Search

We study the generation of fermion mass in a context where interactions break a discrete chiral symmetry. Then, fermion mass is not protected by a symmetry, no symmetry is broken by the generation of mass, and a vanishing mass no longer enhances a symmetry. We elaborate these scenarios for template fermionic and Yukawa theories in three dimensions where mass can be generated either by fluctuations, strong dynamics, or the vacuum expectation value of a scalar field. We find that fluctuation-induced contributions to fermion mass are parametrically suppressed in the number of fermion flavours $N$. The generation of fermion mass then takes the form of a rapid crossover which turns into a second order quantum phase transition for large $N$, much like in settings with fundamental chiral symmetry. We further discuss theories where fermion mass can be generated spontaneously without breaking any symmetry other than scale symmetry. Implications of our findings are discussed., Comment: 21 pages, 6 figures; v2: 2 figures and clarifications added, version accepted for publication in PRD

We revisit the stability of the Standard Model vacuum, and investigate its quantum effective potential using the highest available orders in perturbation theory and the most accurate determination of input parameters to date. We observe that the stability of the electroweak vacuum centrally depends on the values of the top mass and the strong coupling constant. We estimate that reducing their uncertainties by a factor of two to three is sufficient to establish or refute SM vacuum stability at the $5\sigma$ level. We further investigate vacuum stability for a variety of singlet scalar field extensions with and without flavor using the Higgs portal mechanism. We identify the BSM parameter spaces for stability and find sizable room for new physics. We further study the phenomenology of Planck-safe models at colliders, and determine the impact on the Higgs trilinear, the Higgs-to-electroweak-boson, and the Higgs quartic couplings, some of which can be significant. The former two can be probed at the HL-LHC, the latter requires a future collider with sufficient energy and precision such as the FCC-hh., Comment: v2: Numerical typo in SM input fixed and Tab. 1, Figs. 1, 2 and related text corrected, clarifications to App A. added

We study an asymptotically free theory of $N$ relativistic Dirac fermions and a real scalar field coupled by Yukawa and scalar self-interactions in three dimensions using functional renormalisation. In the limit of many fermion flavours, the cubic scalar coupling becomes exactly marginal due to quantum fluctuations, leading to a line of strongly-coupled infrared fixed points. Fermion mass can be generated through a quantum phase transition even if chiral symmetry is absent. The line of fixed points terminates at a critical endpoint due to the loss of vacuum stability. Exactly at the endpoint, scale symmetry is broken spontaneously, leading to the generation of fermion mass. Intriguingly, the absence of chiral symmetry is a prerequisite for the spontaneous generation of fermion mass, and not a consequence thereof. We also highlight close similarities between Gross-Neveu and Gross-Neveu--Yukawa theories at and away from critical points, and establish the large-$N$ equivalence of their functional RG flows and quantum effective actions. Further implications including for conformal field theories are indicated., Comment: 24 pages, 5 figures; v2: text added to conclusion, version published in JHEP

The recent LHCb determination of the direct CP asymmetries in the decays $D^0 \to K^+ K^-, \pi^+ \pi^-$ hints at a sizeable breaking of two approximate symmetries of the SM: CP and U-spin. We aim at explaining the data with BSM physics and use the framework of flavorful $Z^\prime$ models. Interestingly, experimental and theoretical constraints very much narrow down the shape of viable models: Viable, anomaly-free models are electron- and muon-phobic and feature a light $Z^\prime$ of 10-20 GeV coupling only to right-handed fermions. The $Z^\prime$ can be searched for in low mass dijets or at the LHC as well as dark photon searches. A light $Z^\prime$ of $\sim$ 3 GeV or $\sim$ 5-7 GeV can moreover resolve the longstanding discrepancy in the $J/\psi, \psi^\prime$ branching ratios with pion form factors from fits to $e^+ e^- \to \pi^+ \pi^-$ data, and simultaneously explain the charm CP asymmetries. Smoking gun signatures for this scenario are $\Upsilon$ and charmonium decays into pions, taus or invisbles., Comment: 2 pages, 4 figures

