Fermionic Spectrum on General Dimensional Hyperdiamond Lattice

Minimally doubled fermions at one-loop level

Single fermionic degrees of freedom together with standard chiral symmetry at finite lattice spacing, correct continuum limit and local interactions only are precluded by the Nielsen-Ninomiya no-go theorem. The class of minimally doubled fermion actions exhibits exactly two chiral modes. Recent interest in these actions has been sparked by the investigation of fermionic actions defined on "hyperdiamond" lattices. Due to the necessity of breaking hypercubic symmetry explicitly, radiative corrections generate operator mixings with relevant and marginal operators that should vanish in continuum Q…

Introducing Fermionic Link Models

Quantum link models (QLMs) are extensions of Wilson-type lattice gauge theories, and show rich physics beyond the phenomena of conventional Wilson gauge theories. Here we explore the physics of $U(1)$ symmetric QLMs, both using a more conventional quantum spin-1/2 representation, as well as a fermionic representation. In 2D, we show that both bosonic and fermionic QLMs display the same physics. We then explore the models in 3D and find different behavior for the two QLMs. For the bosons, we see evidence for a quantum phase transition from a symmetry broken phase to a potential quantum spin liq…

Kaplan格手征费米子的欧几里德谱

The Euclidean Spectrum of Kaplan's Lattice Chiral Fermions

我们考虑（2n+1）维欧几里德狄拉克算子的质量项，看起来像一个域壁，最近提出的卡普兰描述手征费米子在$2n$维。在连续的情况下，我们表明，欧几里德光谱包含{ \it无}束缚态与非零动量。在晶格上，只有当$m$被微调到某些特定值时，才存在没有能隙的束缚态谱，并且色散关系不能描述相对论费米子。尽管有这些特殊性，费米传播子{ \it}在畴壁上具有预期的（1/p斜线）极点。但在非微扰水平上，费米子行列式的相位可能有问题。

具有伴随物质的1+1维大N QCD的弦谱

String Spectrum of 1+1-Dimensional Large N QCD with Adjoint Matter

我们提出了弦论的规范矩阵模型，以消除不需要的非单重态。为此，我们在1+1维中对大N规范理论进行离散光锥量子化，标量或费米子物质场在SU（N）的伴随表示中变换。整个谱由玻色子和费米子闭弦激发组成，当N趋于无穷大时，它们是自由的。我们分析了这种束缚态作为截止和规范耦合的函数的一般特征，对于伴随费米子的情况获得了良好的收敛性。我们讨论可能的扩展模型和寻找新的非临界弦论。

Holographic models of composite Higgs in the Veneziano limit. Part II. Fermionic sector

We continue our study of strongly-coupled, approximately scale-invariant gauge theories with a large number of flavours, which provide a suitable ultraviolet completion of the composite-Higgs scenario. We identify the requisite operators to realise partial compositeness of the Standard-Model fermions. In order to compute the spectrum of composite fermionic states, we extend the bottom-up holographic models, which we previously introduced to capture the main features of the non-perturbative dynamics in the Veneziano limit, by adding fermion fields in the bulk. We identify regions in parameter s…

Yang-Mills gauge theories from fermionic lattice models

A doublet of three-dimensional Dirac fermions can effectively describe the low energy spectrum of a fermionic cubic lattice. We employ this fermion doubling to encode a non-Abelian SU(2) charge in the fundamental representation. We explicitly demonstrate that suitable distortion of the tunnelling couplings can introduce a scalar and a Yang-Mills field in the effective low energy description, both coupled to the Dirac fermions. As an application we simulate Yang-Mills monopoles that give rise to localized zero-modes and fermion fractionalization. The generation of the non-Abelian field in the t…