Yukawa International Molecule Workshop / EMMI Program

Renormalization Group Approachfrom Ultra Cold Atoms to the Hot QGP

ABSTRACTANDRONIC, Anton
Hadron production at chemical freeze-out and the QCD phase
diagram from high-energy nucleus-nucleus collisions
We investigate the production of hadrons in high-energy nucleus-nucleus collisions
within the framework of the thermal (or statistical hadronization) model. We discuss
the power and the limitations of the model and how the ﬁts to experimental data are
performed. The relevance of the results for the phase diagram of QCD is discussed.
We address the light-quark hadrons as well as charmonium, which, within the statisticalmodel, can be identiﬁed as a powerful observable for the phase boundary.

BERGES, Juergen
Universality far from Equilibrium

DELAMOTTE, Bertrand
Non-perturbative renormalization analysis of the Kardar-ParisiZhang equation

FLÖRCHINGER, Stefan
Turbulent ﬂuctuations in heavy ion collisions
For large Reynolds number (which is inverse to viscosity), ﬂuids are known to develop turbulence. Therefore, the phenomenological evidence for a small viscosity suggeststhat the hydrodynamical description of heavy ion collisions may have a turbulent regime.
Assuming that averaged velocities are described by Bjorkens model, we investigate local ﬂuctuations around it. These perturbations are governed by non-linear equations

1and we characterize classes of qualitatively diﬀerent evolution in terms of Reynolds numbers. Perturbations at diﬀerent rapidities are found to decouple quickly, and the local
evolution becomes eﬀectively two-dimensional. The resulting Navier-Stokes equation of
non-relativistic form (obtained after suitable coordinate transformations) can be discussed
within the theory of Kolmogorov and Kraichnan. In particular, unlike three-dimensional
turbulent ﬂow, two-dimensional viscous ﬂuid dynamics can show the interesting phenomenon of inverse cascading of energy into large scale structures. We speculate on
possible phenomenological implications of these ﬁndings.

GRAHL, Martin
Study of the two-ﬂavor linear sigma model in presence of theaxial anomaly with the Functional Renormalization GroupThe SU (2)A × U (2)V -symmetric chiral linear sigma model in presence of the axial
anomaly is studied in the local potential approximation of the Functional Renormalization Group. The RG ﬂow is studied in a truncation which reproduces recent results for
the U (2)A × U (2)V -symmetric model in the limit of vanishing axial anomaly strength,c = 0. We search for the conjectured O(4) ﬁxed point in presence of anomaly, c 6= 0, andanalyze its stability properties.

HARADA, Koji
A Wilsonian view on the nuclear eﬀective ﬁeld theory
We explain how a Wilsonian renormalization group analysis of the nuclear eﬀective
ﬁeld theory systematically determines the power counting on the basis of the scaling dimensions of operators near the (nontrivial) ﬁxed point. We emphasize that, when pions
are included, the separation of the one-pion-exchange potential into its short-distance andlong-distance parts is essential, since their scaling properties are diﬀerent in the S-waves.

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HEBELER, Kai
New Applications of Renormalization Group Methods in Nuclear Physics
Renewed interest in the physics of nuclei is stimulated by experiments at rare isotope
facilities, which open the way to new regions of exotic nuclei, and by astrophysical observations and simulations of neutron stars and supernovae, which require controlled constraints
on the equation of state of nucleonic matter. The use of Renormalization Group methods
to lower the characteristic resolution of inter-nucleon interactions is opening new avenues
for calculations of low-energy nuclear structure and reactions. I will give an overview overrecent developments and discuss various results for the nuclear equation of state and theconsequences for the structure of neutron stars, short-range correlations and the role ofmany-body forces in nuclear systems.

IGARASHI, Yuji
Realization of symmetries and reduction of the Polchinski ﬂow
equations in the ERG
We describe realization of symmetries which are naively incompatible with the regularization scheme in the ERG approach. The Ward-Takahashi identities for such symmetries
are derived for the Wilson eﬀective action using a functional method. We also discuss asuitable truncation of the Wilson action which makes it possible to reduce the Polchinski
ﬂow equation to its 1PI part, the Wetterich equation.

IPP, Andreas
Scalar theory pressure beyond the local potential approximation
Strict perturbation theory of a scalar theory at ﬁnite temperature exhibits the same
poor convergence properties as QCD or QED, already at moderately large couplings. It

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is therefore an ideal test bed to implement improved convergence schemes like improved
calculations using the Non-Perturbative Renormalization Group (NPRG).
In this talk I want to present results beyond the already successful Local Potential
Approximation (LPA). We apply an improved scheme that has been developed by Blaizot,
Mendez-Galain, and Wschebor (BMW). This scheme permits a good determination of the
momentum dependence of the n-point functions at zero temperature. Applied to ﬁnite
temperature, one can expect this method to capture accurately the contributions to thethermodynamical functions of thermal ﬂuctuations from various momentum ranges. This
scheme involves also non trivial momentum dependent self-energies. We ﬁnd that results
obtained with this new scheme are not too diﬀerent from those of the LPA. This suggeststhat the LPA may already capture the main contribution to the exact pressure. Thisagreement persists up to the largest couplings, where strict perturbation theory fails miserably. This may also hint to the validity of the quasiparticle picture of such a system.