We investigate a family of four-dimensional quantum field theories with weakly interacting ultraviolet fixed points up to four loop order in perturbation theory. Key new ingredients are the three loop gauge contributions to quartic scalar beta functions, which we compute in the $\overline{\text{MS}}$ scheme for a template $SU(N_c)$ gauge theory coupled to $N_f$ fundamental fermions and elementary scalars. We then determine fixed point couplings, field and mass anomalous dimensions, and universal scaling exponents up to the first three non-trivial orders in a small Veneziano parameter. The phase diagram and UV-IR connecting trajectories are found and contrasted with asymptotic freedom. Further, the size of the conformal window, unitarity, and mechanisms leading to the loss of conformality are investigated. Our results provide blueprints for concrete 4d non-supersymmetric conformal field theories with standard model-like field content, and invite further model building., Comment: 17 pages, 2 external figures; v2: finite-N RGEs provided in appendix, minor adjustments, v3: new figure; match published version

We explain why vector-like fermions are natural candidates to lift the Standard Model vacuum instability. Results are further discussed from the viewpoint of criticality. Several models allow for vector-like quarks and leptons in the TeV-range which can be searched for at the LHC., Comment: Proceedings Moriond EW 2023, 6 pages, 5 figures

We study relativistic fermions in three euclidean dimensions with four- and six-fermion interactions of the Gross-Neveu type. In the limit of many fermion flavors, and besides the isolated free fixed point, the theory displays a line of interacting ultraviolet fixed points. At the endpoint of the critical line, we establish that mass is generated through the spontaneous breaking of quantum scale invariance. Curiously, broken parity symmetry is a prerequisite for the spontaneous generation of mass rather than a consequence thereof. We also calculate critical exponents and find that hyperscaling relations are violated. Further similarities with critical scalar theories, and implications for conformal field theories and higher spin theories are discussed., Comment: 8 pages, 1 figure; v2: clarifications in Sec.V, accepted for publication in Physical Review D

The recent measurement of the CP-asymmetry in the decay $D \to K^+ K^-$ by LHCb, combined with $\Delta A_{\text{CP}}$, evidences a sizable CP-asymmetry in $D \to \pi^+ \pi^-$ decays, which requires a dynamical enhancement of standard model higher-order contributions over tree-level ones by a factor of two. The data furthermore imply huge U-spin breaking, about 4-5 times larger than the nominal standard model one of $\lesssim 30 \%$ in charm. Enhanced breakdown of the two approximate symmetries points to models that violate U-spin and CP and disfavors flavor singlet contributions such as chromomagnetic dipole operators as explanations of the data. We analyze the reach of flavorful $Z^\prime$ models for charm CP-asymmetries. Models feature explicit U-spin and isospin breaking, allowing for correlations with $D \to \pi^0 \pi^0$ and $D^+ \to \pi^+ \pi^0$ decays with corresponding CP-asymmetries at a similar level and sign as $D \to \pi^+ \pi^-$, about $ {\cal{O}}(1-2) \cdot 10^{-3}$. Experimental and theoretical constraints narrow down the shape of viable models: anomaly-free models are leptophobic -- or at least electro- and muo-phobic -- with light $Z^\prime$ below ${\cal{O}}(20)$ GeV, and can be searched for in low mass dijets at the LHC, $\Upsilon$ and charmonium decays, and dark photon signatures. A $Z^\prime$ around $\sim 3$ GeV or $\sim (5-7)$ GeV can relieve the tensions in the $J/\psi \to \pi^+ \pi^-$ and $\psi^\prime \to \pi^+ \pi^-$ branching ratios with pion form factors from fits to Babar and JLab data, and simultaneously explain the charm CP asymmetries. Models also feature sizable branching ratios into light right-handed neutrinos or vector-like dark fermions, which can be searched for in $e^+ e^- \to$~hadrons + invisibles at Belle II and BESIII. Due to the low new physics scale dark fermions may induce an early Landau pole which requires UV-completion near the TeV-scale., Comment: 13 pages, 5 figures. v2: Fig.1 and discussion on U-Spin improved, minor corrections and references added, v3: match published version

Evidence for almost spatial flatness of the Universe has been provided from several observational probes, including the Cosmic Microwave Background (CMB) and Baryon Acoustic Oscillations (BAO) from galaxy clustering data. However, other than inflation, and in this case only in the limit of infinite time, there is no strong a priori motivation for a spatially flat Universe. Using the renormalization group (RG) technique in curved spacetime, we present in this work a theoretical motivation for spatial flatness. Starting from a general spacetime, the first step of the RG, coarse-graining, gives a Friedmann-Lema\^itre-Robertson-Walker (FLRW) metric with a set of parameters. Then, we study the rescaling properties of the curvature parameter, and find that zero spatial curvature of the FLRW metric is singled out as the unique scale-free, non-singular background for cosmological perturbations., Comment: Matches accepted version to JCAP; minor changes; conclusions unchanged

