Scale and conformal invariance in higher derivative shift symmetric theories

Abstract

The critical behavior of infinite families of shift symmetric interacting theories with higher derivative kinetic terms (non unitary) is considered. Single scalar theories with shift symmetry are classified according to their upper critical dimensions and studied at the leading non trivial order in perturbation theory. For two infinite families, one with quartic and one with cubic interactions, beta functions, criticality conditions and universal anomalous dimensions are computed. At the order considered, the cubic theories enjoy a one loop non renormalization of the vertex, so that the beta function depends non trivially only on the anomalous dimension. The trace of the energy momentum tensor is also investigated and it is shown that these two families of QFTs are conformally invariant at the fixed point of the RG flow.

Weyl Covariance and the Energy Momentum Tensors of Higher-Derivative Free Conformal Field Theories

“…Naturally one may wonder how the picture presented could be extended when interactions are present. There have recently been some perturbative investigations (in the ε-expansion) devoted to the study of several families of critical theories which are CFTs [14,[45][46][47][48]. Therefore it would be very interesting to push further the analysis of these conformal theories and look at the relation to Weyl invariance in curved space, including also the possible existence of obstructions.…”

“…To completely fix all parametric dependencies of T µν , we require that the EMT should comply with the general off-shell form that comes from varying the Weyl invariant action (14), which in flat space are…”

Weyl covariance and the energy momentum tensors of higher-derivative free conformal field theories

“…Naturally one may wonder how the picture presented could be extended when interactions are present. There have recently been some perturbative investigations (in the ε-expansion) devoted to the study of several families of critical theories which are CFTs [14,[46][47][48][49]. Therefore it would be very interesting to push further the analysis of these conformal theories and look at the relation to Weyl invariance in curved space, including also the possible existence of obstructions.…”

Renormalization group flows between Gaussian fixed points

“…In perturbation theory, one would normally consider two cases: either Z 1 = 0 or Z 2 = 0. These CFTs have been discussed recently in [5]. Beyond perturbation theory, the action (1.2) and its generalizations containing higher derivative terms, are part of a single "theory space", where all terms can be present simultaneously.…”

“…In the chart U 1 it consists of two segments: first the line going from GFP 2 in the UV to NGFP 1 in the IR, and then the trajectory with Z2 = 0, joining NGFP 1 in the UV to GFP 1 in the IR. 5 We will be interested in the infinitely many trajectories that are contained between these two extremes, see figure 1.…”