SU（N）规范理论在任意表示R中的费米子的相图可以在有限体积流形上计算，如S^1 x S^3。当S ^3很小时，微扰分析是可能的，并且在大N极限下可以得到纯杨-米尔斯理论的禁闭-解除禁闭跃迁的弱耦合模拟。我们计算了伴随QCD [SU（N）规范理论与伴随费米子]的大N相图，其中对S ^1上的费米子施加周期性边界条件，使得对于足够轻的伴随费米子质量，约束相是有利的。我们计算了质量乘以S^3的半径的值，在该值以下，对于S^1 / S^3的所有体积，限制相都是有利的，并讨论了N体积大减少的含义。我们还计算了N = 3的相图，并与最近的晶格结果进行了比较。
英文摘要：
The phase diagram of SU(N) gauge theories with fermions in an arbitrary representation R can be calculated on finite volume manifolds such as S^1 x S^3. When S^3 is small a perturbative analysis is possible and the weak-coupling analogue of the pure Yang-Mills theory confinement-deconfinement transition is accessible in the large N limit. We calculate the large N phase diagram of adjoint QCD [SU(N) gauge theory with adjoint fermions] where periodic boundary conditions are applied to fermions on S^1 such that the confined phase is favored for light enough adjoint fermion mass. We calculate the value of the mass times the radius of S^3 below which the confined phase is favored for all volumes of S^1 / S^3 and discuss the implications for large N volume reduction. We calculate also the phase diagram for N = 3 and compare with recent lattice results.
We analyze the large $N$ limit of adjoint QCD, an $SU(N)$ gauge theory with $N_f$ flavors of massless adjoint Majorana fermions, compactified on $S^3 \times S^1$. We focus on the weakly-coupled confining small-$S^3$ regime. If the fermions are given periodic boundary conditions on $S^1$, we show that there are large cancellations between bosonic and fermionic contributions to the twisted partition function. These cancellations follow a pattern previously seen in the context of misaligned supersymmetry, and lead to the absence of Hagedorn instabilities for any $S^1$ size $L$, even though the bo…
We discuss an exotic phase that adjoint QCD possibly exhibits in the deep infrared (IR). It is a confining phase, with a light spectrum consisting of massless composite fermions. The discrete chiral symmetry is broken, with unbroken continuous chiral symmetry. We argue that it may give a description of the IR of adjoint QCD with three massless Weyl flavors and that it passes all consistency checks known to us.
We study strings between static quarks in QCD with $n_f$ adjoint fermions, including $N=1$ Super Yang-Mills (SYM), in the calculable regime on $\mathbb R^3\times \mathbb S^1$. We find that they have many qualitatively new features not previously known. The difference from other realizations of abelian confinement is due to the composite nature of magnetic bions, whose Dirac quantum with fundamental quarks is two, and to the unbroken part of the Weyl group. In particular we show that strings are composed of two domain walls, that quarks are not confined on domain walls, that strings can end on …
Large-N reduction in QCD-like theories with massive adjoint fermions
具有重伴随费米子的大N量子色动力学在长距离上模拟了纯杨-米尔斯理论。我们研究这个理论上的四个和三个环面，并分析认为存在一个大小体积等效。对于任何有限质量，中心对称不破缺相存在于足够小的体积，这个阶段可以用来研究大体积极限通过江口-河合等价。有限温度版本的体积无关性意味着R^3 x S^1上的热力学可以通过S^1上的酉矩阵量子力学来研究，只要改变温度。为了证实这一点的非微扰，我们数值研究零维和一维的理论，使用蒙特卡罗模拟。有限N次修正的阶数为1/N。我们介绍了各种扭曲版本的约化QCD系统地抑制有限N修正。利用扭曲模型，我们在1^3 × 2晶格上观察到了禁闭/解除禁闭的转变。结果与Yang-Mills理论的大体积模拟结果一致。我们还评论说，扭曲模型可以作为一个非微扰制定的非交换杨米尔斯理论。
In this work we consider the $SU(N)$ gauge theory with two Dirac fermions in the adjoint representation, in the limit of large $N$. In this limit the infinite-volume physics of this model can be studied by means of the corresponding twisted reduced model defined on a single site lattice. Making use of this strategy we study the reduced model for various values of $N$ up to 289. By analyzing the eigenvalue distribution of the adjoint Dirac operator we test the conformality of the theory and extract the corresponding mass anomalous dimension.
The infrared effective theory of adjoint QCD with one Dirac flavour is still under debate. The theory could be confining, conformal, or with a massless fermion in the infrared. The study of chiral symmetry seems to be important to answer this question. While previous investigations have considered Wilson fermions, we present here the first results for this theory based on overlap fermions to avoid explicit chiral symmetry breaking. These indicate spontaneous chiral symmetry breaking by the formation of a fermion condensate. We have also investigated the running coupling of the theory, which in…
We study four dimensional $SU(2)$ Yang-Mills theory with two massless adjoint Weyl fermions. When compactified on a spatial circle of size $L$ much smaller than the strong-coupling scale, this theory can be solved by weak-coupling nonperturbative semiclassical methods. We study the possible realizations of symmetries in the $\mathbb R^4$ limit and find that all continuous and discrete $0$-form and $1$-form 't Hooft anomaly matching conditions are saturated by a symmetry realization and massless spectrum identical to that found in the small-$L$ limit, with only a single massless flavor-doublet …
Gauge theories with fermions in adjoint and fundamental representations are relevant for many different applications including composite Higgs models and general aspects of the confinement problem. We present first results from simulations of SU(2) gauge theory with two Dirac fermions in the fundamental representation and one adjoint flavor. In this context, we also discuss applications towards simulations of supersymmetric QCD.
