
TL;DR
This paper explores the extension of W-algebras to negative ranks, demonstrating their finite generation and uncovering connections between different known W-algebras through analytic continuation.
Contribution
It introduces the definition of WA_{-n-1} algebras for negative ranks and reveals new relationships between existing W-algebras.
Findings
WA_{-n-1} algebras are finitely generated.
Connections between CP(k)-models and U(1)-cosets of Polyakov-Bershadsky-algebras.
Extension of W-algebras to negative integer ranks.
Abstract
Recently it has been discovered that the W-algebras (orbifold of) WD_n can be defined even for negative integers n by an analytic continuation of their coupling constants. In this letter we shall argue that also the algebras WA_{-n-1} can be defined and are finitely generated. In addition, we show that a surprising connection exists between already known W-algebras, for example between the CP(k)-models and the U(1)-cosets of the generalized Polyakov-Bershadsky-algebras.
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