ITOU, Etsuko
Infrared ﬁxed point for many ﬂavor SU(N ) gauge theory
SU(N ) gauge theories with various number of fermions and their representations havea non-trivial ﬁxed point in IR region. The theory in such a conformal window shows
both an asymptotically freedom and a conformal property in IR region. The motivation
to studying the IR behavior of such theories, is not only to distinguishing IR propertiesof gauge theory, but also phenomenologically important since such theories are potential
candidates to explain the origin of electro-weak symmetry breaking beyond the standard
model.
I would like to report some recent results for the nonperturbative running coupling
and the measurement of the anomalous dimension of composite operators around the ﬁxed
point using the lattice simulation.

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ITOH, Katsumi
Anomalies in the ERG Approach
The antiﬁeld formalism adapted in the exact renormalization group is found to be
useful for describing a system with some symmetry, especially the gauge symmetry. In
the formalism, the vanishing of the quantum master operator implies the presence of asymmetry. The QM operator satisﬁes a simple algebraic relation that will be shown tobe related to the Wess-Zumino condition for anomalies. We also explain how an anomaly
contributes to the QM operator.

JOCHIM, Selim
Few-body physics with ultracold fermions

KLEIN, Bertram
Chiral symmetry breaking and ﬁnite-volume eﬀects
Chiral symmetry breaking is - in addition to conﬁnement - the phenomenon that moststrongly determines the properties QCD ground state and inﬂuences the QCD phasetransition at ﬁnite temperature and chemical potential.
Since the spontaneous breaking of chiral symmetry gives rise to Nambu-Goldstonebosons, which in turn lead to long-range correlations, the associated phenomena are very
sensitive to ﬁnite-volume eﬀects. This is important for lattice simulations of QCD in aﬁnite-volume box and inﬂuences the phase transition. The ﬁnite volume can also be atool to probe the system for additional information.
We have used the functional RG to investigate such phenomena in the framework ofmodels for chiral symmetry breaking in QCD. The FRG is uniquely suited to these investigations since it accounts for the relevant long-range ﬂuctuation and the critical behavior
over a wide range of scales. I will give an overview over the application to diﬀerent phe-5nomena in this context.

KONDO, Kei-Ichi
Understanding the entanglement between conﬁnement and chiralsymmetry-breaking from QCD
We discuss a possible ﬁrst-principle derivation of a low-energy eﬀective model of quantum chromodynamics (QCD), which enables one to understand the entanglement between
conﬁnement and chiral-symmetry-breaking. We have some implications for improving
Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) models. Moreover, we consider
how magnetic monopoles contribute to conﬁnement and chiral-symmetry breaking. The
basic ingredients are a reformulation of QCD based on new variables, non-Abelian Stokes
theorems for the Wilson and Polyakov loops, and the ﬂow equation of the Wetterich typein the Wilsonian renormalization group.

KOPIETZ, Peter
Non-equlilibrium time evolution of bosons from the function
renornmalization group
We develop a functional renormalization group approach to obtain the time evolutionof the momentum distribution function of interacting bosons out of equilibrium. Using an
external out-scattering rate as ﬂow parameter, we derive formally exact renormalizationgroup ﬂow equations for the non-equilibrium self-energies in the Keldysh basis. A simple
perturbative truncation of these ﬂow equations leads to an approximate solution of thequantum Boltzmann equation which does not suﬀer from secular terms and gives accurate results even for long times. We demonstrate this explicitly within a simple exactly
solvable toy model describing a quartic oscillator with oﬀ-diagonal pairing terms.
References:
T. Kloss and P. Kopietz, Phys. Rev. B83, 205118 (2011).

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KUNIHIRO, Teiji
RG derivation of relativistic hydrodynamic equations as the infrared dynamics of Boltzmann equation

MITTER, Mario
Aspects of two- and three-ﬂavor chiral phase transitions
The two- and three-ﬂavor chiral phase transition is investigated within a non-perturbative
functional renormalization group approach at non-vanishing temperature and quark chemical potential. The temperature dependence of an axial symmetry violating ’t Hooft interaction and the consequences are discussed for a two-ﬂavor theory. The inﬂuence of thestrange quark on the chiral phase transition and on the critical endpoint in the phase
diagram are explored.

