Ring objects in the equivariant derived Satake category arising from Coulomb branches (with an appendix by Gus Lonergan)

Abstract

This is the second companion paper of arXiv:1601.03586. We consider the morphism from the variety of triples introduced in arXiv:1601.03586 to the affine Grassmannian. The direct image of the dualizing complex is a ring object in the equivariant derived category on the affine Grassmannian (equivariant derived Satake category). We show that various constructions in arXiv:1601.03586 work for an arbitrary commutative ring object. The second purpose of this paper is to study Coulomb branches associated with star shaped quivers, which are expected to be conjectural Higgs branches of $3d$ Sicilian theories in type $A$ by arXiv:1007.0992.

38 pages; v2. 66 pages, proofs in some results in Sec.5 are corrected. A new appendix by Gus Lonergan on a new proof of the commutativity of the convolution product; v3. the appendix is mentioned in the title; v4. A remark (5.22) on quantization of results in Sect.5 is added; v5. the definition of ${\mathcal{S}}_N^{\circ }$ is added; v6. Errata

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Cited by in corpus (15)

• Coulomb Branch Operators and Mirror Symmetry in Three Dimensions
• Shifted quantum affine algebras: integral forms in type $A$ (with appendices by Alexander Tsymbaliuk and Alex Weekes)
• Chiral algebras of class $\mathcal{S}$ and Moore-Tachikawa symplectic varieties
• Generators for Coulomb branches of quiver gauge theories
• Line bundles over Coulomb branches
• Coulomb Branches of Star-Shaped Quivers
• Representation theory of W-algebras and Higgs branch conjecture
• Associated varieties and Higgs branches (a survey)
• Quantized Coulomb Branches, Monopole Bubbling and Wall-Crossing Phenomena in 3d $\mathcal{N}=4$ Theories
• Double affine Grassmannians and Coulomb branches of 3d N=4 quiver gauge theories
• Derived gluing construction of chiral algebras
• Branes and DAHA Representations
• On 'categories' of quantum field theories
• Steenrod Operators, the Coulomb Branch and the Frobenius Twist, I
• Line Operators in 4d Chern-Simons Theory and Cherkis Bows