NDLI: Deformation Quantization and Superconformal Symmetry in Three Dimensions

Content Provider	Springer Nature Link
Author	Beem, Christopher Peelaers, Wolfger Rastelli, Leonardo
Copyright Year	2017
Abstract	We investigate the structure of certain protected operator algebras that arise in three-dimensional $${\mathcal{N}=4}$$ 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 $${\mathcal{N}=4}$$ SCFTs.
Starting Page	345
Ending Page	392
Page Count	48
File Format	PDF
ISSN	00103616
Journal	Communications in Mathematical Physics
Volume Number	354
Issue Number	1
e-ISSN	14320916
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2017-02-20
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Theoretical, Mathematical and Computational Physics Mathematical Physics Quantum Physics Complex Systems Classical and Quantum Gravitation, Relativity Theory
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Mathematical Physics

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