In the limit of many fermion flavors it is demonstrated that the sextic Gross-Neveu theory in three dimensions displays a line of interacting UV fixed points, characterised by an exactly marginal sextic interaction. We determine the conformal window of UV-complete theories, universal scaling dimensions, and the phase diagram using renormalisation group methods. Massless theories arise naturally, and the generation of mass proceeds without the breaking of a discrete symmetry. Striking similarities with critical scalar theories at large $N$ are highlighted, and implications from the viewpoint of conformal field theory and the AdS/CFT conjecture are indicated., Comment: 6 pages, 4 figures; v2: reasoning and Fig. 2 improved, accepted for publication with Physical Review Letters

We address the notorious metastability of the standard model (SM) and promote it to a model building task: What are the new ingredients required to stabilize the SM up to the Planck scale without encountering subplanckian Landau poles? Using the SM extended by vector-like fermions (VLFs), we chart out the corresponding landscape of Higgs stability. We find that the gauge portal mechanism, triggered by new SM charge carriers, opens up sizeable room for stability in a minimally invasive manner. We also find models with Higgs criticality, and Yukawa portals opening up at stronger coupling. Several models allow for VLFs in the TeV-range, which can be searched for at the LHC. For nontrivial flavor structure severe flavor-changing neutral current constraints arise which complement those from stability, and push lower fermion masses up to $\mathcal{O}(10^3\,\text{TeV})$., Comment: 18 pages, 16 figures. v2: match published version

We derive new functional renormalisation group flows for quantum gravity, in any dimension. The key new achievement is that the equations apply for any theory of gravity whose underlying Lagrangian $\sim f(R_{\mu\nu\rho\sigma})$ is a function of the Riemann tensor and the inverse metric. The results centrally exploit the benefits of maximally symmetric spaces for the evaluation of operator traces. The framework is highly versatile and offers a wide range of new applications to study quantum gravitational effects in extensions of Einstein gravity, many of which have hitherto been out of reach. The phase diagram and sample flows for Einstein-Hilbert gravity, Gauss-Bonnet, and selected higher-order theories of gravity are given. We also provide an algorithm to find the flow for general polynomial Riemann curvature interactions. The setup vastly enhances the reach of fixed point searches, enabling novel types of search strategies including across the operator space spanned by polynomial curvature invariants, and in extensions of general relativity relevant for cosmology. Further implications, and links with unimodular versions of gravity are indicated., Comment: 49 pages, 3 figures, v2: clarifications added, typos removed, to appear with PRD

We demonstrate that interacting ultraviolet fixed points in four dimensions exist at strong coupling, and away from large-$N$ Veneziano limits. This is established exemplarily for semi-simple supersymmetric gauge theories with chiral matter and superpotential interactions by using the renormalisation group and exact methods from supersymmetry. We determine the entire superconformal window of ultraviolet fixed points as a function of field multiplicities. Results are in accord with the $a$-theorem, bounds on conformal charges, Seiberg duality, and unitary. We also find manifolds of Leigh-Strassler models exhibiting lines of infrared fixed points. At weak coupling, findings are confirmed using perturbation theory up to three loop. Benchmark models with low field multiplicities are provided including examples with Standard~Model-like gauge sectors. Implications for particle physics, model building, and conformal field theory are indicated., Comment: 17 pages, 7 figures

We search for weakly interacting fixed points in extensions of the minimally supersymmetric standard model (MSSM). Necessary conditions lead to three distinct classes of anomaly-free extensions involving either new quark singlets, new quark doublets, or a fourth generation. While interacting fixed points arise prolifically in asymptotically free theories, their existence is significantly constrained as soon as some of the non-abelian gauge sectors are infrared free. Performing a scan over $\sim 200$k different MSSM extensions using matter field multiplicities and the number of superpotential couplings as free parameters, we find mostly infrared conformal fixed points, and a small subset with ultraviolet ones. All settings predict low-scale supersymmetry-breaking and a violation of $R$-parity. Despite of residual interactions, the running of couplings out of asymptotically safe fixed points is logarithmic as in asymptotic freedom. Some fixed points can be matched to the Standard Model though the matching scale comes out too low. Prospects for higher matching scales and asymptotic safety beyond the MSSM are indicated., Comment: 26 pages, 9 figures

