Taking off the square root of Nambu-Goto action and obtaining Filippov-Lie algebra gauge theory action

TL;DR

This paper introduces a new method to remove the square root from the Nambu-Goto action for p-branes, resulting in a gauged Polyakov-like action with a Filippov-Lie n-algebra structure, expanding the theoretical framework of brane dynamics.

Contribution

It generalizes the Polyakov approach to p-branes by incorporating a Filippov-Lie n-algebra gauge theory, providing a novel lower-dimensional action formulation.

Findings

Derived a modified d-dimensional Polyakov action with Nambu n-bracket potential.

Demonstrated realization of (p+1)-dimensional diffeomorphism in the reduced action.

Connected gauge fixing to a product of d-dimensional and n-dimensional volume-preserving diffeomorphisms.

Abstract

We propose a novel prescription to take off the square root of Nambu-Goto action for a p-brane, which generalizes the Brink-Di Vecchia-Howe-Tucker or also known as Polyakov method. With an arbitrary decomposition as d+n=p+1, our resulting action is a modified d-dimensional Polyakov action which is gauged and possesses a Nambu n-bracket squared potential. We first spell out how the (p+1)-dimensional diffeomorphism is realized in the lower dimensional action. Then we discuss a possible gauge fixing of it to a direct product of $d$-dimensional diffeomorphism and n-dimensional volume preserving diffeomorphism. We show that the latter naturally leads to a novel Filippov-Lie n-algebra based gauge theory action in d-dimensions.