Eric Sharpe
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View article: A Nakayama result for the quantum K theory of homogeneous spaces
A Nakayama result for the quantum K theory of homogeneous spaces Open
We prove that the ideal of relations in the (equivariant) quantum K ring of a homogeneous space is generated by quantizations of each of the generators of the ideal in the classical (equivariant) K ring. This extends to quantum K theory a …
View article: Quantum K-theory levels in physics and math
Quantum K-theory levels in physics and math Open
The purpose of this paper is to describe the basics of a dictionary between Chern-Simons levels in three-dimensional gauged linear sigma models (GLSMs) and the (coincidentally-named) Ruan-Zhang levels for twisted quantum K-theory in mathem…
View article: Schubert defects in Lagrangian Grassmannians
Schubert defects in Lagrangian Grassmannians Open
A bstract 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 Lagrangia…
View article: Notes on gauging noninvertible symmetries. Part II. Higher multiplicity cases
Notes on gauging noninvertible symmetries. Part II. Higher multiplicity cases Open
A bstract In this paper we discuss gauging noninvertible zero-form symmetries in two dimensions, extending our previous work. Specifically, in this work we discuss more general gauged noninvertible symmetries in which the noninvertible sym…
View article: Anomaly resolution by non-invertible symmetries
Anomaly resolution by non-invertible symmetries Open
In this paper we generalize previous results on anomaly resolution to noninvertible symmetries. Briefly, given a global symmetry G of some theory with a 't Hooft anomaly rendering it ungaugeable, the idea of anomaly resolution is to extend…
View article: Quantum K theory of Grassmannians, Wilson line operators and Schur bundles
Quantum K theory of Grassmannians, Wilson line operators and Schur bundles Open
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 presentatio…
View article: An overview of Bagger-Witten line bundles
An overview of Bagger-Witten line bundles Open
We give a brief overview of recent progress in understanding Bagger-Witten line bundles, which are bundles over moduli spaces of two-dimensional N=2 SCFTs whose existence is a consequence of the global U(1)_R symmetry of the theories. Our …
View article: Dilaton shifts, probability measures, and decomposition
Dilaton shifts, probability measures, and decomposition Open
In this paper we discuss dilaton shifts (Euler counterterms) arising in decomposition of two-dimensional quantum field theories with higher-form symmetries. Relative shifts between universes are fixed by locality and take a universal form,…
View article: Notes on gauging noninvertible symmetries, part 2: higher multiplicity cases
Notes on gauging noninvertible symmetries, part 2: higher multiplicity cases Open
In this paper we discuss gauging noninvertible zero-form symmetries in two dimensions, extending our previous work. Specifically, in this work we discuss more general gauged noninvertible symmetries in which the noninvertible symmetry is n…
View article: Chern-Simons theory, decomposition, and the A model
Chern-Simons theory, decomposition, and the A model Open
In this paper, we discuss how gauging one-form symmetries in Chern-Simons theories is implemented in an A-twisted topological open string theory. For example, the contribution from a fixed H/Z bundle on a three-manifold M, arising in a BZ …
View article: Decomposition squared
Decomposition squared Open
In this paper, we test and extend a proposal of Gu, Pei, and Zhang for an application of decomposition to three-dimensional theories with one-form symmetries and to quantum K theory. The theories themselves do not decompose, but, OPEs of p…
View article: Notes on gauging noninvertible symmetries. Part I. Multiplicity-free cases
Notes on gauging noninvertible symmetries. Part I. Multiplicity-free cases Open
A bstract In this paper we discuss gauging noninvertible zero-form symmetries in two dimensions. We specialize to certain gaugeable cases, specifically, fusion categories of the form $$ \textrm{Rep}\left(\mathcal{H}\right) $$ for $$ \m…
View article: Quantum cohomology from mixed Higgs-Coulomb phases
Quantum cohomology from mixed Higgs-Coulomb phases Open
A bstract We generalize Coulomb-branch-based gauged linear sigma model (GLSM)–computations of quantum cohomology rings of Fano spaces. Typically such computations have focused on GLSMs without superpotential, for which the low energy limit…
View article: A survey of recent developments in GLSMs
A survey of recent developments in GLSMs Open
In this article we briefly survey some developments in gauged linear sigma models (GLSMs). Specifically, we give an overview of progress on constructions of GLSMs for various geometries, GLSM-based computations of quantum cohomology, quant…
View article: Dilaton shifts, probability measures, and decomposition
Dilaton shifts, probability measures, and decomposition Open
In this paper we discuss dilaton shifts (Euler counterterms) arising in decomposition of two-dimensional quantum field theories with higher-form symmetries. These take a universal form, reflecting underlying (noninvertible, quantum) symmet…
View article: Notes on gauging noninvertible symmetries, part 1: Multiplicity-free cases
Notes on gauging noninvertible symmetries, part 1: Multiplicity-free cases Open
In this paper we discuss gauging noninvertible zero-form symmetries in two dimensions. We specialize to certain gaugeable cases, specifically, fusion categories of the form Rep(H) for H a suitable Hopf algebra (which includes the special c…
View article: Quantum K Whitney relations for partial flag varieties
Quantum K Whitney relations for partial flag varieties Open
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 start by p…
View article: Quantum cohomology from mixed Higgs-Coulomb branches
Quantum cohomology from mixed Higgs-Coulomb branches Open
We generalize Coulomb-branch-based gauged linear sigma model (GLSM)-based computations of quantum cohomology rings of Fano spaces. Typically such computations have focused on GLSMs without superpotential, for which the IR phase of the GLSM…
View article: Decomposition and the Gross-Taylor string theory
Decomposition and the Gross-Taylor string theory Open
It was recently argued by Nguyen-Tanizaki-Unsal that two-dimensional pure Yang-Mills theory is equivalent to (decomposes into) a disjoint union of (invertible) quantum field theories, known as universes. In this paper we compare this decom…
View article: Quantum K theory rings of partial flag manifolds
Quantum K theory rings of partial flag manifolds Open
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 …
View article: Decomposition, trivially-acting symmetries, and topological operators
Decomposition, trivially-acting symmetries, and topological operators Open
Trivially-acting symmetries in two-dimensional conformal field theory include twist fields of dimension zero which are local topological operators. We investigate the consequences of regarding these operators as part of the global symmetry…
View article: Three-dimensional orbifolds by 2-groups
Three-dimensional orbifolds by 2-groups Open
In this paper we generalize previous work on decomposition in three-dimensional orbifolds by 2-groups realized as analogues of central extensions, to orbifolds by more general 2-groups. We describe the computation of such orbifolds in phys…
View article: Topological Strings on Non-Commutative Resolutions
Topological Strings on Non-Commutative Resolutions Open
In this paper we propose a definition of torsion refined Gopakumar-Vafa (GV) invariants for Calabi-Yau threefolds with terminal nodal singularities that do not admit Kähler crepant resolutions. Physically, the refinement takes into account…