One-loop effective brane action

TL;DR

This paper calculates the one-loop effective action for a p-brane in Minkowski space, showing that certain symmetries are preserved at this quantum level and identifying the divergence structure.

Contribution

It provides a detailed computation of the one-loop effective action for a p-brane, highlighting the divergence structure and symmetry preservation in the quantum corrections.

Findings

Infrared divergences absorbed into quantum fluctuations.

Remaining ultraviolet divergences are finite in number.

D= p+2 Poincaré symmetry and D=p+1 general covariance are preserved.

Abstract

The one-loop effective action for a $p$ brane embedded in a $D=p+2$ Minkowski spacetime in the static gauge is calculated. Rescaling the quantum fluctuation by $\sqrt{-g_0}$ evaluated on the background brane leads to the one-loop effective action expressed only in terms of infrared and ultraviolet divergent geometric scalars. After the infrared divergences are absorbed into the quantum fluctuation, there remains the finite number of ultraviolet divergences. This implies that the $D=p+2$ Poincar\'{e} symmetry and the $D=p+1$ general coordinate invariance are preserved in one-loop order.