Stefano Anselmi
Title: Beyond linear theory an analytical approach to matter cosmological perturbations
Abstract: The large-scale structure of our universe grows through a process of gravitational instability. On very large scales the matter distribution is well modeled by linear perturbation theory, whereas on small scales the dynamics is highly non-linear and perturbation theory fails. The intermediate range, (around 100 Mpc) contains crucial information on cosmology and particle physics, such as the absolute scale of neutrino masses, the nature of Dark Energy, and the statistics of the primordial cosmological perturbations. This region will be probed at high precision by future galaxy surveys, therefore it is mandatory to develop (semi)analytic methods to accurately describe such mildly non-linear scales. We will discuss how cosmological perturbation theory can be formulated in terms of tools familiar in quantum field theory, namely Feynman diagrams and the renormalization group (RG). We will discuss some noticeable cases where classes of diagrams can be resummed to all orders in perturbation theory. Moreover, we will discuss how these resummations can be improved by means of an RG method, in which time is the flow parameter.
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Nikolaos Antoniou
Title: Search for the origin of mass in experiments with relativistic nuclei
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Dario Benedetti
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Federico Benitez
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Astrid Eichhorn
Title: Ghosts in asympotically safe quantum gravity
Abstract: We investigate the asymptotic-safety scenario for quantum gravity with the functional renormalisation group. As the gauge-fixing sector is an important ingredient in continuum quantum field theories with local symmetries, we include a non-trivial ghost sector in addition to former truncations. In particular we focus on the ghost wave function renormalisation, which carries the scale-dependence of the standard Faddeev-Popov determinant. We find improved stability properties of the non-Gaußian fixed point, and a negative anomalous dimension for the ghost. In addition to the standard ghost term we also investigate a non-standard curvature-ghost coupling that may alter the gauge-fixing sector at the UV fixed point. We also discuss differences and similarities with the gauge-fixing sector of Yang-Mills theories and examine the issue of predictivity in connection with the ghost sector of quantum gravity.
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Tilman Enss
Title: The Fermi polaron funRG with full frequency and momentum dependence
Abstract: A single, non-relativistic down-spin fermion subject to a strong zero-range interaction with a Fermi sea of up-spin fermions forms a polaronic quasiparticle. Whether the associated quasiparticle weight vanishes beyond a critical interaction strength is still an open question. To answer this we have implemented a functional RG to compute the full frequency and momentum dependence of fermionic and bosonic propagators. Specifically for the polaron problem, we obtain the down-spin spectral function and pair propagator. We examine the dependence of the ground state energy, quasiparticle weight, effective mass and Tan contact coefficient on the coupling strength and discuss implications for the phase diagram of the strongly imbalanced Fermi gas.
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Kevin Geoffrey Falls
Title: Black holes and the renormalisation group
Abstract: In this talk I will discuss recent results on applications of the renormalisation group to black hole physics. In particular I will discuss higher dimensional black holes and apply our findings to the phenomenology of mini-black hole production at colliders. Recently this has become of interest due to the possibility that the fundamental scale of gravity could be of order 1TeV in higher dimensional models of particle physics. Implications of the asymptotic safety scenario for quantum gravity will be presented in detail.
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Leonard Fister
Title: Yang-Mills Propagators at finite Temperature
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Simon Friederich
Title: Functional renormalization group approach to the Hubbard model based on partial bosonization
Abstract: Magnetic and superconducting instabilities in the two-dimensional t-t'-Hubbard model are discussed within a functional renormalization group approach. The fermionic four-point vertex is efficiently parametrized by means of partial bosonization. The exchange of composite bosons in the magnetic, charge density and superconducting channels accounts for the increase of the effective couplings with increasing length scale. We study the onset of local order in various channels and the interplay of the bosonic masses and quartic couplings in the antiferromagnetic and d-wave superconducting ordered phases.
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Kay-Uwe Giering
Title: Self-energy Flow in the Hubbard Model
Abstract: As a candidate model for high T_c superconducting systems the Hubbard model is under heavy investigation. Current RG studies closely inspect the interaction vertex of the model and ordering tendencies in the system have been identified. At present self energy effects are often neglected. Here we examine the flow of both the interaction vertex and the self energy. We parametrise the two-point function in terms of hopping corrections and a field renormalisation factor Z. We compare different methods of extracting this information from the flow equation and study the influence of the two-point function on the interaction vertex flow.
