Abstract
Two dimensional field theories with Bondi-Metzner-Sachs symmetry have been proposed as duals to asymptotically flat spacetimes in three dimensions. These field theories are naturally defined on null surfaces and hence are conformal cousins of Carrollian theories, where the speed of light goes to zero. In this paper, we initiate an investigation of anomalies in these field theories. Specifically, we focus on the BMS equivalent of Weyl invariance and its breakdown in these field theories and derive an expression for Weyl anomaly. Considering the transformation of partition functions under this symmetry, we derive a Carrollian Liouville action different from ones obtained in the literature earlier.
Highlights
In two dimensions, where the underlying symmetry of conformal field theories enhance to two copies the Virasoro algebra, the Weyl anomaly is proportional to the central charge multiplied by the Ricci scalar of the manifold the CFT lives on
We have found the form of the Weyl anomaly or equivalently the trace anomaly in 2d BMSFTs
For this we needed the form of the Operator Product Expansion (OPE) of the stress tensors defined in these field theories and importantly a delta-function identity for the Carrollian manifolds on which these theories are defined
Summary
As is very well known, the power of conformal symmetry in two dimensions is greatly enhanced by the underlying infinite dimensional Virasoro algebra (two copies of it):. The above statement defines CFTs at classical level, the trace of EM tensor suffers from an anomaly and no longer vanishes in quantum theories This is because of the presence of central charge in Virasoro algebra. To set the stage for our calculations for the Weyl or trace anomalies in BMS invariant field theories later in the paper, we briefly review a derivation of the same in 2d CFTs [68]. We will do this for CFTs on backgrounds that are infinitesimally close to flat space. We point the reader to [73, 74] for further details on this
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