He., D-brane

gauge theories from toric singularities and toric duality.

However, the premises of this argument conflict with the

gauge theories of particle physics, and so this version of the argument is no more successful than its predecessors.

Joos,

Gauge Theories of the Strong and Electroweak Interaction, B.

Three-algebras and N = 6 Chern-Simons

gauge theories. Phys.

The presentation is organized into three parts that describe the most important non-perturbative techniques of two-dimensional field theory, two-dimensional

gauge theories with emphasis on applying the previously discussed non-perturbative techniques, and non-perturbative aspects of gauge dynamics in four dimensions.

(The lessons of the hole argument in general relativity do not generalize straightforwardly to arbitrary

gauge theories.) Worlds that differ merely haecceitistically are related to one another by a permutation of individuals.

According to the predictions of unified

gauge theories, supersymmetry, supergravity, and string theory, there would exist a number of light and massless particles [1].

I begin in Section 2 by sketching the formalism and interpretative problems of

gauge theories in general.

Aims: Characterizing M-theory compactifications on $G_2$ manifolds, and using these to obtain phenomenologically interesting 4-dimensional

gauge theories. Novelty of research methodology: Utilizing new constructions of $G_2$ holonomy manifolds obtained recently in the mathematics literature.

The topics include three-dimensional supersymmetric

gauge theories and Hilbert series, quantized Coulomb branches of Jordan quiver

gauge theories and cyclotomic rational Cherednik algebras, a journey from the Hitchen section of the oper moduli, pure SU(2) gauge theory partition function and generalized Bessel kernal, contracting the Weierstrass locus to a point, and spectral theory and mirror symmetry.

It is well-known that the three out of four fundamental interactions of nature can be well described by the

gauge theories and associated local gauge symmetries.

Pons, "Equivalence of Faddeev-Jackiw and Dirac approaches for

gauge theories," International Journal of Modern Physics A, vol.