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Lisa Marie Haas
Title: On the QCD phase diagram
Abstract: We study the phase diagram of two flavour QCD at imaginary and real chemical potential with the Exact Renormalisation Group. In particular we compute order parameters for chiral symmetry breaking and quark confinement. Our analytical and numerical results suggest a close relation between the chiral and the confinement phase transition.
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Ulrich Harst
Title: UV Behavior of the Einstein-Yang-Mills System
Abstract: For Quantum Einstein Gravity to be a candidate for a fundamental theory of gravity, it has to be shown, that the non-trivial fixed point is not merely an artifact of the truncation of theory space. A considerable amount of evidence for this conjecture has been collected by including different curvature invariants or matter fields in the truncation. As part of these investigations we studied the renormalization group behavior of the gauge coupling constant in the Einstein-Yang-Mills system using a truncated form of the functional flow equation and find a non-zero correction to the Yang-Mills beta-function due to gravity. Our result is consistent with the Asymptotic Safety conjecture of Quantum Einstein Gravity with a vanishing gauge coupling at the non-trivial fixed point.
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Tina Katharina Herbst
Title: The Phase Structure of the Polyakov-Quark-Meson Model beyond Mean Field
Abstract: The influence of quantum and thermal fluctuations on the chiral and deconfinement phase transitions is studied within the functional renormalization group in the framework of an effective Polyakov-quark-meson model truncation. Furthermore, the importance of the back-reaction of the QCD matter sector to the gluonic sector is discussed and the modifications on the thermodynamics is investigated.
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Aldo Isidori
Title: Spectral function of the Anderson impurity model at finite temperatures
Abstract: Using the functional renormalization group (FRG) and the numerical renormalization group (NRG), we calculate the spectral function of the Anderson impurity model at zero and finite temperatures. In our FRG scheme spin fluctuations are treated non-perturbatively via a suitable Hubbard-Stratonovich field, but vertex corrections are neglected. A comparison with our highly accurate NRG results shows that this FRG scheme provides a good description of the spectral line-shape at zero and finite temperatures both in the weak and strong coupling regimes, although at zero temperature the FRG is not able to reproduce the known exponential narrowing of the Kondo resonance at strong coupling.
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Lukas Janssen
Title: UV fixed-point structure of the 3d Thirring model
Abstract: We investigate the UV fixed-point structure of the three-dimensional Thirring model by means of the functional renormalization group (RG). We classify all possible 4-fermi interactions compatible with the present chiral and discrete symmetries and calculate the purely fermionic RG flow using a full basis of fermionic four-point functions in the point-like limit. Our results show that the UV complete (asymptotically safe) Thirring model lies in a two-dimensional coupling plane which reduces to the conventional Thirring coupling only in the strict large-Nf limit. In addition to the Thirring universality class which is characterized by one relevant direction (also at finite Nf), two further interacting fixed points occur which may define new universality classes of second-order phase transitions also involving parity-broken phases. The Nf-dependence of the Thirring fixed point sheds further light on the existence of an Nf-controlled quantum phase transition above which chiral symmetry remains unbroken for arbitrary large coupling, even though a definite answer will require a direct computation of competing orders.
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Bertram Klein
Title: Scaling, finite-volume effects and the chiral phase transition in QCD
Abstract: The physics of the strong interaction are described by Quantum chromodynamics (QCD). In recent years much interest has been centered on the phase transitions which occur in QCD at finite temperature and for finite quark chemical potential. Non-perturbative methods such as the discretization of the theory on a finite space-time lattice (lattice QCD) are essential to understand these transitions. However, due to explicit breaking of the chiral symmetry of QCD on the lattice and the finite simulation volume, the nature of the phase transition is difficult to establish. In recent years, functional RG methods have also been applied successfully to this problem. We use functional RG methods (Wetterich equation) to investigate the scaling behavior of models for chiral symmetry breaking close to the chiral phase transition line. We establish the scaling behavior at the phase transition and the finite-size scaling behavior in small volumes, and investigate the intermediate behavior between these extremes. This work is relevant for the scaling analysis of lattice QCD results, which currently probe this region. Extending the theory to finite chemical potential, we calculate the behavior of the phase transition line at finite chemical potential and temperature and identify effects of the finite simulation volume on the curvature of the transition line. This behavior has implications for the phase diagram of QCD.