MUKAIYAMA, Takashi
Universal Thermodynamics of a Unitary Fermi gas
Due to the tunability of the interaction and the stable feature of the ultracold fermionicgases near Feshbach resonances, a degenerate two- component fermionic atom system
makes an ideal testing ground for many- body physics. Especially at the unitarity limit
where the inter-atomic scattering length diverges and the eﬀective range of interaction is
negligible, the scattering length, which is a material-speciﬁc interaction parameter, drops
out of the description of the energy of the system. This gives rise to universality: theonly relevant energy scale left in the system is the Fermi energy. According to this universal hypothesis, all the thermodynamic quantities have a simple and uniﬁed form of thefunction of Fermi energy and temperature normalized by Fermi temperature. However, acomplete set of the universal thermodynamic functions has not been determined experimentally so far. In the talk, we present the experimental result of the determination of7

universal thermodynamic functions at the unitarity limit under the assumption of local
density approximation. Using the equation of state and the equation of force balance of aunitary gas in a trap, we are able to determine the internal energy as a function of density
and reduced temperature. Once the universal function for the internal energy is obtained,
all the other universal functions such as the Helmholtz free energy, chemical potential andentropy can be derived through thermodynamic relations. We also determine all of thethermodynamic quantities at the condensation critical temperature and those values arein good agreement with recent theoretical predictions. The obtained universal functions
are crucial for quantitative test of theories for a unitary Fermi gas.

NOWAK, Boris
Nonthermal ﬁxed points in turbulent Bose gases
Far from equilibrium dynamics of Bose gases is analyzed in two and three spatial
dimensions. For such systems, universal power-law distributions i.e. nonthermal ﬁxed
points, previously found within a nonperturbative quantum-ﬁeld theoretic approach, areshown to be related to defect turbulence. In the case of dilute ultracold bosons, the nonthermal ﬁxed point is explained from the statistics of superﬂuid vortices. Characteristic
tails in the velocity statistics of vortices are found, which were recently used to experimentally verify a distinction between classical and quantum turbulence. In the case of
relativistic bosons, new aspects of reheating after cosmological inﬂation are presented.
Domains of negative and positive charge overdensities separated by thin walls similar to
topological defects correspond to the nonthermal ﬁxed point.

PIETRONI, Massimo
Coarse-graining and resummation of cosmological perturbations

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SAUERESSIG, Frank
Asymptotically Safe Gravity From Euclidean to Lorentzian
Signature
The gravitational asymptotic safety program strives for a consistent and predictive
quantum theory of gravity based on a non-trivial ultraviolet ﬁxed point of the renormalization group ﬂow. We investigate this scenario by employing a novel functional renormalization group equation which takes the causal structure of space-time into accountand connects the RG ﬂows for Euclidean and Lorentzian signature by a Wick-rotation.
Remarkably, the structure of the new equation closely resembles the one encounteredwhen studying quantum ﬁeld theory at ﬁnite temperature. 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 thesame universality class at high energies.

SCHAEFER, Bernd-Jochen
With the FRG towards the QCD phase diagram

SCHMIDT, Richard
Renormalization group ﬂow of spectral functions for ultracold
quantum gases
A light impurity in a Fermi sea undergoes a transition from polaron to molecule forincreasing interaction. We develop a new computational functional RG method to compute the spectral functions of the polaron and molecule in a uniﬁed framework with fullself-energy feedback. We discuss the energy spectra, decay widths, and the quasi-particle
weight of the attractive and repulsive polaron as well as the molecule across the transition.

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We ﬁnally propose an experimental procedure to measure the repulsive branch using rf
spectroscopy and calculate the corresponding spectra.

SCHERER, Michael
Finite-size and Particle-number Eects in an Ultracold Fermi
Gas at Unitarity

SKOKOV, Vladimir
Probing QCD phase diagram with ﬂuctuations of conserved
chargesIn this talk, I review some properties of the QCD phase diagram and discuss what
we can learn about it from studies of ﬂuctuations of the conserved charges in experiments with heavy ions. I show the relevance of net-baryon number ﬂuctuations for the
analysis of freeze-out and critical conditions in heavy-ion collisions at LHC and RHIC.
The properties of ﬂuctuations of the electric and net-baryon charges in the vicinity of thechiral crossover transition are discussed within eﬀective chiral models. The calculation
includes non-perturbative dynamics implemented within the functional renormalizationgroup approach. Finally, I present a comparison of the recent experimental data on theprobabilities of the net-proton number with hadron resonance gas model results.

SONODA, Hidenori
Universality of ERG formalism, revisited
Following an old work of Latorre and Morris, I would like to reexamine the universalityof critical phenomena as described by the ERG formalism.

