Universality in Chern-Simons theory

Abstract

We show that the perturbative part of the partition function in the Chern-Simons theory on a 3-sphere as well as the central charge and expectation value of the unknotted Wilson loop in the adjoint representation can be expressed in terms of the universal Vogel's parameters $\alpha ,\beta ,\gamma .$ The derivation is based on certain generalisations of the Freudenthal-de Vries strange formula.

Slightly revised version with minor corrections

References in corpus (3)

• Analytic Continuation Of Chern-Simons Theory
• Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2d qYM theory
• On duality and negative dimensions in the theory of Lie groups and symmetric spaces

Cited by in corpus (28)

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• On universal knot polynomials
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• Casimir eigenvalues for universal Lie algebra
• Refined Chern-Simons versus Vogel universality
• Split Casimir operator for simple Lie algebras, solutions of Yang-Baxter equations and Vogel parameters
• Split Casimir operator for simple Lie algebras in the cube of $\mathsf{ad}$-representation and Vogel parameters
• On Universal Quantum Dimensions
• Knot polynomials for twist satellites
• Universal volume of groups and anomaly of Vogel's symmetry
• Chern-Simons theory with the exceptional gauge group as a refined topological string
• Diophantine equations, Platonic solids, McKay correspondence, equivelar maps and Vogel's universality
• On the map of Vogel's plane
• Universal Chern-Simons partition functions as quadruple Barnes' gamma-functions
• Expanding on the Cardy-like limit of the superconformal index of 4d $\mathcal{N}=1$ ABCD SCFTs
• On Universal Eigenvalues of Casimir Operator
• On a Gopakumar-Vafa form of partition function of Chern-Simons theory on classical and exceptional lines
• $X_2$ series of universal quantum dimensions
• Exact Chern-Simons / Topological String duality
• Can Yang-Baxter imply Lie algebra?
• Two-fold refinement of non simply laced Chern-Simons theories
• Vogel's universality and the classification problem for Jacobi identities
• On refined Chern-Simons / topological string duality for classical gauge groups
• On universal quantum dimensions of certain two-parameter series of representations
• Torus knots in adjoint representation and Vogel's universality
• On partition functions of refined Chern-Simons theories on $S^3$
• Split Casimir operator and universal formulation of the simple Lie algebras
• Torus Knots in Adjoint Representation