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Roman Krcmar
Title: Single impurity in a Luttinger liquid away from half filling
Abstract: Single impurities in one-dimensional rings have drastic effects on its physical properties They affect the finite size scaling of the ground state energy, persistent currents and various correlation functions. This has first been noted using bosonization and the renormalization group [1]. A single impurity cuts the chain. Later using the same approach persistent currents in a ring threated by a magnetic flux have been shown to decay algebraically [2]. These findings are supported by microscopic numerical calculations using the Bethe ansatz and DMRG [3]. More recently a purely fermionic functional renormalization (fRG) method has been suggested as a suitable tool to describe 1D systems [4]. Previous work using this method concentrated on calculations of the ground state energy and the persistent currents at half filling [5,6]. We will extend the fRG method to systems away from half filling. This requires the numerical determination of the chemical potential. Our results ! will be compared to DMRG and Bethe ansatz calculations. This will provide insight into validity and applicability of the the fRG procedure. 1 C.L. Kane and M.P.A. Fisher, Phys. Rev. B 46, 15233 (1992) 2 A. Gogolin and N. Prokof'ev, Phys. Rev. B 50, 4921 (1994) 3 S. Qin, M. Fabrizio, L.Yu, M. Oshikava and I. Affleck, Phys. Rev. B 56, 9766 (1997) 4 V. Meden, W. Metzner, U. Schollwöck, and K. Schönhammer, Phys. Rev. B 65, 045318 (2002) 5 V. Meden and U. Schollwöck, Phys. Rev. B 67, 035106 (2003) 6 A. Gendiar, R. Krcmar and M. Weyrauch, Phys. Rev. B 79, 205118 (2009)
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boris krippa
Title: Exact renormalization group and few body systems
Abstract: We study the applications of the exact renormalization group to few body systems, including the both atomic and nuclear systems. We considered the correlation between the scattering length of two fermionic atoms and the dimer-dimer scattering length, using the same functional renormalization technique as previously applied for systems of many fermions. We also studied the deuteron-deuteron scattering length. We find a strong dependence on the cut-off function used in the renormalization flow for a two-body truncation of the action with both sharp and smooth cutoffs. Adding a simple three-body terms substantially reduced this dependence and including the complete local four body interaction renders the results leads to the cut-off function independent results.
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Markus Leder
Title: Hamiltonian Flow in Coulomb Gauge Yang-Mills Theory
Abstract: A new functional renormalisation group equation for Hamiltonian Yang-Mills theory in Coulomb gauge is derived. The flow equations for the static gluon and ghost propagators are solved under the premise of infrared ghost dominance, using different approximations. The achieved results are then compared to those obtained from the Dyson-Schwinger equations.
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Edouard Marchais
Title: On the Large N Limit in the Functional Renormalisation Group
Abstract: In quantum field theory and statistical physics, the large-N expansion (where N denotes the number of fields) is a powerful technique to study non-perturbative phenomena which are difficult to access in the physical limit of small N. We discuss the large N limit at the example of scalar field theories and discuss the main physics including the phase transition, critical scaling and convergence properties within the functional RG.
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Sergej Moroz
Title: Limit cycles and Efimov effect with functional renormalization group
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Sandor Nagy
Title: Topological phase transition in the sine-Gordon model
Abstract: The renormalization group flow is presented for the two-dimensional sine-Gordon model within the framework of the functional renormalization group method by including the wave-function renormalization. We give a more general view on the topological phase transition appearing in the model by showing that it is a simple crossover between two competing attractive regions on the phase diagram.
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GAURAV NARAIN
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Konstantinos Nikolakopoulos
Title: Myers-Perry black holes within asymptotically safe gravity
Abstract: We apply the asymptotic safety scenario for gravity to higher dimensional rotating black holes. We analyze quantum corrections as implied by the renormalisation group as a function of space-time dimensionality and angular momentum. We find the existence of smallest black holes. In higher dimensions, ultra-spinning solutions cease to exist except for asymptotically heavy black holes. We also study the ergosphere, and the thermodynamic properties of the quantum corrected black holes, and make contact with classical studies of black hole (in-)stabilities.
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Satoshi Ohya
Title: Running Boundary Conditions in Quantum Mechanics
Abstract: We study renormalization group flow of boundary conditions in nonrelativistic quantum mechanics. As an illustrative example, we consider one-dimensional quantum mechanics for a spinless particle that freely propagates in the bulk yet interacts only at the origin. In this setting we find the renormalization group flow of U(2) family of boundary conditions exactly. We show that the well-known scale-independent subfamily of boundary conditions are realized as fixed points. We also discuss the duality between two distinct boundary conditions from the renormalization group point of view.
