scholarly journals Exact large-Ncsolution of an effective theory for Polyakov loops at finite chemical potential

2012 ◽  
Vol 714 (2-5) ◽  
pp. 306-308 ◽  
Author(s):  
Christian Holm Christensen
Keyword(s):  
Chemical Potential ◽  
Effective Theory ◽  
Polyakov Loops

scholarly journals ON THE CHIRAL PERTURBATION THEORY FOR TWO-FLAVOR TWO-COLOR QCD AT FINITE CHEMICAL POTENTIAL

2006 ◽  
Vol 21 (07) ◽  
pp. 559-569 ◽  
Author(s):  
TOMÁŠ BRAUNER
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Chemical Potential ◽  
Effective Theory ◽  
Einstein Condensation ◽  
Chiral Perturbation ◽  
Physical Content ◽  
Chemical Potentials ◽  
Bose Einstein ◽  
Quark Flavors

We construct the chiral perturbation theory for two-color QCD with two quark flavors as an effective theory on the SO(6)/SO(5) coset space. This formulation turns out to be particularly useful for extracting the physical content of the theory when finite baryon and isospin chemical potentials are introduced, and Bose–Einstein condensation sets on.

scholarly journals Aspects of heavy, dense lattice QCD : series expansion methods, baryon versus isospin density and large Nc

2021 ◽  
Author(s):  
◽  
Jonas Benedict Scheunert
Keyword(s):  
Lattice Qcd ◽  
Series Expansion ◽  
Chemical Potential ◽  
Finite Lattice ◽  
Polyakov Loop ◽  
Cluster Method ◽  
Effective Theory ◽  
Valuable Insight ◽  
Sign Problem ◽  
The Continuum

For finite baryon chemical potential, conventional lattice descriptions of quantum chromodynamics (QCD) have a sign problem which prevents straightforward simulations based on importance sampling. In this thesis we investigate heavy dense QCD by representing lattice QCD with Wilson fermions at finite temperature and density in terms of Polyakov loops. We discuss the derivation of $3$-dimensional effective Polyakov loop theories from lattice QCD based on a combined strong coupling and hopping parameter expansion, which is valid for heavy quarks. The finite density sign problem is milder in these theories and they are also amenable to analytic evaluations. The analytic evaluation of Polyakov loop theories via series expansion techniques is illustrated by using them to evaluate the $\SU{3}$ spin model. We compute the free energy density to $14$th order in the nearest neighbor coupling and find that predictions for the equation of state agree with simulations to $\mathcal{O}(1\%)$ in the phase were the (approximate) $Z(3)$ center symmetry is intact. The critical end point is also determined but with less accuracy and our results agree with numerical results to $\mathcal{O}(10\%)$. While the accuracy for the endpoint is limited for the current length of the series, analytic tools provide valuable insight and are more flexible. Furthermore they can be generalized to Polyakov-loop-theories with $n$-point interactions. We also take a detailed look at the hopping expansion for the derivation of the effective theory. The exponentiation of the action is discussed by using a polymer expansion and we also explain how to obtain logarithmic resummations for all contributions, which will be achieved by employing the finite cluster method know from condensed matter physics. The finite cluster method can also be used to evaluate the effective theory and comparisons of the evaluation of the effective action and a direction evaluation of the partition function are made. We observe that terms in the evaluation of the effective theory correspond to partial contractions in the application of Wick's theorem for the evaluation of Grassmann-valued integrals. Potential problems arising from this fact are explored. Next to next to leading order results from the hopping expansion are used to analyze and compare the onset transition both for baryon and isospin chemical potential. Lattice QCD with an isospin chemical potential does not have a sign problem and can serve as a valuable cross-check. Since we are restricted by the relatively short length of our series, we content ourselves with observing some qualitative phenomenological properties arising in the effective theory which are relevant for the onset transition. Finally, we generalize our results to arbitrary number of colors $N_c$. We investigate the transition from a hadron gas to baryon condensation and find that for any finite lattice spacing the transition becomes stronger when $N_c$ is increased and to be first order in the limit of infinite $N_c$. Beyond the onset, the pressure is shown to scale as $p \sim N_c$ through all available orders in the hopping expansion, which is characteristic for a phase termed quarkyonic matter in the literature. Some care has to be taken when approaching the continuum, as we find that the continuum limit has to be taken before the large $N_c$ limit. Although we currently are unable to take the limits in this order, our results are stable in the controlled range of lattice spacings when the limits are approached in this order.

scholarly journals Open effective theory of scalar field in rotating plasma

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Bidisha Chakrabarty ◽  
P. M. Aswin
Keyword(s):  
Scalar Field ◽  
Thermal Noise ◽  
Chemical Potential ◽  
Time Correlation ◽  
Higher Order ◽  
Effective Theory ◽  
Strongly Coupled ◽  
Effective Dynamics ◽  
Fluctuation Dissipation ◽  
Higher Order Terms

Abstract We study the effective dynamics of an open scalar field interacting with a strongly-coupled two-dimensional rotating CFT plasma. The effective theory is determined by the real-time correlation functions of the thermal plasma. We employ holographic Schwinger-Keldysh path integral techniques to compute the effective theory. The quadratic effective theory computed using holography leads to the linear Langevin dynamics with rotation. The noise and dissipation terms in this equation get related by the fluctuation-dissipation relation in presence of chemical potential due to angular momentum. We further compute higher order terms in the effective theory of the open scalar field. At quartic order, we explicitly compute the coefficient functions that appear in front of various terms in the effective action in the limit when the background plasma is slowly rotating. The higher order effective theory has a description in terms of the non-linear Langevin equation with non-Gaussianity in the thermal noise.