We present the first direct and non-perturbative computation of the graviton spectral function in quantum gravity. This is achieved with the help of a novel Lorentzian renormalisation group approach, combined with a spectral representation of correlation functions. We find a positive graviton spectral function, showing a massless one-graviton peak and a multi-graviton continuum with an asymptotically safe scaling for large spectral values. We also study the impact of a cosmological constant. Further steps to investigate scattering processes and unitarity in asymptotically safe quantum gravity are indicated., Comment: 12 pages, 7 figures, journal-published version

$U(1)^\prime$ extensions of the standard model with generation-dependent couplings to quarks and leptons are investigated as an explanation of anomalies in rare $B$-decays, with an emphasis on stability and predictivity up to the Planck scale. To these ends, we introduce three generations of vector-like standard model singlet fermions, an enlarged, flavorful scalar sector, and, possibly, right-handed neutrinos, all suitably charged under the $U(1)^\prime$ gauge interaction. We identify several gauge-anomaly free benchmarks consistent with $B_s$-mixing constraints, with hints for electron-muon universality violation, and the global $b \to s$ fit. We further investigate the complete two-loop running of gauge, Yukawa and quartic couplings up to the Planck scale to constrain low-energy parameters and enhance the predictive power. A characteristic of models is that the $Z^\prime$ with TeV-ish mass predominantly decays to invisibles, i.e. new fermions or neutrinos. $Z^\prime$-production can be studied at a future muon collider. While benchmarks feature predominantly left-handed couplings $C_9^{\mu}$ and $C_{10}^{\mu}$, right-handed ones can be accommodated as well., Comment: 22 pages, 15 figures, v2: match published version

We study four-dimensional gauge theories coupled to fermions in the fundamental and meson-like scalars. All requisite beta functions are provided for general gauge group and fermion representation. In the regime where asymptotic freedom is absent, we determine all interacting fixed points using perturbation theory up to three loop in the gauge and two loop in the Yukawa and quartic couplings. We find that the conformal window of ultraviolet fixed points is narrowed-down by finite-$N$ corrections beyond the Veneziano limit. We also find a new infrared fixed point whose main features such as scaling exponents, UV-IR connecting trajectories, and phase diagram are provided. Both fixed points collide upon varying the number of fermion flavours $N_{\rm f}$, and conformality is lost through a saddle-node bifurcation. We further revisit the prospect for ultraviolet fixed points in the large $N_{\rm f}$ limit where matter field fluctuations dominate. Unlike at weak coupling, we do not find clear evidence for new scaling solutions even in the presence of scalar and Yukawa couplings., Comment: 20 pages, 10 figures

We present the initial release of ARGES, a toolkit for obtaining renormalisation group equations in perturbation theory. As such, ARGES can handle any perturbatively renormalisable four-dimensional quantum field theory. Notable further features include a symbolic rather than numeric computation, input of unconventional scalar and Yukawa sectors, an interactive evaluation and disentanglement as well as capabilities to inject algebraic simplification rules. We provide a conceptual and practical introduction into ARGES, and highlight similarities and differences with complementary packages., Comment: 17 pages, 0 figures, added preprint number and corrected some details regarding PyR@TE3, v3: fix typo in sec. 5.3 and match published version

We investigate collider signatures of standard model extensions featuring vector-like leptons and a flavorful scalar sector. Such a framework arises naturally within asymptotically safe model building, which tames the UV behavior of the standard model towards the Planck scale and beyond. We focus on values of Yukawa couplings and masses which allow to explain the present data on the muon and electron anomalous magnetic moments. Using a CMS search based on $77.4 \, \rm{fb}^{-1}$ at the $\sqrt{s}=13$ TeV LHC we find that flavorful vector-like leptons are excluded for masses below around $300$ GeV if they are singlets under $SU(2)_L$, and around $800$ GeV if they are doublets. Exploiting the flavor-violating-like decays of the scalars, we design novel null test observables based on opposite sign opposite flavor invariant masses. These multi-lepton distributions allow to signal new physics and to extract mass hierarchies in reach of near-future searches at the LHC and the HL-LHC., Comment: 32 pages, 17 figures

