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

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.

40 pages, 1 figure

References in corpus (18)

• New symmetries for the Gravitational S-matrix
• Spacetime structure near generic horizons and soft hair
• The Weyl BMS group and Einstein's equations
• Tensionless Strings and Galilean Conformal Algebra
• Tiny Graviton Matrix Theory: DLCQ of IIB Plane-Wave String Theory, A Conjecture
• Classical and Quantum Nambu Mechanics
• Tensionless Strings from Worldsheet Symmetries
• Null boundary phase space: slicings, news and memory
• A Tale of Three. Tensionless strings and vacuum structure
• T-Witts from the horizon
• Tensionless Superstrings: View from the Worldsheet
• Carrollian hydrodynamics from symmetries
• The tensionless path from closed to open strings
• Rindler on the Worldsheet
• A Rindler Road to Carrollian Worldsheets
• Membrane Paradigm from Near Horizon Soft Hair
• Horizon Strings as 3d Black Hole Microstates
• A New Approach to the Classical and Quantum Dynamics of Branes

Cited by in corpus (4)

• Null Strings Gauged and Reloaded, II: Consistent Classical Treatment of the Null Strings
• Null Strings Gauged and Reloaded, I: Null Strings Have Carroll-Weyl Gauge Symmetry
• Brane Symmetries Revisited: Symmetries of Tensile and Tensionless Branes in Possibly Degenerate Metrics and their Manifestations
• Strings near BTZ black holes: A Carrollian Chronicle