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Vincent Pangon
Title: Structure of the broken phase of the sine-Gordon model
Abstract: We study in this paper the sine-Gordon model using functional Renormalization Group (fRG) at Local Potential Approximation (LPA) using different RG schemes. In $d=2$, using Wegner-Houghton RG we demonstrate that the location of the phase boundary is entirely driven by the relative position to the Coleman fixed point even for strongly coupled bare theory. We show the existence of a set of IR fixed points in the broken phase that are reached independently of the bare coupling. The bad convergence of the Fourier series in the broken phase is discussed and we demonstrate that these fixed-points can be found only using a global resolution of the effective potential. We then introduce the methodology for the use of Average action method where the regulator breaks periodicity and show that it provides the same conclusions for various regulators. The behavior of the model is then discussed in $d\ne 2$ and the absence of the previous fixed points is interpreted.
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Christoph Rahmede
Title: The renormalization group flow of scalar-tensor theory
Abstract: The fascinating idea that gravity is asymptotically safe, and thus displaying an UV fixed point, has received significant support in the past years. I present results for pure gravity showing that the UV fixed point has only a few relevant directions. Including weakly self-coupled matter fields, I show that the gravitational fixed point remains stable. Recursive relations among the critical exponents are deduced which allow to derive the dimension of the ultraviolet critical surface for all scalar matter couplings from the known one for pure gravity. Potential applications of these findings within inflationary cosmology are indicated.
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Adam Rancon
Title: Superfluid-Mott Insulator Transition in Lattice Boson Systems
Abstract: We study the Bose-Hubbard model (interacting bosons on a lattice) in the framework of the non-perturbative renormalization group (NPRG). Contrary to the usual NPRG scheme, where the initial condition of the RG flow is the mean field (Bogoliubov) state, we start from the local limit of decoupled sites (lattice NPRG). Our approach captures the quantum phase transition between the superfluid state and the Mott insulator state. In agreement with previous studies, we find two universality classes the transition at conserved density being in the (d+1) dimensional XY universality class and study the crossover between the corresponding fixed points. We show that this critical behavior is intimately related to the non-trivial infrared behavior in the superfluid phase.
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Urko Reinosa
Title: Exact renormalization group and Phi-derivable approximations
Abstract: We show that the so-called Phi-derivable approximations can be interpreted as particular truncations of the exact renormalization group equations. This point of view not only sheds a new light on the renormalization of Phi-derivable approximations but also provides an efficient way to solve the corresponding non-linear integral equations by formulating them as an initial value problem.
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Bernd-Jochen Schaefer
Title: Fluctuations and the QCD phase diagram
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Sebastian Schierenberg
Title: The Ginsparg-Wilson relation for supersymmetic lattice actions and its consequences
Abstract: The lattice is one possibility to regularize a quantum field theory, which however breaks a lot of symmetries that are present in the continuum by its discrete space-time structure. Naively, this also concerns the supersymmetry of a lattice model. We investigate the properties of the generalized Ginsparg-Wilson relation for supersymmetric lattice models (derived by Bergner, Bruckmann and Pawlowski, Phys. Rev. D 79, 115007). We obtain the relation for an anticommutator of two supercharges. As this anti-commutator is typically a generator of a spatial translation, we get a new condition for translational invariance of a lattice action. This condition differs from the standard translational invariance, being a invariance under finite shifts of the fields by one or more lattice spacings. The anticommutator relation imposes strong constraints on possible solutions of the Ginsparg-Wilson relation, and hence on supersymmetric lattice actions.
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Richard Schmidt
Title: The Fermi polaron funRG with full frequency and momentum dependence
Abstract: A single, non-relativistic down-spin fermion subject to a strong zero-range interaction with a Fermi sea of up-spin fermions forms a polaronic quasiparticle. Whether the associated quasiparticle weight vanishes beyond a critical interaction strength is still an open question. To answer this we have implemented a functional RG to compute the full frequency and momentum dependence of fermionic and bosonic propagators. Specifically for the polaron problem, we obtain the down-spin spectral function and pair propagator. We examine the dependence of the ground state energy, quasiparticle weight, effective mass and Tan contact coefficient on the coupling strength and discuss implications for the phase diagram of the strongly imbalanced Fermi gas.