We perform a comprehensive search for Standard Model extensions inspired by asymptotic safety. Our models feature a singlet matrix scalar field, three generations of vector-like leptons, and direct links to the Higgs and flavor sectors via new Yukawa and portal couplings. A novel feature is that the enlarged scalar sector may spontaneously break lepton flavor universality. We provide a complete two-loop renormalization group analysis of the running gauge, Yukawa, and quartic couplings to find ultraviolet fixed points and the BSM critical surface of parameters, $i.e.$ the set of boundary conditions at the TeV scale for which models remain well-behaved and predictive up to the Planck scale without encountering Landau poles or instabilities. This includes templates for asymptotically safe Standard Model extensions which match the measured values of gauge couplings and the Higgs, top, and bottom masses. We further detail the phenomenology of our models covering production, decay, fermion mixing, anomalous magnetic moments, effects from scalar mixing and chiral enhancement, and constraints on model parameters from data. Signatures at proton-proton and lepton colliders such as lepton flavor violation and displaced vertices, and the prospect for electric dipole moments or charged lepton-flavor-violating type processes, are also indicated., Comment: 40 pages, 23 figures, 11 tables

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 amongst 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., Comment: Typos in Tab.1 and eq. (11) removed

The measurements of the muon and electron anomalous magnetic moments hint at physics beyond the standard model. We show why and how models inspired by asymptotic safety can explain deviations from standard model predictions naturally. Our setup features an enlarged scalar sector and Yukawa couplings between leptons and new vector-like fermions. Using the complete two-loop running of couplings, we observe a well-behaved high energy limit of models including a stabilization of the Higgs. We find that a manifest breaking of lepton universality beyond standard model Yukawas is not necessary to explain the muon and electron anomalies. We further predict the tau anomalous magnetic moment, and new particles in the TeV energy range whose signatures at colliders are indicated. With small CP phases, the electron EDM can be as large as the present bound., Comment: 5 pages, 4 figures; v2: explanations expanded and references added, conclusions unchanged; match with published version

We derive all heat kernel coefficients for Laplacians acting on scalars, vectors, and tensors on fully symmetric spaces, in any dimension. Final expressions are easy to evaluate and implement, and confirmed independently using spectral sums and the Euler-Maclaurin formula. We also obtain the Green's function for Laplacians acting on transverse traceless tensors in any dimension, and new integral representations for heat kernels using known eigenvalue spectra of Laplacians. Applications to quantum gravity and the functional renormalisation group, and other, are indicated., Comment: 33 pages, v2: results on spectral integrals and analytic continuation added; matches with published version

We investigate asymptotically safe extensions of the Standard Model with new matter fields arising in the TeV energy range. The new sector contains singlet scalars and vector-like fermions in representations which permit Yukawa interactions with the Standard Model leptons. Phenomenological implications are explored including charged lepton flavour violation, Drell-Yan processes and lepton anomalous magnetic moments. For the latter, we find that BSM contributions can be sizeable enough to explain the present experimental discrepancies of the electron and muon anomalous magnetic moments with the Standard Model., Comment: 4 pages, 4 figures. Contribution to the 2019 EW session of the 54th Rencontres de Moriond

We study fixed points of quantum gravity with renormalisation group methods, and a procedure to remove convergence-limiting poles from the flow. The setup is tested within the $f(R)$ approximation for gravity by solving exact recursive relations up to order $R^{70}$ in the Ricci scalar, combined with resummations and numerical integration. Results include fixed points, scaling exponents, gap in the eigenvalue spectrum, dimensionality of the UV critical surface, fingerprints for weak coupling, and quantum equations of motion. Our findings strengthen the view that ``most of quantum gravity'' is rather weakly coupled. Another novelty are a pair of de Sitter solutions for quantum cosmology, whose occurrence is traced back to the removal of poles. We also address slight disparities of results in the literature, and give bounds on the number of fundamentally free parameters of quantum gravity., Comment: 29 pages, 7 figures, v2: explanations added, to appear with PRD

We study $3d$ $O(N)$ symmetric scalar field theories using Polchinski's renormalisation group. In the infinite $N$ limit the model is solved exactly including at strong coupling. At short distances the theory is described by a line of asymptotically safe ultraviolet fixed points bounded by asymptotic freedom at weak, and the Bardeen-Moshe-Bander phenomenon at strong sextic coupling. The Wilson-Fisher fixed point arises as an isolated low-energy fixed point. Further results include the conformal window for asymptotic safety, convergence-limiting poles in the complex field plane, and the phase diagram with regions of first and second order phase transitions. We substantiate a duality between Polchinski's and Wetterich's versions of the functional renormalisation group, also showing that that eigenperturbations are identical at any fixed point. At a critical sextic coupling, the duality is worked out in detail to explain the spontaneous breaking of scale symmetry responsible for the generation of a light dilaton. Implications for asymptotic safety in other theories are indicated., Comment: 39 pages, 10 figures. v2: explanations and figure added, accepted for publication with PRD

