On Higher-dimensional Carrollian and Galilean Conformal Field Theories

Abstract

In this paper, we study the Carrollian and Galilean conformal field theories (CCFT and GCFT) in $d>2$ dimensions. We construct the highest weight representations (HWR) of Carrollian and Galilean conformal algebra (CCA and GCA). Even though the two algebras have different structures, their HWRs share similar structure, because their rotation subalgebras are isomorphic. In both cases, we find that the finite dimensional representations are generally reducible but indecomposable, and can be organized into the multiplets. Moreover, it turns out that the multiplet representations in $d>2$ CCA and GCA carry not only the simple chain structure appeared in logCFT or $2d$ GCFT, but also more generally the net structures. We manage to classify all the allowed chain representations. Furthermore we discuss the two-point and three-point correlators by using the Ward identities. We mainly focus on the two-point correlators of the operators in chain representations. Even in this relative simple case, we find some novel features: multiple-level structure, shortage of the selection rule on the representations, undetermined 2-pt coefficients, etc.. We find that the non-trivial correlators could only appear for the representations of certain structure, and the correlators are generally polynomials of time coordinates for CCFT (spacial coordinates for GCFT), whose orders depend on the levels of the correlators.

84 pages, 21 figures. Changes: Add comments in the introduction, section 3.1, 3.2 and 3.5, added examples in section 4.1. Added some citations. Corrected some typos

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Cited by in corpus (17)

• Carrollian Approach to $1+3$D Flat Holography
• One-Loop Quantum Effects in Carroll Scalars
• Symmetry group at future null infinity I: Scalar theory
• A BMS-invariant free fermion model
• Galilean Gauge Theories from Null Reductions
• Quantizing Carrollian field theories
• Symmetry group at future null infinity II: Vector theory
• The Shadow Formalism of Galilean CFT${}_2$
• Quantization of Carrollian conformal scalar theories
• Chern-Simons action and the Carrollian Cotton tensors
• Bulk Reconstruction of Scalar Excitations in Flat${}_3$/CCFT${}_2$ and the Flat Limit from (A)dS${}_3$/CFT${}_2$
• Classification of Conformal Carroll Algebras
• Supersymmetric Carroll Galileons in Three Dimensions
• Universal sectors of two-dimensional Carrollian CFTs
• Unique Carrollian manifolds emerging from Einstein spacetimes
• Character of the highest weight module of BMS algebra realized on codimensional-two boundary
• Conformal Blocks in 2d Carrollian/Galilean CFTs and Excited State Entanglement Entropy