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In this work, we study the quantization of Carrollian conformal scalar theories, including two-dimensional(2D) magnetic scalar and three-dimensional(3D) electric and magnetic scalars. We discuss two different quantization schemes, depending on the choice of the vacuum. We show that the standard canonical quantization corresponding to the induced vacuum yields a unitary Hilbert space and the 2-point correlation functions in this scheme match exactly with the ones computed from the path integral. In the canonical quantization, the BMS symmetry can be realized without anomaly. On the other hand, for the quantization based on the highest-weight vacuum, it does not have a unitary Hilbert space. In 2D, the correlators in the highest-weight vacuum agree with the ones obtained by taking the $c\to 0$ limit of the 2D CFT, and there is an anomalous term in the commutation relations between the Virasoso generators, whose form is similar to the one in 2D CFT. In 3D, there is no good definition of the highest-weight vacuum without breaking the rotational symmetry. In our study, we find that the usual state-operator correspondence in CFT does not hold in the Carrollian case., Comment: 44 pages, 3 figures. v2: ctations added

In this work, we study the tensionless (super)string in the formalism of path-integral quantization. We introduce BMS $bc$ and $\beta\gamma$ ghosts intrinsically by accounting for the Faddeev-Popov determinants appeared in fixing the gauges. We then do canonical quantization and obtain the critical dimensions for different tensionless strings. We find that among four kinds of tensionless superstrings, the $\mathcal{N}=2$ homogeneous and inhomogeneous doublet tensionless superstrings have the same critical dimension as the usual superstrings. Taking the BMS $bc$ and $\beta\gamma$ ghosts as new types of BMS free field theories, we find that their enhanced underlying symmetries are generated by BMS-Kac-Moody algebras, with the Kac-Moody subalgebras being built from a three-dimensional non-abelian and non-semi-simple Lie algebra., Comment: 49 pages, 3 tables; v2: typos corrected; v3: discussion of the enlarged BMS symmetry completed, references added; v4: matches JHEP version

In this paper, we propose a novel way to construct off-shell actions of $d$-dimensional Carrollian field theories by considering the null-reduction of the Bargmann invariant actions in $d+1$ dimensions. This is based on the fact that $d$-dimensional Carrollian symmetry is the restriction of the $(d+1)$-dimensional Bargmann symmetry to a null hyper-surface. We focus on free scalar field theory and electromagnetic field theory, and show that the electric and magnetic sectors of these theories originate from different Bargmann invariant actions in one higher dimension. In the cases of the massless free scalar field and $d=4$ electromagnetic field, we verify Carrollian conformal invariance of the resulting theories, and find that there appear naturally chain representations and staggered modules of Carrollian conformal algebra., Comment: 59 pages, major revisions, results unchanged

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., Comment: 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