Intrinsic approach to 1 + 1D Carrollian Conformal Field Theory

Abstract

The 3D Bondi-Metzner-Sachs (BMS3) algebra that is the asymptotic symmetry algebra at null infinity of the 1 + 2D asymptotically flat space-time is isomorphic to the 1 + 1D Carrollian conformal algebra. Building on this connection, various preexisting results in the BMS3-invariant field theories are reconsidered in light of a purely Carrollian perspective in this paper. In direct analogy to the covariant transformation laws of the Lorentzian tensors, the flat Carrollian multiplets are defined and their conformal transformation properties are established. A first-principle derivation of the Ward identities in a 1 + 1D Carrollian conformal field theory (CCFT) is presented. This derivation introduces the use of the complex contour-integrals (over the space-variable) that provide a strong analytic handle to CCFT. The temporal step-function factors appearing in these Ward identities enable the translation of the operator product expansions (OPEs) into the language of the operator commutation relations and vice versa, via a contour-integral prescription. Motivated by the properties of these step-functions, the iϵ-forms of the Ward identities and OPEs are proposed that permit for the hassle-free use of the algebraic properties of the latter. Finally, utilizing the computational techniques developed, it is shown that the modes of the quantum energy-momentum tensor operator generate the centrally extended version of the infinite-dimensional 1 + 1D Carrollian conformal algebra.

Non-Lorentzian Kač-Moody Algebras

“…In 2D Carroll CFT, the above generator equation for any conserved charge operator Q A is related to the following contour integral prescription involving an OPE [43] 2 :…”

“…To derive the current-current OPEs using the machinery just developed, we shall assume that no field in the theory has negative scaling dimension with the identity being the only field with ∆ = 0. Under these assumptions, the OPEs between the EM tensor components were derived using only symmetry arguments in [43]; the results are: 2 .…”

“…We now show under the assumption that no field in the theory has negative scaling dimension with the identity field being the only one with ∆ = 0 , that the currents J a x (t, x) and J a t (t, x) must transform as a rank-1 2 primary multiplet under 2D CC transformations. From [43], we recall the OPEs of a general 2D CC (multi-component) field Φ (l) (t, x) having scaling dimension ∆, Carrollian boost-charge ξ and boost rank l with the EM tensor components:…”

Non-Lorentzian Kač-Moody algebras

“…Having derived the non-Lorentzian current algebra through a contraction, we now go on to present an intrinsically Carrollian derivation of the same, where we would not be alluding to a limiting procedure at all. This section heavily borrows from the machinery detailed in [43], some of the important features of which are described in appendix A. Although we will try and be self consistent so that the section (with the help of the related appendix A) stands on its own, for any details that we may have inadvertently skipped in what follows, the reader is referred back to [43].…”

Constructing Carrollian Field Theories from Null Reduction

“…The on-shell reduction from Bargmann theories has been discussed in[4]. For the recent studies on the BMS invariant theories, see[33][34][35][36][37][38].…”