High Energy Physics Lattice

We present results from lattice QCD calculations for2ndand4thorder cumulants of conserved charge fluctuations and correlations, and compare these with various HRG model calculations. We show that differences between HRG and QCD calculations already show up in the second order cumulants close to the pseudo-critical temperature for the chiral transition in (2+1)-flavor QCD and quickly grow large at higher temperatures. We also show that QCD results for strangeness fluctuations are enhanced over HRG model calculations which are based only on particles listed in the Particle Data Group tables as 3-star resonances. This suggests the importance of contributions from additional strange hadron resonances. We furthermore argue that additional (repulsive) interactions, introduced either through excluded volume (mean field) HRG models or the S-matrix approach, do not improve the quantitative agreement with2ndand4thorder cumulants calculated in lattice QCD. HRG based approaches fail to describe the thermodynamics of strongly interacting matter at or shortly above the pseudo-critical temperature of QCD.

We evaluate the gluon and quark contributions to the spin of the proton using an ensemble of gauge configuration generated at physical pion mass. We compute all valence and sea quark contributions to high accuracy. We perform a non-perturbative renormalization for both quark and gluon matrix elements. We find that the contribution of the up, down, strange and charm quarks to the proton intrinsic spin is12∑q=u,d,s,cΔΣq+=0.191(15)and to the total spin∑q=u,d,s,cJq+=0.285(45). The gluon contribution to the spin isJg=0.187(46)yieldingJ=Jq+Jg=0.473(71)confirming the spin sum. The momentum fraction carried by quarks in the proton is found to be0.618(60)and by gluons0.427(92), the sum of which gives1.045(118)confirming the momentum sum rule. All scale and scheme dependent quantities are given in theMS¯¯¯¯¯¯¯scheme at 2 GeV.

Using complex Langevin method we probe the possibility of dynamical supersymmetry breaking in variousN=2supersymmetric quantum mechanical models with complex potentials including the ones exhibitingPTsymmetry. Traditional Monte Carlo methods based on importance sampling fail in these situations. From the simulations, we conclude that complex Langevin method can reliably predict the absence or presence of dynamical supersymmetry breaking in the these models.

Monte Carlo simulation of gauge theories with aθterm is known to be extremely difficult due to the sign problem. Recently there has been major progress in solving this problem based on the idea of complexifying dynamical variables. Here we consider the complex Langevin method (CLM), which is a promising approach for its low computational cost. The drawback of this method, however, is the existence of a condition that has to be met in order for the results to be correct. As a first step, we apply the method to 2D U(1) gauge theory on a torus with aθterm, which can be solved analytically. We find that a naive implementation of the method fails because of the topological nature of theθterm. In order to circumvent this problem, we simulate the same theory on a punctured torus, which is equivalent to the original model in the infinite volume limit for|θ|<π. Rather surprisingly, we find that the CLM works and reproduces the exact results for a punctured torus even at largeθ, where the link variables near the puncture become very far from being unitary.

We demonstrate that the complex Langevin method (CLM) enables calculations in QCD at finite density in a parameter regime in which conventional methods, such as the density of states method and the Taylor expansion method, are not applicable due to the severe sign problem. Here we use the plaquette gauge action withβ=5.7and four-flavor staggered fermions with degenerate quark massma=0.01and nonzero quark chemical potentialμ. We confirm that a sufficient condition for correct convergence is satisfied forμ/T=5.2−7.2on a83×16lattice andμ/T=1.6−9.6on a163×32lattice. In particular, the expectation value of the quark number is found to have a plateau with respect toμwith the height of 24 for both lattices. This plateau can be understood from the Fermi distribution of quarks, and its height coincides with the degrees of freedom of a single quark with zero momentum, which is 3 (color)×4 (flavor)×2 (spin)=24. Our results may be viewed as the first step towards the formation of the Fermi sphere, which plays a crucial role in color superconductivity conjectured from effective theories.

In this review we present the current state-of-the-art on complex Langevin simulations and their implications for the QCD phase diagram. After a short summary of the complex Langevin method, we present and discuss recent developments. Here we focus on the explicit computation of boundary terms, which provide an observable that can be used to check one of the criteria of correctness explicitly. We also present the method of Dynamic Stabilization and elaborate on recent results for fully dynamical QCD.

The type IIB matrix model, also known as the IKKT matrix model, is a promising candidate for a nonperturbative formulation of superstring theory. In this talk we study the Euclidean version of the IKKT matrix model, which has a "sign problem" due to the Pfaffian coming from integrating out the fermionic degrees of freedom. To study the spontaneous breaking of the SO(10) rotational symmetry, we apply the Complex Langevin Method (CLM) to the Euclidean IKKT matrix model. We conclude that the SO(10) symmetry is broken to SO(3), in agreement with the previous studies by the Gaussian Expansion Method (GEM). We also apply the GEM to the deformed model and find consistency with the CLM result. These are proceedings of Takehiro Azuma's talk at Asia-Pacific Symposium for Lattice Field Theory (APLAT 2020) on August 4-7, 2020, based on the paper arXiv:2002.07410.

We discuss the problem of possible boundary terms at poles of the drift in the complex Langevin method, which spoil correctness of the method. For the simplest, however paradigmatic cases we can find complete answers. Lessons for more generic cases as well as open mathematical problems are discussed.

The Monte Carlo evaluation of path integrals is one of a few general purpose methods to approach strongly coupled systems. It is used in all branches of Physics, from QCD/nuclear physics to the correlated electron systems. However, many systems of great importance (dense matter inside neutron stars, the repulsive Hubbard model away from half-filling, dynamical and non-equilibrium observables) are not amenable to the Monte Carlo method as it currently stands due to the so-called "sign-problem". We review a new set of ideas recently developed to tackle the sign problem based on the complexification of field space and the Picard-Lefshetz theory accompanying it. The mathematical ideas underpinning this approach, as well as the algorithms so far developed, are described together with non-trivial examples where the method has already been proved successful. Directions of future work, including the burgeoning use of machine learning techniques, are delineated.

In the post-Higgs discovery era, the primary goal of the Large Hadron collider is to discover new physics Beyond the Standard Model. One fundamental question is does new beyond the Standard Model composite dynamics provides the origin of the Higgs field and potential. After reviewing the main motivations to consider composite models based on a new strongly interacting sector, we summarise the efforts of the lattice community to investigate the viability of models featuring a composite Higgs sector. We argue that first principle calculations are necessary in view of the fast improvements in accuracy of experimental measurements in the Higgs sector. We stress the importance for lattice calculations to provide a testing benchmark for non perturbative mechanisms. It is highlighted that the rich phenomenology of non-abelian gauge theories raises a number of questions that can be explored using lattice calculations. First principle results therefore provide crucial insights in the theory landscape that could guide the next generation of Composite Higgs models.