Weyl Invariant p-brane and Dp-brane actions

TL;DR

This paper introduces new Weyl invariant actions for p-branes and Dp-branes, providing a conformal framework that reproduces known models and allows for a complete canonical analysis, including supersymmetric extensions.

Contribution

It proposes conformal invariant p-brane and Dp-brane actions with auxiliary fields, enabling a full canonical formalism and supersymmetric generalizations.

Findings

Weyl invariant actions reproduce Nambu-Goto and Born-Infeld actions upon elimination of auxiliary fields.

Complete canonical formalism developed for quadratic p-brane actions.

Supersymmetric extension maintains conformal and kappa-symmetry.

Abstract

Conformal invariant new forms of $p$-brane and D$p$-brane actions are proposed. The field content of these actions are: an induced metric, gauge fields, an auxiliary metric and an auxiliary scalar field that implements the Weyl invariance. This scalar field transforms with a conformal weight that depends on the brane dimension. The proposed actions are Weyl invariant in any dimension and the elimination of the auxiliary metric and the scalar field reproduces the Nambu-Goto action for $p$-branes and the Born-Infeld action for D$p$-branes. As a consequence of the fact that in the $p$-brane case, the action is quadratic in $\partial_0 X$, we develop a complete construction for the associated canonical formalism, solving the problem in previous formulations of conformal $p$-brane actions where the Hamiltonian can not be constructed. We obtain the algebra of constraints and identify the generator of the Weyl symmetry. In the construction of the corresponding supersymmetric generalization of this conformal $p$-brane action we show that the associated $\kappa$-symmetry is consistent with the conformal invariance. In the D$p$-brane case, the actions are quadratic in the gauge fields. These actions can be used to construct new conformal couplings in any dimension $p$ to the auxiliary scalar field now promoted as a dynamical variable.