Stress Tensor for Large-$D$ membrane at subleading orders

TL;DR

This paper extends the calculation of the membrane stress tensor to subleading order in large dimension D, demonstrating that membrane dynamics follow from stress tensor conservation in various asymptotic spacetimes.

Contribution

It provides the first derivation of the membrane stress tensor at order 1/D in asymptotically flat, AdS, and dS spaces, linking membrane equations to stress tensor conservation.

Findings

Derived the membrane stress tensor at subleading order in 1/D.

Showed membrane equations follow from stress tensor conservation.

Applicable to asymptotically flat, AdS, and dS spacetimes.

Abstract

In this note, we have extended the result of \citep{radiation} to calculate the membrane stress tensor up to ${\cal O}\left(\frac{1}{D}\right)$ localized on the codimension-one membrane world volume propagating in asymptotically at/AdS/dS space-time. We have shown that the subleading order membrane equation follows from the conservation equation of this stress tensor.