Boundary lines and Askey-Wilson type moments
Tadashi Okazaki, Douglas J. Smith
TLDR
This paper derives exact, closed-form expressions for Wilson line defect half-indices in 3d N=2 gauge theories using Askey-Wilson type moments.
Key contributions
- Formulates Wilson line defect half-indices for 3d N=2 gauge theories as Askey-Wilson type moments.
- Identifies dual line operators as vortex line defects in the Landau-Ginzburg description.
- Shows these vortex defects induce singular behavior in chiral multiplets and add 1D degrees of freedom.
- Obtains exact closed-form expressions for half-indices by incorporating singular structure as an effective spin shift.
Why it matters
This work provides exact mathematical tools for understanding complex quantum field theories. By linking defect indices to Askey-Wilson moments, it offers new insights into the interplay between gauge theories and special functions, advancing theoretical physics.
Original Abstract
The Wilson line defect half-indices for 3d $\mathcal{N}=2$ gauge theories with boundary confining phases admit a formulation in terms of the Askey-Wilson type moments. In the dual Landau-Ginzburg description the dual line operators can be realized as vortex line defects which induce singular behavior of chiral multiplets associated with the minimal monopole operators, together with additional one-dimensional degrees of freedom. By incorporating such a singular structure as an effective spin shift into the index computation, we obtain exact closed-form expressions for the line defect half-indices which are Askey-Wilson type moments.
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