Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 35 min ago
PreprintCC BY 4.0arXiv

Quasimap critical cohomology, Coulomb branches, and quantum groups

  • Tommaso Maria Botta
  • Spencer Tamagni
Open at sourcePDFDOICite

Abstract

This article presents a systematic study of the critical cohomology of QMξ(bbP1, X), the moduli space of based quasimaps from bbP1 to a Nakajima quiver variety X. We develop two derived equivalent presentations of this moduli space as a global critical locus. Accordingly, we obtain two equivalent explicit realizations of the canonical DT sheaf of the moduli space. Using each critical presentation, we describe canonical actions of shifted Yangians and quantized Coulomb branches on the quasimap critical cohomologies. We produce, by geometric means, a canonical morphism from an appropriate Hall algebra to the Coulomb branch, and show that the two actions we describe are compatible via this morphism under an additional hypothesis. We conjecture the compatibility holds generally, and reduce the claim to a sheaf-theoretic statement that may be approached via Joyce conjecture.

Related

  1. Quivers with Involutions and Shifted affine iQuantum groups via Coulomb Branches
    Yaolong Shen, Changjian Su, Zichang Wang +1
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Quivers with Involutions and Shifted Twisted Yangians via Coulomb Branches
    Yaolong Shen, Changjian Su, Rui Xiong
    Communications in Mathematical PhysicsPeer-reviewedLicence not statedFull text14 citedGeometry & topologyOpenAlex
  3. A1 - Coulomb branches over finite fields and Selberg Character sums
    Junzhe Lyu, Andrey Smirnov
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryMathematical physicsarXiv
  4. Duality functors for Coulomb branches I
    Sabin Cautis, Eric Vasserot
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. Categorified Cluster Structures on Coulomb Branches of Certain Star-Shaped Quivers
    Tianle Liu
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{botta2026quasimap,
  title = {{Quasimap critical cohomology, Coulomb branches, and quantum groups}},
  author = {Tommaso Maria Botta and Spencer Tamagni},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.29400},
  eprint = {2608.29400},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29400},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Quasimap critical cohomology, Coulomb branches, and quantum groups
AU  - Tommaso Maria Botta
AU  - Spencer Tamagni
PY  - 2026
DA  - 2026/08/29
PB  - arXiv
DO  - 10.48550/arxiv.2608.29400
UR  - https://arxiv.org/abs/2608.29400
AB  - This article presents a systematic study of the critical cohomology of QM^ξ(bbP^1, X), the moduli space of based quasimaps from bbP^1 to a Nakajima quiver variety X. We develop two derived equivalent presentations of this moduli space as a global critical locus. Accordingly, we obtain two equivalent explicit realizations of the canonical DT sheaf of the moduli space. Using each critical presentation, we describe canonical actions of shifted Yangians and quantized Coulomb branches on the quasimap critical cohomologies. We produce, by geometric means, a canonical morphism from an appropriate Hall algebra to the Coulomb branch, and show that the two actions we describe are compatible via this morphism under an additional hypothesis. We conjecture the compatibility holds generally, and reduce the claim to a sheaf-theoretic statement that may be approached via Joyce conjecture.
ER  -