scholarly journals Strong coupling methods in QCD thermodynamics

2021 ◽  
Author(s):  
Owe Philipsen
Keyword(s):  
Monte Carlo ◽  
Strong Coupling ◽  
Chemical Potential ◽  
Yang Mills ◽  
Coupling Methods ◽  
Sign Problem ◽  
Monte Carlo Studies ◽  
Long Time ◽  
Scaling Region ◽  
Strong Coupling Expansions

AbstractFor a long time, strong coupling expansions have not been applied systematically in lattice QCD thermodynamics, in view of the success of numerical Monte Carlo studies. The persistent sign problem at finite baryo-chemical potential, however, has motivated investigations using these methods, either by themselves or combined with numerical evaluations, as a route to finite density physics. This article reviews the strategies, by which a number of qualitative insights have been attained, notably the emergence of the hadron resonance gas or the identification of the onset transition to baryon matter in specific regions of the QCD parameter space. For the simpler case of Yang–Mills theory, the deconfinement transition can be determined quantitatively even in the scaling region, showing possible prospects for continuum physics.

scholarly journals Lattice study of area law for double-winding Wilson loops

2018 ◽  
Vol 175 ◽  
pp. 12010
Author(s):  
Akihiro Shibata ◽  
Seikou Kato ◽  
Kei-Ichi Kondo ◽  
Ryutaro Matsudo
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Strong Coupling ◽  
Wilson Loop ◽  
Strong Coupling Expansion ◽  
Wilson Loops ◽  
Yang Mills ◽  
Lattice Monte Carlo ◽  
Area Law

We study the double-winding Wilson loops in the SU(N) Yang-Mills theory on the lattice. We discuss how the area law falloff of the double-winding Wilson loop average is modified by changing the enclosing contours C1 and C2 for various values of the number of color N. By using the strong coupling expansion, we evaluate the double-winding Wilson loop average in the lattice SU(N) Yang-Mills theory. Moreover, we compute the double-winding Wilson loop average by lattice Monte Carlo simulations for SU(2) and SU(3). We further discuss the results from the viewpoint of the Non-Abelian Stokes theorem in the higher representations.

scholarly journals Direct test of the AdS/CFT correspondence by Monte Carlo studies of $ \mathcal{N}=4 $ super Yang-Mills theory

2013 ◽  
Vol 2013 (11) ◽  
Author(s):  
Masazumi Honda ◽  
Goro Ishiki ◽  
Sang-Woo Kim ◽  
Jun Nishimura ◽  
Asato Tsuchiya
Keyword(s):  
Monte Carlo ◽  
Direct Test ◽  
Yang Mills ◽  
Monte Carlo Studies ◽  
Super Yang Mills Theory

scholarly journals QUANTUM MONTE CARLO METHOD APPLIED TO STRONGLY CORRELATED DILUTE FERMI GASES WITH FINITE EFFECTIVE RANGE

2009 ◽  
Vol 18 (04) ◽  
pp. 919-925 ◽  
Author(s):  
GABRIEL WLAZŁOWSKI ◽  
PIOTR MAGIERSKI
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Quantum Monte Carlo ◽  
Chemical Potential ◽  
Exact Diagonalization ◽  
Effective Range ◽  
Fermi Gases ◽  
Strongly Correlated ◽  
Sign Problem ◽  
Quantum Monte Carlo Method

We discuss the Auxiliary Field Quantum Monte Carlo (AFQMC) method applied to dilute neutron matter at finite temperatures. We formulate the discrete Hubbard-Stratonovich transformation for the interaction with finite effective range which is free from the sign problem. The AFQMC results are compared with those obtained from exact diagonalization for a toy model. Preliminary calculations of energy and chemical potential as a function of temperature are presented.

scholarly journals Lattice $$ \mathcal{N} $$ = 4 super Yang-Mills at strong coupling

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Simon Catterall ◽  
Joel Giedt ◽  
Goksu Can Toga
Keyword(s):  
Strong Coupling ◽  
Lattice Theory ◽  
Numerical Study ◽  
Lattice Action ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Sign Problem ◽  
Wide Range ◽  
Phase Out ◽  
Sign Problems

