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>2d>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>2d>2 CCA and GCA carry not only the simple chain structure appeared in logCFT or 2d2d 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.

Quantum Carroll/fracton particles

“…One way to see this is by looking at the two-point functions of Carroll field theories which have two branches by only imposing Carroll symmetries [12,73,80], with further refinements once the extended symmetries are taken into account.…”

Report on scipost_202312_00031v2

“…It is also possible to obtain the two magnetic Carroll actions (2.23) and (2.26) by taking 14 There is also a second way of obtaining the magnetic Carroll 1 Lagrangian (2.23). This consists in replacing the off-diagonal mass term in the parent Lagrangian (2.10) with the following diagonal one…”

Symmetry group at future null infinity II: Vector theory

“…Recently, the BMS group is identified as the so-called conformal Carroll group of level 2 [19][20][21] in the context of Carrollian manifold [22][23][24]. We may also study the representation of the BMS group [25,26] and construct field theories with Carrollian symmetry [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45]. However, the relation between the Carrollian field theory and the bulk theory is not straightforward in this method.…”