scholarly journals STRONG-COUPLING GAUGE THEORY OF NODAL SPINONS AND ANTIFERROMAGNETIC LONG-RANGE ORDER

2006 ◽  
Vol 21 (39) ◽  
pp. 2947-2960
Author(s):  
IKUO ICHINOSE
Keyword(s):  
Phase Transition ◽  
Gauge Theory ◽  
Strong Coupling ◽  
Long Range ◽  
Chemical Potential ◽  
Quantum Critical Point ◽  
Range Order ◽  
Effective Theory ◽  
Long Range Order ◽  
Density Region

In this paper we shall study a gauge theory of nodal spinons which appears as a low-energy effective theory for antiferromagnetic (AF) Heisenberg models. In most of the studies on the nodal spinons given so far, the gauge interaction between spinons was assumed weak and nonperturbative effects like instantons and vortices were ignored. In this paper, we shall study strong-coupling gauge theory of nodal spinons and reveal its nontrivial phase structure. To this end, we employ recently developed lattice gauge theory techniques for studying finite-temperature and finite-density gauge theory. At low temperature and low spinon-density region, an AF long-range order exists. As temperature and/or density of spinons increase, a phase transition to nonmagnetic phase takes place. Order of the phase transition is of second (first) order for low (high) density region of spinons. At a quantum critical point at vanishing temperature T = 0, abrupt change of spinon density occurs as a function of the chemical potential. Implications of the results to the heavy-fermion materials and the high-T c cuprates are discussed.

scholarly journals Analytic results for the effective theory of thermal Polyakov loops

1986 ◽  
Vol 172 (3-4) ◽  
pp. 369-376 ◽  
Author(s):  
P.H. Damgaard ◽  
A. Patkós
Keyword(s):  
Effective Theory ◽  
Polyakov Loops

Center-symmetric effective theory for two-color quark matter

Open Physics ◽  
2012 ◽  
Vol 10 (6) ◽  
Author(s):  
Tomáš Brauner
Keyword(s):  
Order Parameter ◽  
Large Scale ◽  
Chemical Potential ◽  
Three Dimensional ◽  
Polyakov Loop ◽  
Effective Theory ◽  
Leading Order ◽  
Baryon Chemical Potential ◽  
Yang Mills ◽  
Model Independent

AbstractWe revisit the center-symmetric dimensionally reduced effective theory for two-color Yang-Mills theory at high temperature. This effective theory includes an order parameter for deconfinement and thus allows to broaden the range of validity of the conventional three-dimensional effective theory (EQCD) towards the confining phase transition. We extend the previous results by including the effects of massive quarks with nonzero baryon chemical potential. The parameter space of the theory is constrained by leading-order matching to the Polyakov loop effective potential of two-color QCD. Once all the parameters are fixed, the effective theory can provide model-independent predictions for the physics above the deconfinement transition, thus bridging the gap between large-scale numerical simulations and semi-analytical calculations within phenomenological models.

scholarly journals Taylor and fugacity expansion for the effective ℤ3 spin model of QCD at finite density

2014 ◽  
Vol 29 (32) ◽  
pp. 1450198 ◽  
Author(s):  
Eva Grünwald ◽  
Ydalia Delgado Mercado ◽  
Christof Gattringer
Keyword(s):  
Monte Carlo Simulation ◽  
Taylor Expansion ◽  
Chemical Potential ◽  
Spin Model ◽  
Effective Theory ◽  
Series Expansions ◽  
Complex Action ◽  
The Best Approximation ◽  
Parameter Values ◽  
Fugacity Expansion

Different series expansions in the chemical potential μ are studied and compared for an effective theory of QCD which has a flux representation where the complex action is overcome. In particular we consider fugacity series, Taylor expansion and a modified Taylor expansion and compare the outcome of these series to the reference results from a Monte Carlo simulation in the flux representation where arbitrary μ is accessible. It is shown that for most parameter values the fugacity expansion gives the best approximation to the data from the flux simulation, followed by our newly proposed modified Taylor expansion. For the conventional Taylor expansion we find that the results coincide with the flux data only for very small μ.

scholarly journals Strangeness neutrality and QCD thermodynamics

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
Wei-jie Fu ◽  
Jan M. Pawlowski ◽  
Fabian Rennecke
Keyword(s):  
Chemical Potential ◽  
Heavy Ion ◽  
Density Fluctuations ◽  
Effective Theory ◽  
Thermodynamic Quantities ◽  
Functional Renormalization Group ◽  
Ion Collisions ◽  
Perturbative Quantum ◽  
The Impact ◽  
Quark Flavors

Since the incident nuclei in heavy-ion collisions do not carry strangeness, the global net strangeness of the detected hadrons has to vanish. We investigate the impact of strangeness neutrality on the phase structure and thermodynamics of QCD at finite baryon and strangeness chemical potential. To this end, we study the low-energy sector of QCD within a Polyakov loop enhanced quark-meson effective theory with 2+1 dynamical quark flavors. Non-perturbative quantum, thermal, and density fluctuations are taken into account with the functional renormalization group. We show that the impact of strangeness neutrality on thermodynamic quantities such as the equation of state is sizable.

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