Stefan Rechenberger

Asymptotically Safe Lorentzian Gravity

The gravitational asymptotic safety program strives for a consistent and predictive quantum theory of gravity based on a nontrivial ultraviolet fixed point of the renormalization group (RG) flow. We investigate this scenario by employing a novel functional renormalization group equation which takes the causal structure of space-time into account and connects the RG flows for Euclidean and Lorentzian signature by a Wick rotation. Within the Einstein-Hilbert approximation, the β functions of both signatures exhibit ultraviolet fixed points in agreement with asymptotic safety. Surprisingly, the two fixed points have strikingly similar characteristics, suggesting that Euclidean and Lorentzian quantum gravity belong to the same universality class at high energies.

The R^2 phase-diagram of QEG and its spectral dimension

Within the gravitational asymptotic safety program, the renormalization group (RG) flow of the

Towards an asymptotic-safety scenario for chiral Yukawa systems

{R}^{2}

A functional renormalization group equation for foliated spacetimes

truncation in three and four spacetime dimensions is analyzed in detail. In particular, we construct RG trajectories which emanate from the non-Gaussian UV fixed point and possess long classical regimes where the effective average action is well approximated by the classical Einstein-Hilbert action. As an application we study the spectral dimension of the effective quantum Einstein gravity spacetimes resulting from these trajectories, establishing that the picture of a multifractal spacetime is robust under the extension of the truncated theory space. We demonstrate that regimes of constant spectral dimension can either be attributed to universal features of RG fixed points or singular loci in the

An asymptotic safety scenario for gauged chiral Higgs–Yukawa models

\ensuremath{\beta}

Phase transition and critical behavior of d = 3 chiral fermion models with left-right asymmetry

functions.

Magnetic-field induced critical endpoint

AbstractWe search for asymptotic safety in a Yukawa system with a chiral U(NL)L  ⊗ U(1)R symmetry, serving as a toy model for the standard-model Higgs sector. Using the functional RG as a nonperturbative tool, the leading-order derivative expansion exhibits admissible non-Gaußian fixed points for 1≤NL≤57 which arise from a conformal threshold behavior induced by self-balanced boson-fermion fluctuations. If present in the full theory, the fixed point would solve the triviality problem. Moreover, as one fixed point has only one relevant direction even with a reduced hierarchy problem, the Higgs mass as well as the top mass are a prediction of the theory in terms of the Higgs vacuum expectation value. In our toy model, the fixed point is destabilized at higher order due to massless Goldstone and fermion fluctuations, which are particular to our model and have no analogue in the standard model.

Crystalline Ground States in Polyakov-loop extended Nambu--Jona-Lasinio Models

A bstractWe derive an exact functional renormalization group equation for the projectable version of Hořava-Lifshitz gravity. The flow equation encodes the gravitational degrees of freedom in terms of the lapse function, shift vector and spatial metric and is manifestly invariant under background foliation-preserving diffeomorphisms. Its relation to similar flow equations for gravity in the metric formalism is discussed in detail, and we argue that the space of action functionals, invariant under the full diffeomorphism group, forms a subspace of the latter invariant under renormalization group transformations. As a first application we study the RG flow of the Newton constant and the cosmological constant in the ADM formalism. In particular we show that the non-Gaussian fixed point found in the metric formulation is qualitatively unaffected by the change of variables and persists also for Lorentzian signature metrics.

Higher Derivative Gravity from the Universal Renormalization Group Machine

We investigate chiral Higgs–Yukawa models with a non-abelian gauged left-handed sector reminiscent to a sub-sector of the standard model. We discover a new weak-coupling fixed-point behavior that allows for ultraviolet complete RG trajectories which can be connected with a conventional long-range infrared behavior in the Higgs phase. This non-trivial ultraviolet behavior is characterized by asymptotic freedom in all interaction couplings, but a quasi conformal behavior in all mass-like parameters. The stable microscopic scalar potential asymptotically approaches flatness in the ultraviolet, however, with a non-vanishing minimum increasing inversely proportional to the asymptotically free gauge coupling. This gives rise to non-perturbative—though weak-coupling—threshold effects which induce ultraviolet stability along a line of fixed points. Despite the weak-coupling properties, the system exhibits non-Gaußian features which are distinctly different from its standard perturbative counterpart: e.g., on a branch of the line of fixed points, we find linear instead of quadratically running renormalization constants. Whereas the Fermi constant and the top mass are naturally of the same order of magnitude, our model generically allows for light Higgs boson masses. Realistic mass ratios are related to particular RG trajectories with a “walking” mid-momentum regime.

An Asymptotic-safety mechanism for chiral Yukawa systems

We investigate the critical behavior of three-dimensional relativistic fermion models with a U(N{sub L}){sub L} x U(1){sub R} chiral symmetry reminiscent of the Higgs-Yukawa sector of the standard model of particle physics. We classify all possible four-fermion interaction terms and the corresponding discrete symmetries. For sufficiently strong correlations in a scalar parity-conserving channel, the system can undergo a second-order phase transition to a chiral-symmetry broken phase, which is a 3d analog of the electroweak phase transition. We determine the critical behavior of this phase transition in terms of the critical exponent {nu} and the fermion and scalar anomalous dimensions for N{sub L{>=}}1. Our models define new universality classes that can serve as prototypes for studies of strongly correlated chiral fermions.