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I suppose that you don't really mean for both spaces to be spheres, so I will interpret your question about the (4,7) split. The context here is eleven-dimensional supergravity and the studies of suc …

(By the way, the use of "holomorphic" and "antiholomorphic" is wrong in your question. This may be confusing people, which perhaps explains why nobody has answered this question yet.) Conformal Killi …

Tony Phillips, a topologist at Stony Brook who taught me differential topology when I was a first-year graduate student, has worked on lattice gauge theory since the mid-to-late 1980s. You can try to …

The original reference for Wick's theorem is, not surprisingly, Wick's original 1950 paper: The Evaluation of the Collision Matrix published in the Physical Review 80 (2) pp. 268-272. He also shows h …

The Hilbert scheme of points on a K3 surface plays an important rôle in providing a strong coupling test of S-duality by Vafa and Witten. This is the original paper on what is known as Vafa-Witten th …

Of course there are. A nice early example is the Wess--Zumino--Witten model based on a non-semisimple group admitting a bi-invariant lorentzian metric: @article{Nappi:1993ie, author = …

Yes. This follows from the fact that $G_2$ acts on the octonions via automorphisms. Let $e_i$, $i=1,\dots,7$ be a choice of 7 imaginary octonion units and let $1$ denote the identity. Then by defin …

Sure you can. In fact, this usually goes by the name of strings without strings. The basic observation is that when you quantise the sigma model when $M$ is, say, Minkowski spacetime, what you end u …

Let $(M,g)$ be an orientable pseudo-riemannian manifold. Each tangent space $T_xM$ is a pseudo-euclidean space and hence has an associated Clifford algebra $CL(T_xM)$, which is the fibre at $x\in M$ …

The geodesics you seek are the so-called homogeneous geodesics. Not all geodesics will be of this form, but there certainly exist. In the literature, for some reason, people consider left-invariant …

You would actually not expect 22 dilatons. Let me try to explain. As you have pointed out, a putative field theory limit of the closed bosonic string would consist of a metric, a 2-form (which is th …

I'm afraid that this answer will be somewhat physics-y. Apologies if this is deemed inappropriate for MO. First of all, I think that it is slightly misleading to say that one has "fractional charge …

I am quite late answering this question, even though I followed it when it first appeared, but it must have slipped my mind. Anyway, it's been a while now and nobody seems to have mentioned my favour …

Let $(M,g)$ be a four-dimensional lorentzian manifold. Then for all $p\in M$, the tangent space $T_p M$ to $M$ at $p$ is a lorentzian inner product space relative to the restriction $g_p$ of the metr …

Although it’s behind an Elsevier pay-wall, there is one paper which explains in cohomological terms the picture-changing operator in the context of string field theory. If I remember correctly it is …