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Giulio Schober
Title: Dynamical Renormalization Group with Wick-Ordering Fixed Point Iteration for the Fermi Surface
Abstract: We study a renormalization scheme with dynamical adjustment of propagators and apply it to fermionic models used in solid-state physics. To analyze the Fermi surface flow, we use a regulator function which regulates the frequency behaviour but admits all momenta in a fixed region around the Fermi surface. At positive temperature, we prove finiteness of the two- and four-point function in a truncated (skeleton) flow to all orders of perturbation theory. Moreover, we solve the existence problem for the full flow in a truncation of the infinite renormalization group hierarchy where the two- and four-point functions are kept.
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Julien Serreau
Title: Decoherence and thermalization of a pure quantum state in quantum field theory
Abstract: We study the real-time evolution of a self-interacting O(N) scalar field initially prepared in a pure, coherent quantum state. We present a complete solution of the nonequilibrium quantum dynamics from a 1/N-expansion of the two-particle-irreducible effective action at next-to-leading order, which includes scattering and memory effects. We demonstrate that, restricting one's attention (or ability to measure) to a subset of the infinite hierarchy of correlation functions, one observes an effective loss of putity/coherence and, on longer time scales, thermalization. We point out that the physics of decoherence is well described by classical statistical field theory.
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Denes Sexty
Title: Nonequilibrium transport of fermions through an Anderson quantum dot
Abstract: The non-equilibrium time evolution of an Anderson quantum dot coupled between two lead-reservoirs forming a chemical-potential gradient for fermions is investigated. We use Kadanoff-Beym dynamic equations derived from the two-particle irreducible effective action in non-perturbative resummation. The method allows the determination of the non-equilibrium (transient) as well as stationary transport through the quantum dot, and results are compared to pure perturbative approximations for different values of the interactions between the fermions. Our aim is to study the non-equilibrium transport in the Kondo regime in the framework of an extended renormalization-group treatment.
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Vladmir Skokov
Title: Meson fluctuations and thermodynamics of the Polyakov loop extended quark-meson model
Abstract: Thermodynamics and the phase structure of the Polyakov loop-extended two flavor chiral quark-meson model (PQM) are explored. The analysis of the PQM model is based on the functional renormalization group (FRG) method. An appropriate truncation of the effective action with quarks coupled to background gluonic fields is introduced. Within this scheme, we derive the renormalization group flow equation for the scale-dependent thermodynamic potential at finite temperature and density in the presence of a symmetry breaking external field. The influence of fluctuations and of the background gluon field on the properties of net-quark number density fluctuations and their higher moments is explored. We study the dependence of the kurtosis of quark number fluctuations on the pion mass and show that, in the presence of a symmetry breaking term, the fluctuations lead to a smoothing of observables near the crossover transition.
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Franziska Synatschke-Czerwonka
Title: Flow equations for supersymmetric Wess-Zumino models
Abstract: Supersymmetric Wess-Zumino models allow for important insights into the nature of dynamical supersymmetry breaking. In this talk we will employ the ERG to investigate the $N=1$ Wess-Zumino model in three dimensions at zero and at finite temperature. We will discuss supersymmetry breaking and the phase diagram at zero temperature and through the thermal boundary conditions. Also we will recover many aspects of finite temperature QFT such as dimensional reduction and the the Stefan-Boltzmann law.
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Haruhiko Terao
Title: On the SU(N) gauge beta functions in the conformal window
Abstract: It is well-known that IR fixed points appear for the SU(N) gauge theories in the conformal window. We consider how the beta functions change as the number of flavors is reduced by studying the Exact Renormalization Group flows for these theories. We treat simple ERG equations obtained by applying some approximations and truncation of effective operators with expectation that qualitative aspect of the RG flows are maintained with these approximations. We would like to show that there are two distinct renormalized theories, and therefore two beta functions, in the conformal window. One has a UV fixed point as well as the IR fixed point but another has the IR fixed point only. We may find the non-trivial way how the beta functions alter from QED-like one to the QCD-like one as the number of flavors.
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Gian Paolo Vacca
Title: RG flow for Yukawa matter and Einstein gravity
Abstract: Quantum interaction of scalar, fermionic and graviton fields are studied using a truncation of the exact renormalization group flow, including the field anomalous dimensions. The fixed point structure, relevant for the asymptotic safety paradigm, is discussed.
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Omar Zanusso
Title: Asymptotic safety in the gauged nonlinear sigma model.
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