All known examples of four dimensional quantum field theories with asymptotic freedom or asymptotic safety at weak coupling involve non-abelian gauge interactions. We demonstrate that this is not a coincidence: no weakly coupled fixed points, ultraviolet or otherwise, can be reliably generated in theories lacking gauge interactions. Implications for particle physics, critical phenomena, and conformal field theory are indicated., Comment: 4 pages, 1 table. v2: discussion and outlook expanded, references added, to appear with PRL

We investigate the asymptotic safety conjecture for quantum gravity including curvature invariants beyond Ricci scalars. Our strategy is put to work for families of gravitational actions which depend on functions of the Ricci scalar, the Ricci tensor, and products thereof. Combining functional renormalisation with high order polynomial approximations and full numerical integration we derive the renormalisation group flow for all couplings and analyse their fixed points, scaling exponents, and the fixed point effective action as a function of the background Ricci curvature. The theory is characterised by three relevant couplings. Higher-dimensional couplings show near-Gaussian scaling with increasing canonical mass dimension. We find that Ricci tensor invariants stabilise the UV fixed point and lead to a rapid convergence of polynomial approximations. We apply our results to models for cosmology and establish that the gravitational fixed point admits inflationary solutions. We also compare findings with those from $f(R)$-type theories in the same approximation and pin-point the key new effects due to Ricci tensor interactions. Implications for the asymptotic safety conjecture of gravity are indicated., Comment: 55 pages, 14 figures. v2: Added more discussion and new Sec.2E (Gravitational path integral). Version accepted for publication with PRD

Interacting fixed points in four-dimensional gauge theories coupled to matter are investigated using perturbation theory up to three loop order. It is shown how fixed points, scaling exponents, and anomalous dimensions are obtained as a systematic power series in a small parameter. The underlying ordering principle is explained and contrasted with conventional perturbation theory and Weyl consistency conditions. We then determine the conformal window with asymptotic safety from the complete next-to-next-to-leading order in perturbation theory. Limits for the conformal window arise due to fixed point mergers, the onset of strong coupling, or vacuum instability. A consistent picture is uncovered by comparing various levels of approximation. The theory remains perturbative in the entire conformal window, with vacuum stability dictating the tightest constraints. We also speculate about a secondary conformal window at strong coupling and estimate its lower limit. Implications for model building and cosmology are indicated., Comment: 14 pages, 2 figures, 2 tables. v2: Added some discussion and references. New appendix with details of two-loop quartic calculations. Version accepted for publication in PRD

We study the asymptotic safety conjecture for quantum gravity in the presence of matter fields. A general line of reasoning is put forward explaining why gravitons dominate the high-energy behaviour, largely independently of the matter fields as long as these remain sufficiently weakly coupled. Our considerations are put to work for gravity coupled to Yang-Mills theories with the help of the functional renormalisation group. In an expansion about flat backgrounds, explicit results for beta functions, fixed points, universal exponents, and scaling solutions are given in systematic approximations exploiting running propagators, vertices, and background couplings. Invariably, we find that the gauge coupling becomes asymptotically free while the gravitational sector becomes asymptotically safe. The dependence on matter field multiplicities is weak. We also explain how the scheme dependence, which is more pronounced, can be handled without changing the physics. Our findings offer a new interpretation of many earlier results, which is explained in detail. The results generalise to theories with minimally coupled scalar and fermionic matter. Some implications for the ultraviolet closure of the Standard Model or its extensions are given., Comment: 29 pages, 18 figures, 1 table; v2: extended discussion in Sec. 2, refs updated; v3: matches journal version

We explain how asymptotic safety arises in four-dimensional supersymmetric gauge theories. We provide asymptotically safe supersymmetric gauge theories together with their superconformal fixed points, R-charges, phase diagrams, and UV-IR connecting trajectories. Strict perturbative control is achieved in a Veneziano limit. Consistency with unitarity and the a-theorem is established. We find that supersymmetry enhances the predictivity of asymptotically safe theories., Comment: 4 pages, 3 figures, 2 tables. v2: typo corrected, minor clarification added; version published in PRL

