Norcor vs the Abominable Gauge Completion

TL;DR

The paper presents a covariant, normal-coordinate approach to systematically expand the 11D supermembrane action in a supergravity background with respect to fermionic coordinates $\\theta^\\alpha$, avoiding the complications of gauge completion. By working in superspace and evaluating at $\\theta=0$, the authors express expansions in terms of component fields (graviton, gravitino, and 3-form) and derive explicit low-order results for the vielbein and the membrane action, including a concrete second-order membrane action. The work provides a general framework applicable to other branes and backgrounds, with straightforward paths to higher-order fermionic terms and simplifications in bosonic backgrounds. This method offers an unambiguous, covariant alternative for high-precision calculations in M-theory contexts, enabling cross-checks with AdS$\\times$S backgrounds and comparisons with previous gauge-completion results.

Abstract

We use normal coordinate methods to obtain the expansion with respect to fermionic coordinates of the 11-dimensional supermembrane action in a supergravity background. Likewise, expansions for various branes in other dimensions can be obtained. These methods allow a systematic and unambiguous expansion of the vielbein to any order in the fermionic coordinates and avoid the complications encountered in the gauge completion approach.