What question did this study set out to answer?

This research aims to analyze the one-point restriction of conformal blocks associated with vertex operator algebras.

February 28, 2026Open Access

One-point restricted conformal blocks and the fusion tensor product

Key Points

This research aims to analyze the one-point restriction of conformal blocks associated with vertex operator algebras.
Investigated the one-point restriction of conformal blocks on the projective line with specific points.
Restricted modules attached to the point infinity to derive a new formula.
Constructed a left A(V)-module from two vertex operator algebra modules.
Derived fusion rules using the new module representation.
Provided a new formula for computing fusion rules in terms of the constructed module.
Showed that the construction induces the fusion tensor product on the module category for strongly rational vertex operator algebras.

Abstract

Abstract We investigate a one-point restriction of conformal blocks on (P¹, , 1, 0) (P 1, ∞, 1, 0) associated with modules over a vertex operator algebra V. By restricting the module attached to the point ∞ to its bottom degree, we obtain a new formula for computing fusion rules in terms of a new left A (V) -module M¹ M² M 1 ⊙ M 2 over the Zhu algebra A (V), constructed from two V -modules M¹ M 1 and M² M 2. As a consequence, for strongly rational vertex operator algebras, the construction of M¹ M² M 1 ⊙ M 2 induces the fusion tensor product on the module category Mod (A (V) ) Mod (A (V) ).

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