SciPost Submission Page
On Higher-dimensional Carrollian and Galilean Conformal Field Theories
by Bin Chen, Reiko Liu, Yu-fan Zheng
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Yu-fan Zheng |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202210_00048v2 (pdf) |
| Date accepted: | 2023-02-13 |
| Date submitted: | 2022-12-04 10:33 |
| Submitted by: | Zheng, Yu-fan |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
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.
List of changes
In this version of our paper, we made revisions mainly in section 3.2. We explained why we used Young tableau and how it corresponds to the tensor representations in this section according to suggestions from the referee. We also modified some expressions in section 3.1 to match expressions in revised section 3.2 which does not change the original statement.
Published as SciPost Phys. 14, 088 (2023)