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Regarding the first part of this question, in four spacetime dimensions there are no known generic violations of the cosmic censorship hypothesis while above four dimensions there is good evidence tha …

Regarding your first question, physicists are interested in classifying modular invariant partition functions for two-dimensional rational conformal field theories. Simple currents are a useful tool f …

The rational numbers $\mathbb{Q}$ are central to number theory, so I think it would be reasonable to claim a connection between number theory and ``real” physics if there were a physical system with p …

You might find "An Introduction to Conformal Field Theory" by M. Gaberdiel (arXiv:hep-th/9910156v2) useful. He has a brief discussion of how in some cases chiral algebras can be assembled into Conform …

There a number of papers by Alain Connes on Dimensional Regularization (Dim Reg) in the context of noncommutative field theory. Some of his papers cite P. Breitenlohner and D. Maison, "Dimensional re …

Greg Moore recently gave the Felix Klein lectures and a draft of notes for his lectures is available at http://www.physics.rutgers.edu/~gmoore/FelixKleinLectureNotes.pdf You will find in the first …

I suspect part of the confusion is due to the fact that the $SU(2)$ appearing in the Standard Model gauge group $U(1)\times SU(2) \times SU(3)$ is different from the $SU(2)$ of the Cassen-Condon paper …

I'm not sure exactly what kind of information you want, and CFT is an enormous subject, but here is some information on the physical interpretation of the complex coordinates and correlation functions …

Many string theorists would like to know more algebraic geometry. There are a few of us who know algebraic geometry at a pretty high level (not me) but many more who would like to learn more and feel …

As a physicist "in nature" perhaps I can give a few examples that illustrate how non-analytic functions can appear in physics and counter the idea that physicists do not worry about the justification …

In supersymmetric field theories and string theories there are special states called BPS states which are annihilated by some of the supercharges and whose mass is determined in terms of their charges …

The Higgs mechanism in the Standard Model doesn't have much to do with deformation quantization as other people have explained. However there is a version of the Higgs mechanism in string theory which …

The bimonster acts as the automorphism group of a particular bosonic closed string theory and D-brane states in this theory that preserve a chiral subalgebra transform in representations of the bimons …

The answers here have focused on the mathematical aspects of VOAs and the motivation coming from QFT, the specialization to Conformal Field Theory, and then the further specialization to two-dimension …

$4=11-7$ and $11$ is the maximal dimension for supersymmetry with spins $\le 2$ while $7$ is the first dimension in which there exist compact manifolds of exceptional holonomy.