Fundamental Membranes and the String Dilaton

TL;DR

This paper investigates the quantization of supermembrane theory to understand how the world-sheet action depends on the string dilaton, revealing that critical dimension restrictions prevent non-critical membrane analogs.

Contribution

It introduces a Polyakov-type quantization approach for supermembranes, establishing the critical dimension as essential for consistent dilaton dependence.

Findings

Target-space dimension must be 11 for consistent quantization.

No non-critical membrane analogs exist.

Unique dependence of the world-sheet action on the dilaton is confirmed.

Abstract

We study the quantization of the bosonic sector of supermembrane theory in double dimensional reduction, in order to extract the dependence of the resulting world-sheet action on the string dilaton (which cannot be obtained from a purely kinematic reduction). Our construction relies on a Polyakov-type approach with all six metric components on the world-volume as independent quantum fields, and shows that the correct and unique answer is only obtained if the target-space dimension of the theory is restricted to the critical value ($D=11$ for the supermembrane). As a corollary, our analysis implies that there are no analogs of the non-critical string for (super-)membrane theory.