Signatures of gravitational fixed points at the LHC

We study quantum-gravitational signatures at the CERN Large Hadron Collider (LHC) in the context of theories with extra spatial dimensions and a low fundamental Planck scale in the TeV range. Implications of a gravitational fixed point at high energies are worked out using Wilson¿s renormalization group. We find that relevant cross sections involving virtual gravitons become finite. Based on gravitational lepton pair production we conclude that the LHC is sensitive to a fundamental Planck scale of up to 6 TeV

Towards Functional Flows for Hierarchical Models

The recursion relations of hierarchical models are studied and contrasted with functional renormalisation group equations in corresponding approximations. The formalisms are compared quantitatively for the Ising universality class, where the spectrum of universal eigenvalues at criticality is studied. A significant correlation amongst scaling exponents is pointed out and analysed in view of an underlying optimisation. Functional flows are provided which match with high accuracy all known scaling exponents from Dyson's hierarchical model for discrete block-spin transformations. Implications of the results are discussed.Comment: 17 pages, 4 figures; wording sharpened, typos removed, reference added; to appear with PR

Completeness and consistency of renormalisation group flows

We study different renormalisation group flows for scale dependent effective actions, including exact and proper-time renormalisation group flows. These flows have a simple one loop structure. They differ in their dependence on the full field-dependent propagator, which is linear for exact flows. We investigate the inherent approximations of flows with a non-linear dependence on the propagator. We check explicitly that standard perturbation theory is not reproduced. We explain the origin of the discrepancy by providing links to exact flows both in closed expressions and in given approximations. We show that proper-time flows are approximations to Callan-Symanzik flows. Within a background field formalism, we provide a generalised proper-time flow, which is exact. Implications of these findings are discussed.Comment: 33 pages, 15 figures, revtex, typos corrected, to be published in Phys.Rev.

Ising exponents from the functional renormalisation group

We study the 3d Ising universality class using the functional renormalisation group. With the help of background fields and a derivative expansion up to fourth order we compute the leading index, the subleading symmetric and anti-symmetric corrections to scaling, the anomalous dimension, the scaling solution, and the eigenperturbations at criticality. We also study the cross-correlations of scaling exponents, and their dependence on dimensionality. We find a very good numerical convergence of the derivative expansion, also in comparison with earlier findings. Evaluating the data from all functional renormalisation group studies to date, we estimate the systematic error which is found to be small and in good agreement with findings from Monte Carlo simulations, \epsilon-expansion techniques, and resummed perturbation theory.Comment: 24 pages, 3 figures, 7 table

Asymptotic safety and Kaluza-Klein gravitons at the LHC

We study Drell-Yan production at the LHC in low-scale quantum gravity models with extra dimensions. Asymptotic safety implies that the ultra-violet behavior of gravity is dictated by a fixed point. We show how the energy dependence of Newton's coupling regularizes the gravitational amplitude using a renormalization group improvement. We study LHC predictions and find that Kaluza-Klein graviton signals are well above Standard Model backgrounds. This leaves a significant sensitivity to the energy scale Lambda_T where the gravitational couplings cross over from classical to fixed point scaling.Comment: 25 pages, 14 figure

Gauge invariance, background fields and modified Ward identities

In this talk the gauge symmetry for Wilsonian flows in pure Yang-Mills theories is discussed. The background field formalism is used for the construction of a gauge invariant effective action. The symmetries of the effective action under gauge transformations for both the gauge field and the auxiliary background field are separately evaluated. Modified Ward-Takahashi and background field identities are used in my study. Finally it is shown how the symmetry properties of the full theory are restored in the limit where the cut-off is removed.Comment: 6 pages, to appear in the Proceedings of the 2nd Conference on the Exact Renormalization Group, Rome 200

Optimization of field-dependent nonperturbative renormalization group flows

We investigate the influence of the momentum cutoff function on the field-dependent nonperturbative renormalization group flows for the three-dimensional Ising model, up to the second order of the derivative expansion. We show that, even when dealing with the full functional dependence of the renormalization functions, the accuracy of the critical exponents can be simply optimized, through the principle of minimal sensitivity, which yields $\nu = 0.628$ and $\eta = 0.044$.Comment: 4 pages, 3 figure

Further evidence for asymptotic safety of quantum gravity

The asymptotic safety conjecture is examined for quantum gravity in four dimensions. Using the renormalisation group, we find evidence for an interacting UV fixed point for polynomial actions up to the 34th power in the Ricci scalar. The extrapolation to infinite polynomial order is given, and the self-consistency of the fixed point is established using a bootstrap test. All details of our analysis are provided. We also clarify further aspects such as stability, convergence, the role of boundary conditions, and a partial degeneracy of eigenvalues. Within this setting we find strong support for the conjecture

Asymptotic safety with Majorana fermions and new large N equivalences

Using Majorana fermions and elementary mesons we find new massless quantum field theories with weakly interacting ultraviolet fixed points. We also find new classes of large N equivalences among SU, SO, and Sp gauge theories with different types of matter fields and Yukawa interactions. Results include a triality of asymptotically safe theories and dualities between asymptotically free matter-gauge theories with identical fixed points, phase diagrams, and scaling exponents. Implications for conformal field theory and orbifold reductions are indicated