Motivated by M-theory compactification on elliptic Calabi-Yau threefolds, we present a correspondence between networks of small resolutions for singular elliptic fibrations and Coulomb branches of five-dimensional N=1 gauge theories. While resolutions correspond to subchambers of the Coulomb branch, partial resolutions correspond to higher codimension loci at which the Coulomb branch intersects the Coulomb-Higgs branches. Flops between different resolutions are identified with reflections on the Coulomb branch. Physics aside, this correspondence provides an interesting link between elliptic fibrations and representation theory.
On Algebraic Singularities, Finite Graphs and D-Brane Gauge Theories: A String Theoretic Perspective
在这篇文章中，我们将从弦论的角度，讨论四维超对称规范理论的构造和代数奇点的解析之间的某些美丽的内在关系。我们回顾了一些详细的数学，如orbifolds，辛代数和代数表示，以及物理，如规范的线性西格玛模型，几何工程，Hanany-Witten设置和D-膜探针所需的背景。我们调查方面的世界体积规范动力学使用D-膜决议的各种卡-丘奇，特别是Gorenstein的concentrations和环面奇。注意力将集中在构造这些奇异背景的规范理论的一般方法上，包括有无NS-NS B-场的存在，以及T-场到膜的设置和膜在镜像几何中的包裹圈。应用程序等不同的和优雅的数学作为crepant决议的代数奇点，表示有限群和有限图，模不变量的仿射李代数等自然会出现。各种观点和概括麦凯的信件也将被考虑。本文是作者博士论文前三卷的部分摘录，这篇论文是在A。Hanany -他非常感激-在麻省理工学院理论物理中心，并且，在朋友的建议下，他张贴到ArXiv pro hac vice;这是他最真诚的希望，随后的页面可能对初学者有一些小用处。
We conjecture that the leading two-derivative tree-level amplitudes for gluons and gravitons can be derived from gauge invariance together with mild assumptions on their singularity structure. Assuming locality (that the singularities are associated with the poles of cubic graphs), we prove that gauge-invariance in just (n-1) particles together with minimal power-counting uniquely fixes the amplitude. Unitarity in the form of factorization then follows from locality and gauge invariance. We also give evidence for a stronger conjecture: assuming only that singularities occur when the sum of a s…
In this work, we first review the issues on the singularities and the boundary conditions in light cone gauge and how to regularize them properly. Then we will further review how these singularities and the boundary conditions can result in the gauge link at the infinity in the light cone direction in the Drell-Yan process. Except for reviewing, we also have verified that the gauge link at the light cone infinity has no dependence on the path not only for the Abelian field but also for non-Abelian gauge field.
The structure of singularities in perturbative massless gauge theories is investigated in coordinate space. The pinch singularities in coordinate-space integrals occur at configurations of vertices which have a direct interpretation in terms of physical scattering of particles in real space-time in the same way as for the loop momenta in the case of momentum-space singularities. In the analysis of vertex functions in coordinate space, the well-known factorization into hard, soft, and jet functions is found. By power-counting arguments, it is found that coordinate-space integrals of vertex func…
Excision of `repulson' singularities: a spacetime result and its gauge theory analogue
我们讨论时空奇异性的解决方案的背景下，重力/规范对应，膜系统产生的规范理论与八个超荷和超多重态。讨论的对象是非专家。与C. V. Johnson和J.Polchinski撰写关于hep-th/9911161的谈话，以各种形式发表于：PASCOS-99，阿斯彭冬季会议“超越标准模型”，班夫CIAR重力+宇宙学计划会议。
Perturbative QCD calculations in the light-cone gauge have long suffered from the ambiguity associated with the regularization of the poles in the gluon propagator. In this work we study sub-gauge conditions within the light-cone gauge corresponding to several known ways of regulating the gluon propagator. Using the functional integral calculation of the gluon propagator, we rederive the known sub-gauge conditions for the theta-function gauges and identify the sub-gauge condition for the principal value (PV) regularization of the gluon propagator's light-cone poles. The obtained sub-gauge cond…
Building on author's previous results in singular semi-Riemannian geometry and singular general relativity, the behavior of gauge theory at singularities is analyzed. The usual formulations of the field equations at singularities are accompanied by infinities which block the evolution equations, mainly because the metric is singular, hence the usual differential operators, constructed from the metric, blow up. However, it is possible to give otherwise equivalent formulations of the Einstein, Maxwell and Yang-Mills equations, which in addition admit solutions which can be extended beyond the si…
Discontinuity of gauge theory in the gauge condition $n\cdot\partial n\cdot A=0$, which emerges at $n\cdot k=0$, is studied here. Such discontinuity is different from that one confronts in axial gauge and can not be regularized by conventional analytical continuation method. The Faddeev-Popov determinate of the gauge $n\cdot\partial n\cdot A=0$, which is solved explicitly in the manuscript, behaves like a $δ$-functional of gauge potentials once singularities in the functional integral is neglected and the length along $n^μ$ direction of the space tends to infinity. As a sequence, perturbation …
We investigate the singularity structure of the $(-1)^F$ graded partition function in QCD with $n_f \geq 1$ massive adjoint fermions in the large-$N$ limit. Here, $F$ is fermion number and $N$ is the number of colors. The large $N$ partition function is made reliably calculable by taking space to be a small three-sphere $S^3$. Singularites in the graded partition function are related to phase transitions and to Hagedorn behavior in the $(-1)^F$-graded density of states. We study the flow of the singularities in the complex "inverse temperature" $β$ plane as a function of the quark mass. This a…
We calculate the three- and four-loop corrections to the massless fermion propagator in three-dimensional quenched Quantum Electrodynamics with four-component fermions. The three-loop correction is finite and gauge invariant but the four-loop one has singularities except in the Feynman gauge where it is also finite. Our results explicitly show that, up to four loops, gauge-dependent terms are completely determined by lower order ones in agreement with the Landau-Khalatnikov-Fradkin transformation.
The singularity structure of the Coulomb and Higgs branches of good $3d$ $\mathcal{N}=4$ circular quiver gauge theories (CQGTs) with unitary gauge groups is studied. The central method employed is the Kraft--Procesi transition. CQGTs are described as a generalisation of a class of linear quivers. This class degenerates into the familiar class $T_ρ^σ(SU(N))$ in the linear case, however the circular case does not have the degeneracy and so the class of CQGTs contains many more theories and much more structure. We describe a collection of good, unitary, CQGTs from which the entire class can be fo…
