Ultra-violet Behavior of Bosonic Quantum Membranes

TL;DR

This paper explores the quantum behavior of bosonic membranes by treating them as sigma models, analyzing their ultraviolet properties, and deriving background field equations, with implications for understanding M-theory corrections.

Contribution

It introduces a sigma model approach to bosonic membranes and investigates their UV behavior to inform supersymmetric M-theory corrections.

Findings

Quantum corrections lead to background field equations similar to Einstein's equations.

Membrane theory is non-renormalizable on the world volume by power counting.

Insights into supersymmetric membranes may inform higher-order M-theory corrections.

Abstract

We treat the action for a bosonic membrane as a sigma model, and then compute quantum corrections by integrating out higher membrane modes. As in string theory, where the equations of motion of Einstein's theory emerges by setting $\beta = 0$, we find that, with certain assumptions, we can recover the equations of motion for the background fields. Although the membrane theory is non-renormalizable on the world volume by power counting, the investigation of the ultra-violet behavior of membranes may give us insight into the supersymmetric case, where we hope to obtain higher order M-theory corrections to 11 dimensional supergravity.