Indications against dynamical CPT symmetry restoration in quantum gravity

Abstract

CPT symmetry is at the heart of the Standard Model of particle physics and experimentally very well tested, but expected to be broken in some approaches to quantum gravity. It thus becomes pertinent to explore which of the two alternatives is realized: (i) CPT symmetry is emergent, so that it is restored in the low-energy theory, even if it is broken beyond the Planck scale, (ii) CPT symmetry cannot be emergent and must be fundamental, so that any approach to quantum gravity, in which CPT is broken, is ruled out. We explore this by calculating the Renormalization Group flow of CPT violating interactions under the impact of quantum fluctuations of the metric. We find that CPT symmetry cannot be emergent and conclude that quantum-gravity approaches must avoid the breaking of CPT symmetry. As a specific example, we discover that in asymptotically safe quantum gravity CPT symmetry remains intact, if it is imposed as a fundamental symmetry, but it is badly broken at low energies if a tiny amount of CPT violation is present in the transplanckian regime.

Figures (7)

• Figure 1: Diagrams which contribute to the anomalous scaling dimension of the CPT-violating couplings. The double lines represent metric fluctuations, while the curly line represents any matter field, i.e., scalars, fermions or gauge fields. The dashed line with cross indicates the insertion of the external vector field $n_{\mu}$, which can sit either at the vertex or the propagator. The FRG-regulator can be inserted on either of the internal lines of a given diagram.
• Figure 2: Region in the gravitational parameter space, where $f_{\gamma}>0$ (orange), and $f_{\phi}>0$ (blue). We show the small overlap of both regions in green. In this region, CPT symmetry in the scalar and gauge sector is emergent. In contrast, violations of CPT symmetry in the fermion sector still grow towards low energies, even in the green region. The red star indicates the asymptotically safe fixed point for Standard Model matter content Christiansen:2017bsy. Its size should not be understood as an estimation of systematic uncertainties; those are expected to be larger.
• Figure 3: Gauge dependence of $f_{\gamma}$. Blue: allowed regions for $\Lambda$, orange: region where $f_{\gamma}>0$. For $\beta_h<1.5$ the orange region is almost gauge-independent.
• Figure 4: Gauge dependence of $f_{\phi}$. The blue line shows the value of $G$ above which $f_{\phi}$ is positive, while the orange line shows where the scalar sector acquires an additional relevant direction, indication the onset of a strong gravity regime.
• Figure 5: Gauge dependence of $f_{\psi}$. Blue: allowed regions for $\Lambda$, orange: region where $f_{\psi}>0$.