We study interacting fixed points and phase diagrams of simple and semi-simple quantum field theories in four dimensions involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. Particular emphasis is put on new phenomena which arise due to the semisimple nature of the theory. Using matter field multiplicities as free parameters, we find a large variety of interacting conformal fixed points with stable vacua and crossovers inbetween. Highlights include semi-simple gauge theories with exact asymptotic safety, theories with one or several interacting fixed points in the IR, theories where one of the gauge sectors is both UV free and IR free, and theories with weakly interacting fixed points in the UV and the IR limits. The phase diagrams for various simple and semi-simple settings are also given. Further aspects such as perturbativity beyond the Veneziano limit, conformal windows, and implications for model building are discussed., Comment: 62 pages, 16 figures, 9 tables. v2: References added, minor typos corrected; version accepted for publication in PRD

We investigate critical $N$-component scalar field theories and the spontaneous breaking of scale invariance in three dimensions using functional renormalisation. Global and local renormalisation group flows are solved analytically in the infinite $N$ limit to establish the phase diagram including the Wilson-Fisher fixed point and a line of asymptotically safe UV fixed points characterised by an exactly marginal sextic coupling. We also study the Bardeen-Moshe-Bander phenomenon of spontaneously broken scale invariance and the stability of the vacuum for general regularisation. Our findings clarify a long-standing puzzle about the apparent unboundedness of the effective potential. Implications for other theories are indicated., Comment: v2: 31 pages, 6 figures; explanations and refs added, figs improved, to appear (PRD)

Building on recent advances in the understanding of gauge-Yukawa theories we explore possibilities to UV-complete the Standard Model in an asymptotically safe manner. Minimal extensions are based on a large flavor sector of additional fermions coupled to a scalar singlet matrix field. We find that asymptotic safety requires fermions in higher representations of $SU(3)_C\times SU(2)_L$. Possible signatures at colliders are worked out and include $R$-hadron searches, diboson signatures and the evolution of the strong and weak coupling constants., Comment: 52 pages, 23 figures, 7 tables, published version. v2: clarifications and results (weak sector, Fig 18) added, some plots updated post-Moriond 2017, typos removed

The Wilson-Fisher fixed point with $O(N)$ universality in three dimensions is studied using the renormalisation group. It is shown how a combination of analytical and numerical techniques determine global fixed point solutions to leading order in the derivative expansion for real or purely imaginary fields with moderate numerical effort. Universal and non-universal quantitites such as scaling exponents and mass ratios are computed, for all $N$, together with local fixed point coordinates, radii of convergence, and parameters which control the asymptotic behaviour of the effective action. We also explain when and why finite-$N$ results do not converge pointwise towards the exact infinite-$N$ limit. In the regime of purely imaginary fields, a new link between singularities of fixed point effective actions and singularities of their counterparts by Polchinski are established. Implications for other theories are indicated., Comment: 28 pages, 10 figures, v2: explanations and refs added, to appear (NPB)

We classify the weakly interacting fixed points of general gauge theories coupled to matter and explain how the competition between gauge and matter fluctuations gives rise to a rich spectrum of high- and low-energy fixed points. The pivotal role played by Yukawa couplings is emphasized. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated., Comment: 21 pages, 5 figures, 3 tables. v2: results for supersymmetry added; to appear (EPJC)

The availability of scaling solutions in renormalisation group improved versions of cosmology are investigated in the high-energy limit. We adopt $f(R)$-type models of quantum gravity which display an interacting ultraviolet fixed point at shortest distances. Expanding the gravitational fixed point action to very high order in the curvature scalar, we detect a convergence-limiting singularity in the complex field plane. Resummation techniques including Pad\'e approximants as well as infinite order approximations of the effective action are used to maximise the domain of validity. We find that the theory displays near de Sitter solutions as well as an anti-de Sitter solution in the UV whereas real de Sitter solutions, for small curvature, appear to be absent. The significance of our results for inflation, and implications for more general models of quantum gravity are discussed., Comment: 27 pages, 11 figures, 3 tables. v2: explanations added, to appear with CQG

Local and global scaling solutions for $O(N)$ symmetric scalar field theories are studied in the complexified field plane with the help of the renormalisation group. Using expansions of the effective action about small, large, and purely imaginary fields, we obtain and solve exact recursion relations for all couplings and determine the $3d$ Wilson-Fisher fixed point analytically. For all $O(N)$ universality classes, we further establish that Wilson-Fisher fixed point solutions display singularities in the complex field plane, which dictate the radius of convergence for real-field expansions of the effective action. At infinite $N$, we find closed expressions for the convergence-limiting singularities and prove that local expansions of the effective action are powerful enough to uniquely determine the global Wilson-Fisher fixed point for any value of the fields. Implications of our findings for interacting fixed points in more complicated theories are indicated., Comment: 36 pages, 9 figures, Sec IV H and Refs added

