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Pure Yang-Mills theory (YM) can be easily defined on $\mathbb{T}^4$ on a periodic lattice, using the Wilson lattice gauge theory approach. In reality, we know some of these mathematical results on $\m …

Coleman–Mandula theorem (by Sidney Coleman and Jeffrey Mandula) [1] is a no-go theorem in theoretical physics. It states that "space-time and internal symmetries cannot be combined in any but a trivia …

Locally Symmetric Spaces are the basis of the Langlands program—a set of ambitious and interconnected conjectures connecting representation theory to number theory, firstly proposed in 1967 by Robert …

In general Yang-Mills theory [1] seems to be different from the dimensional reduced Kaluza–Klein theory. However, the historical account was that people tried to trace back the origin of non-Abelian …

We know that group cohomology $H^2(G,U(1))$ consists of 2-cocycles $\beta(A,B)\in U(1)$ corresponding to elements in the group $H^2(G,U(1))$, where $A\in G,B \in G$. Note that $\beta(A,B)$ satisfies 2 …

question: What are the mathematical theories suitable to describe the "continuous Phase transitions between Category Theories"? The phase transitions mean that in terms of the quantum statistical p …

Yang-Mills gauge theory is given by the action $$ S_\text{YM}[A] = \int_M\mathrm{Tr}_\mathfrak{g}(F\wedge \star F)$$ whose Euler-Lagrange equations are the classical equations of motion. The classical …

In Wikipedia, it states about the magnetic monopole of the gauge theory is determined by the fact: This argument for monopoles is a restatement of the lasso argument for a pure U(1) theory. It gen …

Atiyah-Hitchin-Singer Ref 1 states that the number of virtual dimensions of the instanton moduli space for SU(N) Yang-Mills theory with topological charge $\mathcal{Q}$ over a manifold $X$ is given b …

In Looijenga's work below, if I understand correctly, it shows that Statement 1: At an algebraic variety, the moduli space of SU($N$) flat connections on a 2-torus $T^2$ is given by the space o …

Questions: I would like to have a precise description of the meanings of the Moduli Space of Flat Connections, such that it is understandable by mathematical physicists and physicists. For 3d Chern-S …

If I understand correctly, in the Refs below: We can see that the moduli space of SU($N$) flat connections over a torus, is equivalent to a complex projective space $\mathbb{P}^{N-1}$ Namely, $$ M_{\r …

A nonlinear σ model (NLSM) describes a scalar field Σ which takes on values in a nonlinear manifold called the target manifold T. The target manifold T is equipped with a Riemannian metric g. Σ is …

This is related to a previous question, where a nonlinear σ model (NLSM) describes a scalar field Σ which takes on values in a nonlinear manifold called the target manifold T. There we ask the general …

GSO (Gliozzi-Scherk-Olive) projection is an ingredient used in constructing a consistent model in superstring theory. The projection is a selection of a subset of possible vertex operators in the worl …