Virasoro Algebra and Asymptotic Symmetries from Fractional Bosonic Strings

TL;DR

This paper explores the fractional bosonic string theory, deriving Virasoro operators and their algebra, and demonstrates the recovery of Poincaré invariance at the boundary, contributing to the understanding of fractional conformal symmetries.

Contribution

It introduces fractional Virasoro operators and shows they satisfy the Witt algebra, extending the symmetry structure of fractional bosonic strings.

Findings

Virasoro operators of all orders are constructed.

The algebra of these operators satisfies the Witt algebra.

Poincaré invariance is recovered at the boundary of the theory.

Abstract

The aim of this work is to further study the fractional bosonic string theory. In particular, we wrote the energy-momentum tensor in the fractional conformal gauge and study their symmetries. We introduced the Virasoro operators of all orders. In fact, we found the same $L_0 (\widetilde{L}_0)$ operator originally defined in the work of fractional bosonic string up to a shift transformation. Also, we compute the algebra of our Fractional Virasoro Operators, finding that the satifies the $Witt$ algebra. Lastly, we showed that in the boundary of our theory we recover the lost conservation law associated to $\tau$-diffeomorphism, proving that we have Poincar\'e invariance at the boundary.