Towards Quantizing Null p-branes: Light-Cone Gauge Analysis and Physical Hilbert Space

TL;DR

This paper investigates the quantization of null p-branes in flat spacetime, analyzing their gauge symmetries, constraints, and the structure of their physical Hilbert space, with particular focus on membranes in four dimensions.

Contribution

It provides a canonical quantization framework for null p-branes, classifies solutions to the constraints, and explores the physical Hilbert space structure, including special membrane cases.

Findings

Solutions to the sandwich constraints are classified into p+1 distinct classes.

The physical Hilbert space structure is explicitly constructed and characterized.

Special analysis of membranes in four dimensions reveals unique physical implications.

Abstract

We study null $p$-branes, $p$-branes with a Carrollian $p+1$-dimensional worldvolume embedded in a generic $D$-dimensional flat Minkowski target space. This theory has a generalized BMS$_{p+1}$ gauge symmetry. By fixing the light-cone gauge, the BMS symmetry is partly fixed, leaving $p$ ``momentum constraints'' alongside $p$-dimensional area-preserving diffeomorphisms. We quantize the theory in the light-cone gauge via canonical quantization and construct the physical Hilbert space by imposing the remaining constraints using sandwich conditions: the constraints must vanish when sandwiched between any two physical states. We show that solutions to the sandwich conditions are classified into $p+1$ distinct classes, which we completely specify. In addition, we discuss special and interesting case of membranes in four dimensions and examine the physical implications of the quantized null $p$-brane and its associated physical Hilbert space.