Posters
Borchardt Julia
Title: Solving functional flows by pseudo-spectral methods
Abstract: TBA
Defenu Nicolo
Title: Fixed Points Structure and Effective Fractional Dimension for O(N) Models with Long-Range Interactions
Abstract: We study O(N) models with power–law interactions by using functional renormalization group methods: we show that both in Local Potential Approximation (LPA) and in LPA' their critical exponents can be computed from the ones of the corresponding short–range O(N) models at an effective fractional dimension. In LPA such effective dimension is given by D_{eff}=\frac {2d}{\sigma}, where d is the spatial dimension and d+\sigma is the exponent of the power–law decay of the interactions. In LPA' the prediction by Sak [Phys. Rev. B 8 , 1 (1973)] for the critical exponent \eta is retrieved and an effective fractional dimension D^\prime_{eff} is obtained. Using these results we present analytical predictions for the critical exponent \nu as a function of\sigma and N, and for the multicritical points of long–range O(N) models. Finally, we propose an improved LPA'' approximation to describe the full theory space of the models where both short–range and long–range couplings are present: the long–range fixed points are found to emerge from a long–range Gaussian fixed point at a critical value of \sigma, different for every universality class, and then they merge with the correspondent short–range fixed point.
Eichhorn Astrid and Scherer Michael
Title: Planck scale, Higgs mass and scalar dark matter
Abstract: This study is inspired by a scenario, in which the Standard Model, enhanced by an additional dark matter scalar, could be extended up to the Planck scale, while accommodating the low measured value of the Higgs mass. To that end, we study a toy model for a gauge singlet dark matter scalar coupled to the Higgs-top-quark sector of the Standard Model. Using functional methods to derive Renormalization Group flow equations in that model, we examine several choices for the ultraviolet, bare potential in the Higgs-dark-matter sector. Our results indicate that the dark matter scalar can decrease the lower bound on the Higgs mass in the Standard Model. We then use the fact that higher-order couplings which are driven to tiny values by the Renormalization Group flow towards low energies can easily be of order one at the ultraviolet cutoff scale. Our study indicates that the inclusion of these couplings can significantly increase the ultraviolet cutoff scale and therefore the range of validity of the model while yielding a low value for the Higgs mass in the infrared. This is achieved within a setting where the dark matter scalar accounts for the complete dark matter relic density in our universe.
Fejos Gergely
Title: Fluctuation induced first order transition in the U(n)xU(n) models using a chiral invariant expansion of the FRG flows
Abstract: Based on a chiral invariant expansion, a numerical solution of coupled flow equations will be presented for the effective potential. Regardless of the flavour number n, a fluctuation induced first order chiral transition is observed. I will present the properties of the transition in the whole range of the parameter space for n=2,3,4 and a large-n analysis will also be discussed.
Guilleux Maxime
Title: NPRG flow of an O(N) scalar field inDe Sitter space-time
Abstract: Cosmological evidence seems to support an early phase of accelerated expansion called inflation. Although the theoretical description at tree level in perturbation theory is sufficient for many purposes, a complete quantum treatment is necessary to fully understand the inflation epoch. We approach this issue using QFT in curved space-time, more specifically an O(N) scalar field in De Sitter space-time. The non-trivial quantum effects that occur require resummation techniques. Using the Non-Perturbative Renormalisation Group, we write the flow equation for the effective action. In the local potential approximation, we derive the flow of the potential minimum and study the symmetry restoration in different approximations: polynomial ansatz and large N limit.
Horinouchi Yusuke
Title: Universal Three-body Parameter in Efimov Physics and Renormalization-Group Limit Cycle
Abstract: The universal three-body parameter in the Efimov effect is among the greatest recent experimental discoveries in the field of ultracold atoms. This experimental finding has been numerically vindicated [J. Wang et al., Phys. Rev. Lett. 108, 263001 (2012)] and its physical origin has been clarified [P. Naidon et al., Phys. Rev. Lett. 112, 105301 (2014)]. A major missing link in this subject is a relation between the universal three-body parameter and the fundamental property of the Efimov effect, i.e. a renormalization-group limit cycle. In the presentation, we show that they are in fact closely connected, by means of the functional renormalization-group method, the non-perturbative character of which plays a decisive role in revealing this connection.
