Positive traces on certain SL(2) Coulomb branches

2025/07/25 by Klyuev, Daniil, Vulakh, Joseph · 1 citation
#FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2507.19447

Abstract

For a noncommutative algebra A and an antilinear automorphism ρ of A there is a notion of a positive trace. Positive traces appear in study of supersymmetric gauge theories. We classify positive traces on A in two cases. The first case is when A is a quantization of a Kleinian singularity of type D, with certain restriction on the quantization parameter. The second case is when A=K^SL(2,ℂ[[t]])\rtimes ℂ_q^×(Gr_PGL2) is an algebra containing K-theoretic Coulomb branches of pure SL(2) and PGL(2) gauge theories.

Citations

• Dualities of K-theoretic Coulomb branches from a once-punctured torus
• Schur Quantization and Complex Chern-Simons theory
• Differential operators on the base affine space of SL_n and quantized Coulomb branches
• Sphere quantization of Higgs and Coulomb branches and Analytic Symplectic Duality
• Unitarizability of Harish-Chandra bimodules over generalized Weyl and q-Weyl algebras
• A one-dimensional theory for Higgs branch operators
• Deformations of symplectic singularities and Orbit method for semisimple Lie algebras

Cited by

• Residue construction of quantized Coulomb branches

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