We study the phase diagram and the stability of the ground state for certain four-dimensional gauge-Yukawa theories whose high-energy behaviour is controlled by an interacting fixed point. We also provide analytical and numerical results for running couplings, their crossover scales, the separatrix, and the Coleman-Weinberg effective potential. Classical and quantum stability of the vacuum is established., Comment: 22 pages, 7 figures; explanations added, match with published version

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., Comment: 44 pages, 17 figures, explanations and Sec VII D added; to appear (PRD)

We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet fixed points, strictly controlled by perturbation theory. Extensions towards strong coupling and beyond the large-N limit are discussed., Comment: 31 pages, 7 figures, explanations and references added, typos corrected; to appear (JHEP)

We study quantum gravity effects for Myers-Perry black holes assuming that the leading contributions arise from the renormalization group evolution of Newton's coupling. Provided that gravity weakens following the asymptotic safety conjecture, we find that quantum effects lift a degeneracy of higher-dimensional black holes, and dominate over kinematical ones induced by rotation, particularly for small black hole mass, large angular momentum, and higher space-time dimensionality. Quantum-corrected space-times display inner and outer horizons, and show the existence of a black hole of smallest mass in any dimension. Ultra-spinning solutions no longer persist. Thermodynamic properties including temperature, specific heat, the Komar integrals, and aspects of black hole mechanics are studied as well. Observing a softening of the ring singularity, we also discuss the validity of classical energy conditions.

A coarse-grained version of the effective action is used to study the thermodynamics of black holes, interpolating from largest to smallest masses. The physical parameter of the black hole are linked to the running couplings by thermodynamics, and the corresponding equation of state includes quantum corrections for temperature, specific heat, and entropy. If quantum gravity becomes asymptotically safe, the state function predicts conformal scaling in the limit of small horizon area, and bounds on black hole mass and temperature. A metric-based derivation for the equation of state, and quantum corrections to the thermodynamical, statistical, and phenomenological definition of entropy are also given. Further implications and limitations of our study are discussed., Comment: 26 pages, 3 figures; v2: eqs (20), (42), and comments added, version to appear in Phys. Rev. D

The phase diagram of four-dimensional Einstein-Hilbert gravity is studied using Wilson's renormalization group. Smooth trajectories connecting the ultraviolet fixed point at short distances with attractive infrared fixed points at long distances are derived from the non-perturbative graviton propagator. Implications for the asymptotic safety conjecture and further results are discussed., Comment: 4 pages, 4 figures

We perform a global renormalization group study of O(N) symmetric Wess-Zumino theories and their phases in three euclidean dimensions. At infinite N the theory is solved exactly. The phases and phase transitions are worked out for finite and infinite short-distance cutoffs. A distinctive new feature arises at strong coupling, where the effective superfield potential becomes multi-valued, signalled by divergences in the fermion-boson interaction. Our findings resolve the long-standing puzzle about the occurrence of degenerate O(N) symmetric phases. At finite N, we find a strongly-coupled fixed point in the local potential approximation and explain its impact on the phase transition. We also examine the possibility for a supersymmetric Bardeen-Moshe-Bander phenomenon, and relate our findings with the spontaneous breaking of supersymmetry in other models., Comment: 23 pages, 18 figures

We derive a supersymmetric renormalization group (RG) equation for the scale-dependent superpotential of the supersymmetric O(N) model in three dimensions. For a supersymmetric optimized regulator function we solve the RG equation for the superpotential exactly in the large-N limit. The fixed-point solutions are classified by an exactly marginal coupling. In the weakly coupled regime there exists a unique fixed point solution, for intermediate couplings we find two separate fixed point solutions and in the strong coupling regime no globally defined fixed-point potentials exist. We determine the exact critical exponents both for the superpotential and the associated scalar potential. Finally we relate the high-temperature limit of the four-dimensional theory to the Wilson-Fisher fixed point of the purely scalar theory., Comment: 13 pages,4 figures

I discuss the renormalisation group approach to gravity, its link to Steven Weinberg's asymptotic safety scenario, and give an overview of results with applications to particle physics and cosmology., Comment: 14 pages, 6 figures, to appear in the Philosophical Transactions A of the Royal Society, London