Kemler Sandra
Title: Renormalization Group Approach to Density Functional Theory
Abstract: We study a two-point particle irreducible (2PPI) approach to many-body physics which relies on a renormalization group (RG) flow equation for the associated effective action. This approach relates to Density Functional Theory and can in principle be used to study ground-state properties of non-relativistic many-body systems from microscopic interactions, such as (heavy) nuclei. We apply our formalism to a 0+1-dimensional model, namely the quantum anharmonic oscillator and use the well-known exact solution to benchmark our approximations of the full RG flow. Moreover, we present flow equations for specific types of 1+1-dimensional field theories which allow us study the ground-state properties of spinless fermions in a harmonic trap as well as so-called Alexandrou-Negele nuclei.
King Callum
Title: Asymptotic safety in the presence of a Higgs field
Abstract: We study an asymptotically safe fixed point of quantum gravity in the presence of scalar fields such as the Higgs. Assuming that the fundamental gravitational action is a high order polynomial of the Ricci scalar, we analyse fixed points and scaling exponents up to high order in the approximation. We conclude that the previously known fixed point in pure gravity persists in the presence of the Higgs field. Extensions towards more scalar fields are discussed as well.
Knorr Benjamin
Title: Convergence of Derivative Expansion in SUSY Models
Abstract: We study the convergence of the derivative expansion in manifestly SUSY-covariant models. In SUSY quantum mechanics, we calculate the energy gap with both SUSY-preserving and -breaking ansaetze, which can be compared to exact results from diagonalizing the Hamiltonian. In three dimensions, the equivalent of the Wilson-Fischer fixed point is obtained. In both studies, globally adapted spectral methods are used to arrive at high precision results.
Meibohm Jan and Reichert Manuel
Title: Fermionic Matter in Asymptotically Safe Quantum Gravity
Abstract: We present a way of how to include fermionic matter in quantum gravity. We employ the spin-base invariance formalism define a notion of gamma matrices in curved spacetime. By a combination of the geometric flow equation for Newton's coupling and the fermionic contribution to the graviton 3-point function we obtain the flow of the Newton coupling in the presence of fermions. This way, the asymptotic safety scenario can be verified for an arbitrary number of fermion fields.
Nink Andreas
Title: Field Parametrization Dependence in Single- and Bi-metric Truncations
Abstract: Motivated by conformal field theory studies we investigate Quantum Einstein Gravity with a new field parametrization where the dynamical metric is basically given by the exponential of a fluctuating field. Special care is taken of possible fixed points and related structures of the corresponding RG flow with regard to the Asymptotic Safety program, for both single- and bi-metric truncations.
Pagani Carlo
Title: Quantum gravity with torsion and non-metricity
Abstract: We study the renormalization of theories of gravity with an arbitrary (torsion-ful and non-metric) connection. The class of actions we consider is of the generalized Palatini type, including the most general terms with up to two derivatives of the metric, but no derivatives of the connection. It contains 22 independent parameters. We calculate the one loop beta functions of these parameters.
Rentrop Jan
Title: Toy model 2PI functional RG calculations
Abstract: Generating functionals have long been written in a two-particle irreducible (2PI) form. Also, some functional renormalization group (RG) schemes have been proposed based on
these functionals. These mainly differ from one another with respect to the (non-)diagonality of the external source field and the introduction of the flow parameter. However, only a few results obtained with these schemes are available. We investigate the quantum anharmonic oscillator as a toy model. This research is a preliminary step to applying 2PI functional RG to non-relativistic quantum many-body problems in low dimensions. The introduction of Keldysh formalism into these 2PI functional RG schemes bears the possibility to treat steady-state non-equilibrium situations and prevents the ill posed problem of analytic continuation.
Veschgini Kambis
Title: Schwinger-Dyson Renormalization Group
Abstract: We use the Schwinger-Dyson equations as a starting point to derive renormalization flow equations. We show that Katanin's scheme arises as a simple truncation of these equations. We then give the full renormalization group equations up to third order in the irreducible vertex. Furthermore, we show that to the fifth order, there exists a functional of the self-energy and the irreducible four-point vertex whose saddle point is the solution of Schwinger-Dyson equations.