The mass anomalous dimension is determined in SU(2) gauge theory coupled to $N_f$ fermions in the adjoint representation for $N_f = 2$, $3/2$, $1$ and $1/2$, where half-integer flavor numbers correspond to Majorana fermions. The numerical method is based on gradient flow. The results show near-conformal behavior for $N_f = 2$, $3/2$ and $1$. Particular emphasis is placed on $N_f = 2$, which is relevant for a strongly interacting extension of the Standard Model and has been studied in several previous investigations. We check whether the method is able to resolve discrepancies in earlier result…
Phase Structure of Confining Theories on R^3 x S^1
最近关于R^3 x S^1的类QCD理论的研究表明，当S^1的周长L足够小时，可以存在受限相。伴随QCD和双迹形变理论在一定条件下就是这样的理论，我们给出了它们的相图的一些新结果。首先，我们用Polyakov-Nambu-JonaLasinio模型给出了SU（3）伴随QCD相图中大L和小L受限区之间的联系。然后我们考虑了SU（2）双迹形变理论，研究了Higgs和小L禁闭相之间的矛盾。
In this work we investigate the infrared behaviour of a Yang-Mills theory coupled to a massless fermion in the adjoint representation of the gauge group SU(2). This model has many interesting properties, corresponding to the $\mathcal{N}=2$ Super-Yang-Mills theory without scalars and in the recent years there has been an increasing interest toward understanding whether confinement and fermion condensation occur at low energy. We simulate the theory on the lattice close to the massless limit using the overlap discretization of the fermion action, allowing a precise and clean study of the chiral…
We study chemical-potential dependence of confinement and mass gap in QCD with adjoint fermions in spacetime with one spatial compact direction. By calculating the one-loop effective potential for the Wilson line in the presence of chemical potential, we show that a center-symmetric phase and a center-broken phase alternate when the chemical potential in unit of the compactification scale is increased. In the center-symmetric phase we use semiclassical methods to show that photons in the magnetic bion plasma acquire a mass gap that grows with the chemical potential as a result of anisotropic i…
Recent work explores the candidate phases of the 4d adjoint quantum chromodynamics (QCD$_4$) with an SU(2) gauge group and two massless adjoint Weyl fermions. Both Cordova-Dumitrescu and Bi-Senthil propose possible low energy 4d topological quantum field theories (TQFTs) to saturate the higher 't Hooft anomalies of adjoint QCD$_4$ under a renormalization-group (RG) flow from high energy. In this work, we generalize the symmetry-extension method [arXiv:1705.06728] to higher symmetries, and formulate higher group cohomology and cobordism theory approach to construct higher-symmetric TQFTs. We pr…
In this work we present the results of our investigation of \su{2} gauge theory with two Dirac fermions in the adjoint representation (aQCD2), which belongs to the class of strongly interacting gauge theories that are of basic interest for extensions of the Standard Model. We have done numerical lattice simulations of this theory at two different values of the gauge coupling and several fermion masses. Our results include the particle spectrum and the mass anomalous dimension. The spectrum contains new exotic fermion-gluon states and flavour-singlet mesons. The mass anomalous dimension is dete…
Non-perturbative volume-reduction of large-N QCD with adjoint fermions
我们利用非微扰格点方法研究了具有单个伴随Dirac费米子的四维大N量子色动力学的体积约化“Eguchi-Kawai”模型。我们探索了这个单点理论在夸克质量和规范耦合的空间中的相图，使用威尔逊费米子的颜色在8 <= N <= 15的范围内。我们的证据表明，N的这些值足够大，可以确定N->oo的相图的性质。我们确定了参数空间中（Z_N）^4中心对称性保持不变的区域。根据以前的理论工作，使用轨道折叠范式，并假设平移不变性在无限体积理论中不会自发地被打破，在这个区域中，体积减少成立：当N->oo时，单位点和无限体积理论变得等价。我们发现强有力的证据表明，该区域包括轻和重夸克（质量在截止尺度），我们的结果是一致的，该区域向连续极限延伸。我们还比较了重叠狄拉克算符在基本表象中的作用量密度和本征值密度与在大N纯规范理论中得到的结果。
Theories with fermions in the adjoint representation have several interesting applications in extensions of the standard model. The conformal window for these theories is of particular interest for technicolour extensions. We present here our newest results for the spectrum of $N_f=2$ adjoint QCD and compare them with the predictions for a conformal behaviour. The comparison with supersymmetric Yang-Mills theory, investigated with the same methods, will help to distinguish more clearly the conformal and the confining scenario. The spectrum includes additional fermionic states that are not pres…