Abstract In this paper we present results from numerical simulations of $$ \mathcal{N} $$ N = 4 super Yang-Mills for two color gauge theory over a wide range of ’t Hooft coupling 0 < λ ≤ 30 using a supersymmetric lattice action [1]. Numerical study of this lattice theory has been stymied until recently by both sign problems and the occurrence of lattice artifact phases at strong coupling. We have recently developed a new action that appears capable of solving both problems. The resulting action possesses just SU(2) rather than U(2) gauge symmetry. By explicit computations of the fermion Pfaffian we present evidence that the theory possesses no sign problem and exists in a single phase out to arbitrarily strong coupling. Furthermore, preliminary work shows that the logarithm of the supersymmetric Wilson loop varies as the square root of the ’t Hooft coupling λ for large λ in agreement with holographic predictions.

scholarly journals The SU(3) spin model with chemical potential by series expansion techniques

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Jangho Kim ◽  
Anh Quang Pham ◽  
Owe Philipsen ◽  
Jonas Scheunert
Keyword(s):  
Equation Of State ◽  
Strong Coupling ◽  
Chemical Potential ◽  
Spin Model ◽  
Strong Coupling Regime ◽  
Nearest Neighbour ◽  
Reasonable Accuracy ◽  
New Methods ◽  
Current Series ◽  
Sign Problem

Abstract The SU(3) spin model with chemical potential corresponds to a simplified version of QCD with static quarks in the strong coupling regime. It has been studied previously as a testing ground for new methods aiming to overcome the sign problem of lattice QCD. In this work we show that the equation of state and the phase structure of the model can be fully determined to reasonable accuracy by a linked cluster expansion. In particular, we compute the free energy to 14-th order in the nearest neighbour coupling. The resulting predictions for the equation of state and the location of the critical end points agree with numerical determinations to $$ \mathcal{O} $$ O (1%) and $$ \mathcal{O} $$ O (10%), respectively. While the accuracy for the critical couplings is still limited at the current series depth, the approach is equally applicable at zero and non-zero imaginary or real chemical potential, as well as to effective QCD Hamiltonians obtained by strong coupling and hopping expansions.

scholarly journals $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills thermodynamics to order λ2

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Qianqian Du ◽  
Michael Strickland ◽  
Ubaid Tantary
Keyword(s):  
Strong Coupling ◽  
Finite Temperature ◽  
Weak Coupling ◽  
Chemical Potential ◽  
Entropy Density ◽  
Thermal Mass ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Debye Mass ◽  
Infrared Divergences

Abstract We calculate the resummed perturbative free energy of $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills in four spacetime dimensions (SYM4,4) through second order in the ’t Hooft coupling λ at finite temperature and zero chemical potential. Our final result is ultraviolet finite and all infrared divergences generated at three-loop level are canceled by summing over SYM4,4 ring diagrams. Non-analytic terms at $$ \mathcal{O} $$ O (λ3/2) and $$ \mathcal{O} $$ O (λ2 log λ) are generated by dressing the A0 and scalar propagators. The gauge-field Debye mass mD and the scalar thermal mass MD are determined from their corresponding finite-temperature self-energies. Based on this, we obtain the three-loop thermodynamic functions of SYM4,4 to $$ \mathcal{O} $$ O (λ2). We compare our final result with prior results obtained in the weak- and strong-coupling limits and construct a generalized Padé approximant that interpolates between the weak-coupling result and the large-Nc strong-coupling result. Our results suggest that the $$ \mathcal{O} $$ O (λ2) weak-coupling result for the scaled entropy density is a quantitatively reliable approximation to the scaled entropy density for 0 ≤ λ ≲ 2.

scholarly journals LARGE-NC UNIVERSALITY IN QCD AND QCD-LIKE THEORIES

2013 ◽  
Vol 21 ◽  
pp. 140-142
Author(s):  
MASANORI HANADA ◽  
YOSHINORI MATSUO ◽  
NAOKI YAMAMOTO
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
String Theory ◽  
Chemical Potential ◽  
Direct Application ◽  
Baryon Chemical Potential ◽  
Lattice Monte Carlo ◽  
Novel Approach ◽  
Sign Problem

A direct application of the lattice Monte Carlo method to QCD with a finite baryon chemical potential is difficult due to the sign problem. We introduce a novel approach to avoid the sign problem, which is inspired by the string theory.

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