# Actions for the Bosonic String with the Curved Worldsheet

## TL;DR

This paper introduces a new string action with a curved worldsheet, explores its symmetries, and generalizes it to include scalar curvature dependence and Weyl invariance, expanding theoretical understanding of string models.

## Contribution

It presents a novel string action with a curved worldsheet and extends it to include scalar curvature and Weyl invariance, offering new theoretical frameworks.

## Key findings

- The introduced action results in a consistently curved worldsheet.
- The generalized action includes an arbitrary function of scalar curvature.
- Weyl invariance is achieved through an additional scalar field.

## Abstract

At first we introduce an action for the string, which leads to a worldsheet that always is curved. For this action we study the Poincar\'e symmetry and the associated conserved currents. Then, a generalization of the above action, which contains an arbitrary function of the two-dimensional scalar curvature, will be introduced. An extra scalar field enables us to modify these actions to Weyl invariant models.