Carroll fermions in two dimensions

Abstract

Carroll symmetry is a very powerful characteristic of generic null surfaces, as it replaces the usual Poincaré algebra with a vanishing speed of light version thereof. These symmetries have found universal applications in the physics of null manifolds as they arise in diverse situations ranging from black hole horizons to condensed matter systems with vanishing Fermi velocities. In this work, we concentrate on fermions living on two dimensional ($2d$) null manifolds and explore the Carroll invariant structure of the associated field theories in a systematic manner. The free massless versions of these fermions are shown to exhibit $2d$ Conformal Carroll or equivalently the $3d$ Bondi-Metzner-Sachs (BMS) algebra as their symmetry. Due to the degenerate nature of the manifold, we show the presence of two distinct classes of Clifford Algebras. We also find that in two dimensions there are two distinct fermion actions. We study discrete and continuous symmetries of both theories, and quantize them using highest weight representation of the vacuum. We also discuss how the symmetries of $2d$ free fermion CFTs can be continually deformed by infinite boosts or degenerate linear transformations on coordinates, leading to the corresponding BMS invariant theory at singular points.

37 pages, no figures

References in corpus (18)

• The BMS/GCA correspondence
• Conformal Carroll groups and BMS symmetry
• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• Flat Holography: Aspects of the dual field theory
• Entropy of three-dimensional asymptotically flat cosmological solutions
• Entanglement entropy in Galilean conformal field theories and flat holography
• Non-relativistic conformal symmetries and Newton-Cartan structures
• Conformal Carroll groups
• Field Theories with Conformal Carrollian Symmetry
• Magic Fermions: Carroll and Flat Bands
• Conformal Carroll Scalars with Boosts
• Super-BMS${}_3$ algebras from $\mathcal{N}=2$ flat supergravities
• Tensionless Superstrings: View from the Worldsheet
• Carroll covariant scalar fields in two dimensions
• Boosting to BMS
• Intrinsic Approach to $1+1$D Carrollian Conformal Field Theory
• Revisiting the Carrollian Scalar Field
• Carrollian superconformal theories and super BMS

Cited by in corpus (13)

• Super-Carrollian and Super-Galilean Field Theories
• Quantization of Carrollian conformal scalar theories
• Flat Bands and Compact Localised States: A Carrollian roadmap
• Bulk Reconstruction of Scalar Excitations in Flat${}_3$/CCFT${}_2$ and the Flat Limit from (A)dS${}_3$/CFT${}_2$
• Irrelevant and marginal deformed BMS field theories
• Classification of Conformal Carroll Algebras
• Quantization of Carrollian fermions
• A Carroll Limit of AdS/CFT: A Triality with Flat Space Holography?
• Carroll spinors
• Carroll-Schrödinger Equation
• Universal sectors of two-dimensional Carrollian CFTs
• Conformal Blocks in 2d Carrollian/Galilean CFTs and Excited State Entanglement Entropy
• On $\sqrt{T\overline{T}}$ deformed pathways: CFT to CCFT