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TARJUS, Gilles
Nonperturbative functional RG for disordered systems: the caseof the random-ﬁeld Ising model
Quenched disorder induces an extrinsic inhomogeneity in otherwise translationallyinvariant pure systems. As a result, the equilibrium and out-of-equilibrium physics ofdisordered systems may be inﬂuenced by rare collective events and by the proliferationof ?metastable states?. Our objective is to develop a theory describing the long-distancephysics of such systems through a nonperturbative functional renormalization group (NPFRG) method and our ﬁrst focus is the equilibrium behavior of the random-ﬁeld Isingmodel. We formulate the NP-FRG for the critical behavior of the latter in a superﬁeld
formalism, which enables us to follow the underlying supersymmetry and its spontaneous
breaking along the ﬂow. Breaking is shown to occur below a critical dimension and leads
to a breakdown of the so-called ’dimensional reduction’ property.

TERAO, Haruhiko
Non-perturbative beta functions and scaling laws in QCD withmany quark ﬂavors
It has been known that QCD with suﬃciently many ﬂavors becomes scale invariant
at the IR region and the scale invariance is lost as the ﬂavor number is reduced. We will
evaluate the non-perturbative gauge beta function by using the Exact Renormalization
Group equations and show that merger of the IR ﬁxed point and the UV ﬁxed point
occurs at the transition point. We will examine the scaling law for the dynamical scaleby using the non-perturbative beta function and compare it with the Miransky scaling.
We will also show some results on the hyperscaling laws of the chiral order parameterswith respect to a bare fermion mass.

TEZUKA, Masaki
One-dimensional Fermi gases: Density-matrix renormaliza11

tion group study of ground state properties and dynamics
In cold atom systems, the wide controllability of the physical parameters with the
choice of the trapped atoms and the external ﬁelds have made it possible to experimentally investigate various concepts in quantum many-body physics. The atom-atominteraction strength, the potential shape each atom species feels in the space, and thedensities of the atom species can be almost independently manipulated.
The density-matrix renormalization group (DMRG) method allows numerically exact
study of the ground state properties of one-dimensional lattice systems of interacting
atoms. The time evolution of the system under a time-dependent Hamiltonian or after
a sudden change of the Hamiltonian can be studied with high accuracy. We applied
DMRG to two types of systems of interacting one-dimensional two-species Fermi gases:
the population-imbalanced system in a harmonic trap and the population-balanced system
in an optical lattice with the site potential modiﬁed by a second, incommensurate lattice.
The possibility of Fermi condensate with non-zero pair momentum, the Fulde-FerrellLarkin-Ovchinnikov (FFLO, or LOFF) state, has been discussed both in the ﬁeld ofcondensed matter physics and nuclear physics for a long time. We demonstrate that ina harmonically trapped one-dimensional Fermi gas the pair correlation shows a periodic
sign change, consistent with the Larkin-Ovchinnikov type (quasi-)condensation [1, 2].
Studying the superﬂuid–insulator transition due to disorder has also been an interesting issue. The disorder strength λ at the insulating transition point depends on theatom-atom interaction [3]. Time evolution can be used to detect superﬂuidity. We haveadopted the time-dependent DMRG method to study the real-time dynamics [4] of thetwo-component fermions after the shape of the trapping potential is modiﬁed while thequasiperiodic potential is kept on. We report on how the dynamics depends on λ and theinteraction.
References:[1] M. Tezuka and M. Ueda, Phys. Rev. Lett. 100, 110403 (2008).
[2] M. Tezuka and M. Ueda, New J. Phys. 12, 055029 (2010).
[3] M. Tezuka and A. M. Garcı́a-Garcı́a, Phys. Rev. A 82, 043613 (2010).

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[4] A. M. Garcı́a-Garcı́a and M. Tezuka, in preparation.

XU, NuHigh-Energy Nuclear Collisions and the QCD Phase Structure
One of the most exciting goals for the ﬁeld of the high-energy nuclear collisions is
to understand the phase structure of matter with partonic degrees of freedom especiallythe transition from hadronic phase to partonic phase. It is believed that the QCD phase
dominates the evolution brieﬂy during the early time of the Universe. In this talk, after
reviewing basic concepts regarding strong interactions, I will discuss the recent progresses
in the ﬁeld [1-4]. The focus will be given to those measurements that lead to the understanding of the strongly interacting matter created in high-energy nuclear collisions at
RHIC.
References:[1] PHENIX Experiment at RHIC: http://www.phenix.bnl.gov/[2] STAR Experiment at RHIC: http://www.star.bnl.gov/[3] J. Adams, et al., STAR Collaboration, Nucl. Phys. A757, 102 (2005).
[4] K. Adcox, et al., PHENIX Collaboration, Nucl. Phys. A757, 184 (2005).

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