The quantum Hikita conjecture

Kamnitzer, Joel; McBreen, Michael; Proudfoot, Nicholas

doi:10.1016/j.aim.2021.107947

Cited by 11 publications

(9 citation statements)

References 14 publications

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“…At the level of the supersymmetry algebra, the duality acts as an involution that exchanges the R-symmetries SU(2) H with SU(2) C and the flavour symmetries T H and T C . Mirror symmetry implies non-trivial relationships between mathematical structures associated to pairs of 3d N = 4 theories [35][36][37][38].…”

Section: Mirror Symmetrymentioning

confidence: 99%

Supersymmetric Ground States of 3d $\mathcal{N}=4$ Gauge Theories on a Riemann Surface

2022

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This paper studies supersymmetric ground states of 3d \mathcal{N}=4𝒩=4 supersymmetric gauge theories on a Riemann surface of genus gg. There are two distinct spaces of supersymmetric ground states arising from the AA and BB type twists on the Riemann surface, which lead to effective supersymmetric quantum mechanics with four supercharges and supermultiplets of type \mathcal{N}=(2,2)𝒩=(2,2) and \mathcal{N}=(0,4)𝒩=(0,4) respectively. We compute the space of supersymmetric ground states in each case, graded by flavour and R-symmetries and in different chambers for real mass and FI parameters, for a large class of supersymmetric gauge theories. The results are formulated geometrically in terms of the Higgs branch geometry. We perform extensive checks of compatibility with the twisted index and mirror symmetry.

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Section: Mirror Symmetrymentioning

confidence: 99%

Supersymmetric Ground States of 3d $\mathcal{N}=4$ Gauge Theories on a Riemann Surface

2022

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“…Remark 7.10. This result can be interpreted as a K-theoretic analogue of the quantum Hikita conjecture [32], which as a generalization of [28], states that the quantum cohomology ring of X can be identified with the quantized coordinate ring of its singular 3d mirror.…”

Section: Recall That the Affine Grassmannian Grmentioning

confidence: 90%

Virtual Coulomb branch and vertex functions

Zhou¹

2021

Preprint

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We introduce a variation of the K-theoretic quantized Coulomb branch constructed by Braverman-Finkelberg-Nakajima, by application of a new virtual intersection theory. In the abelian case, we define Verma modules for such virtual Coulomb branches, and relate them to the moduli spaces of quasimaps into the corresponding Higgs branches. The descendent vertex functions, defined by K-theoretic quasimap invariants of the Higgs branch, can be realized as the associated Whittaker functions. The quantum q-difference modules and Bethe algebras (analogue of quantum K-theory rings) can then be described in terms of the virtual Coulomb branch. As an application, we prove the wall-crossing result for quantum q-difference modules under the variation of GIT. Nonabelian cases are also treated via abelianization.

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“…An important observation is that the Coulomb branch may not admit any trace, twisted or not. By the quantum Hikita conjecture [36], the space of twisted traces is isomorphic to the quantum cohomology ring of the Higgs branch. A balanced ADE quiver has a rich Higgs branch and a correspondingly rich space of traces.…”

Section: A Choice Of Tracesmentioning

confidence: 99%

Q-operators are 't Hooft lines

Costello,

Gaiotto,

Yagi

2021

Preprint

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The quantum Hikita conjecture

Cited by 11 publications

References 14 publications

Supersymmetric Ground States of 3d $\mathcal{N}=4$ Gauge Theories on a Riemann Surface

Supersymmetric Ground States of 3d $\mathcal{N}=4$ Gauge Theories on a Riemann Surface

Virtual Coulomb branch and vertex functions

Q-operators are 't Hooft lines

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