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I can answer your literal question. Not everyone studies exotic $\mathbb{R}^4$, because the universe of mathematical and theoretical physics is a big one with many interesting ideas, and there's no r …

I'm not a mathematical physicist, so parts of this may be wrong. In quantum field theory, one encounters operators that are supported at points in spacetime, or at least are very local. For example …

I disagree (though not particularly strongly) with the comments claiming that you should learn classical mechanics first. You don't need much physics background to learn to do basic calculations with …

I can't address all uses by all physicists, but in many contexts, they consider only representations at a fixed level that admit a well-behaved energy grading. That is, sometimes an energy grading is …

For the case of vector spaces graded by an abelian group (with braiding determined by an abelian 3-cocycle following Joyal-Street), this was done by Dong and Lepowsky in their 1993 book "Generalized V …

Let $\mathfrak{g}$ be a complex Lie algebra with a distinguished nonzero central element $x$, and let $V$ be an irreducible representation of $\mathfrak{g}$. The usual proof of Schur's lemma can be a …

Section 5 of Borcherds, Barnard, Lectures on Quantum Field Theory is a discussion of the 0-dimensional spacetime case, which gives finite dimensional integrals.

If your VOA $V$ is not rational, then it is quite unlikely that its category of representations is a modular tensor category. That is, you can safely conclude that Theorem 3 contains an unstated assu …

I'm not an expert on black holes, but I can give you a couple pointers. From work of Bekenstein and Hawking in the 1970s, we are pretty sure that macroscopic black holes in our 3+1 dimensional univer …

In general, we expect field theories to be described by some higher categorical structures, where bulk models are assigned objects (also called 0-morphisms), domain walls are assigned morphisms (also …

$S^3 \times S^5$ has isometry group $SO_4(\mathbb{R}) \times SO_6(\mathbb{R})$, which has $SU(2) \times SU(2) \times SU(4)$ as a four-fold cover. Since it appears that you aren't worrying too much ab …

I think the suggested example is not a good fit for illustrating a tensor product decomposition, because $L^2$ functions on an interval are most naturally identified with states of a single particle i …

The ring of functions on your supermanifold is $C^\infty(\mathbb{R}) \otimes \mathbb{C}[a,b]$, where $a$ and $b$ are odd. The even part is then $C^\infty(\mathbb{R}) \oplus C^\infty(\mathbb{R})ab$, w …

The notation $*/\!/G$ refers to the topological groupoid with a single object, whose morphisms are described by the compact Lie group $G$. The double slash in this context means groupoid quotient, an …

The answer to your question is Yes. Consider your covering group $C$ as a central extension: $$1 \to N \to C \to G \to 1$$ and suppose it is given by a 2-cocycle $\alpha \in H^2(G, N)$. Then for any …