The conformal current algebra on supergroups with applications to the spectrum and integrability

Abstract

We compute the algebra of left and right currents for a principal chiral model with arbitrary Wess-Zumino term on supergroups with zero Killing form. We define primary fields for the current algebra that match the affine primaries at the Wess-Zumino-Witten points. The Maurer-Cartan equation together with current conservation tightly constrain the current-current and current-primary operator product expansions. The Hilbert space of the theory is generated by acting with the currents on primary fields. We compute the conformal dimensions of a subset of these states in the large radius limit. The current algebra is shown to be consistent with the quantum integrability of these models to several orders in perturbation theory.

45 pages. Minor corrections

References in corpus (4)

• The Sigma Model on Complex Projective Superspaces
• Conformal invariance and quantum integrability of sigma models on symmetric superspaces
• Principal Chiral Model on Superspheres
• Asymptotic Symmetries of String Theory on AdS3 X S3 with Ramond-Ramond Fluxes

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• Integrability, spin-chains and the AdS3/CFT2 correspondence
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• String States on AdS_3 x S^3 from the Supergroup
• Fusion of line operators in conformal sigma-models on supergroups, and the Hirota equation
• First-principles derivation of the AdS/CFT Y-systems
• Long strings and chiral primaries in the hybrid formalism
• The plane-wave spectrum from the worldsheet
• Quantum Current Algebra for the $Ad{S}_5\times S^5$ Superstring
• Conformal superspace sigma-models
• The Hirota equation for string theory in AdS5xS5 from the fusion of line operators
• Non-chiral current algebras for deformed supergroup WZW models
• Yangian Superalgebras in Conformal Field Theory
• Vertex operators for the plane wave pure spinor string
• Fermionic Coset, Critical Level W^(2)_4-Algebra and Higher Spins
• Harmonic Analysis and Free Field Realization of the Takiff Supergroup of GL(1|1)