Deformation quantization and superconformal symmetry in three dimensions
TLDR
In this paper, the authors investigated the structure of certain protected operator algebras that arise in three-dimensional N=4 superconformal field theories, and they found that these algebra can be understood as a quantization of (either of) the half-BPS chiral ring(s).Abstract:
We investigate the structure of certain protected operator algebras that arise in three-dimensional N=4 superconformal field theories. We find that these algebras can be understood as a quantization of (either of) the half-BPS chiral ring(s). An important feature of this quantization is that it has a preferred basis in which the structure constants of the quantum algebra are equal to the OPE coefficients of the underlying superconformal theory. We identify several nontrivial conditions that the quantum algebra must satisfy in this basis. We consider examples of theories for which the moduli space of vacua is either the minimal nilpotent orbit of a simple Lie algebra or a Kleinian singularity. For minimal nilpotent orbits, the quantum algebras (and their preferred bases) can be uniquely determined. These algebras are related to higher spin algebras. For Kleinian singularities the algebras can be characterized abstractly - they are spherical subalgebras of symplectic reflection algebras - but the preferred basis is not easily determined. We find evidence in these examples that for a given choice of quantum algebra (defined up to a certain gauge equivalence), there is at most one choice of canonical basis. We conjecture that this is the case for general N=4 SCFTs.read more
Citations
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Bootstrap equations for $ \mathcal{N} $ = 4 SYM with defects
Pedro Liendo,Carlo Meneghelli +1 more
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Bootstrap equations forN = 4 SYM with defects
Pedro Liendo,Carlo Meneghelli +1 more
TL;DR: The analysis of 4dN = 4 superconformal theories in the presence of a defect from the point of view of the conformal bootstrap was studied in this paper.
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Boundaries, Mirror Symmetry, and Symplectic Duality in 3d $\mathcal{N}=4$ Gauge Theory
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The F-Theorem and F-Maximization
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Selected topics in analytic conformal bootstrap: A guided journey
TL;DR: In this paper , a pedagogical introduction to the analytic conformal bootstrap program via a journey through selected topics is presented, which includes analytic methods which include the large spin perturbation theory, Mellin space methods and the Lorentzian inversion formula.
References
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TL;DR: In this paper, the three sphere partition function of three dimensional theories with four supercharges and an R-symmetry is computed using localization, resulting in a matrix integral over the Cartan of the gauge group.
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A Path integral approach to the Kontsevich quantization formula
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