Norms of logarithmic primaries of Virasoro algebra
Shintarou Yanagida
TL;DR
This paper provides an algebraic proof of a formula for the norm of logarithmic primary states in the Virasoro algebra, crucial for understanding the AGT correspondence in theoretical physics.
Contribution
It offers a rigorous algebraic derivation of Zamolodchikov's formula, connecting Virasoro algebra norms to gauge theory via the AGT relation.
Findings
Algebraic proof of the logarithmic primary norm formula
Validation of the recursion formula for Gaiotto state norm
Strengthens the mathematical foundation of the AGT correspondence
Abstract
We give an algebraic proof of the formula on the norm of logarithmic primary of Virasoro algebra, which was proposed by Al. Zamolodchikov. This formula appears in the recursion formula for the norm of Gaiotto state, which guarantees the AGT relation for the four-dimensional SU(2) pure gauge theory.
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