum K-theory of gerbes, following up earlier conjectures on ordinary quantum K-theory of gerbes.

hep-th↗

arXiv2025

Schubert defects in Lagrangian Grassmannians

In this paper, we propose a construction of GLSM defects corresponding to Schubert cycles in Lagrangian Grassmannians, following recent work of Closset-Khlaif on Schubert cycles in ordinary Grassmannians. In the case of Lagrangian Grassmannians, there are superpotential terms in both the bulk GLSM as well as on the defect itself, enforcing isotropy constraints. We check our construction by comparing the locus on which the GLSM defect is supported to mathematical descriptions, checking dimensions, and perhaps most importantly, comparing defect indices to known and expected polynomial invariants of the Schubert cycles in quantum cohomology and quantum K theory.

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arXiv2023

Quantum K theory rings of partial flag manifolds

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.

hep-th↗

arXiv2023

Quantum K theory of symplectic Grassmannians

In this paper we discuss physical derivations of the quantum K theory rings of symplectic Grassmannians. We compare to standard presentations in terms of Schubert cycles, but most of our work revolves around a proposed description in terms of two other bases, involving shifted Wilson lines and lambda_y classes, which are motivated by and amenable to physics, and which we also provide for ordinary Grassmannians.

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