
TL;DR
This paper demonstrates that nonlinear $W_3$ and $W_3^{(2)}$ algebras can be embedded into linear algebras, enabling new realizations and revealing relationships, which may aid in developing $W$-string theories.
Contribution
The authors construct linear embeddings of $W_3$ and $W_3^{(2)}$ algebras, providing new realizations and insights into their relationships, with potential applications in string theory.
Findings
Linear embeddings of $W_3$ and $W_3^{(2)}$ algebras are constructed.
New field realizations of $W_3$ and $W_3^{(2)}$ are obtained.
Hidden relationships between $W_3$ and $W_3^{(2)}$ are revealed.
Abstract
We show that the Zamolodchikov's and Polyakov-Bershadsky nonlinear algebras and can be embedded as subalgebras into some {\em linear} algebras with finite set of currents. Using these linear algebras we find new field realizations of and which could be a starting point for constructing new versions of -string theories. We also reveal a number of hidden relationships between and . We conjecture that similar linear algebras can exist for other -algebras as well.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
