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# Tag Info

### Mathematical uses of string theory

Monstrous moonshine, the famous relationship between the dimensions of the irreducible representations of the Monster group and the coefficients in the Fourier expansion of the $j$-invariant. ...
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### Freeman Dyson's approach to string theory

Dyson's A walk through Ramanujan's garden gives the background of this comment: He explains that the "seeds from Ramanujan's garden have been blowing on the wind and have been sprouting all over ...
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### In Gromov-Witten theory, why is the string coupling constant weighted by $2g-2$?

Here is a purely mathematical reason why we prefer to put $u^{2g-2}$ in our generating function instead of, say, $u^g$. The generating function you write, \sum_{g,\beta} GW_{g,\beta}(X) u^{2g-2}Q^...
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### In M-theory, what can hypothesis H tell us that quantization in ordinary cohomology cannot?

Traditional approach. Notice that what is considered in [DMW00; DFM03] and elsewhere to quantize the C-field flux $G_4$ is not just ordinary cohomology, but ordinary cohomology with bells and whistles ...

### Mathematician trying to learn string theory

I want to understand compactifications, Dualities, D-branes, M-branes etc. What makes all this hard to learn in a systematic way is that the theory itself is still incomplete and proceeds in parts ...

### Anomaly in QFT physics v.s. determinant line bundle

The partition function should assign to each possible field configuration $\Phi$ (or field history) in your quantum field theory a number $Z(\Phi)$. That is, it should be a function on the collection ...

### Does $SO(32) \sim_T E_8 \times E_8$ relate to some group theoretical fact?

It's worth noting this fact. Suppose $L$, $L'$ are even unimodular Euclidean lattices, like $\mathrm{E}_8= \Gamma^8$ or $\Gamma^{16}$ or any direct sum of these, but also the Leech lattice and 23 ...

### Mathematical uses of string theory

1) Verlinde's formula: Let $\mathrm{C}$ be a curve of genus $g\geqslant 2$. The Picard group of the Moduli space of rank $2$ bundles on $\mathrm{C}$ with trivial determinant is an infinite cyclic ...
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### What are "branes", and why do they form a category?

Let me start by putting your questions into a bit more context. Kapustin and Witten's story occurs within string theory, a theory of 1-dimensional extended objects. Strings may be "closed," ...
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Although it might seem futile, given how far most of the activity on AdS/CFT is from rigorous mathematics, I think this a good question, provided one is happy, for now, with (very) baby versions of ...

Since the AdS/CFT correspondence links quantum field theory to something as exotic as quantum gravity, I don't think there is any hope for precise mathematical statements coming out of that ...
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### Do all $\mathcal{N}=2$ Gauge Theories "Descend" from String Theory?

The answer is Yes, at least when the ALE space (more precisely the ALF space instead) is of type $A$. Very roughly, one consider Donaldson-Thomas invariants for the same noncompact Calabi-Yau space, ...

### Freeman Dyson's approach to string theory

I don't think it would have convinced Feynman because he didn't like the rabbit hole that string theory seemed to be going down. That instead of trying to explain some phenomenon, that they were ...
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### Manifolds with negative dimension – Definition, References

Smooth manifolds of negative dimension are defined in derived geometry. Recall that if A→M and B→M are two transversal submanifolds of codimension a and b respectively, then their intersection C is ...

### Mathematical uses of string theory

I recall that Richard Wentworth's first paper on precise constants in bosonization formula (which is part of his PhD thesis?) extensively used computational methods from bosonic string theory. I am ...
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### Supersymmetry charge $Q$ as anti-linear and anti-unitary operator

Suppose you are given a super Hilbert space $\mathcal{H} = \mathcal{H}_0 \oplus \mathcal{H}_1$, with bosonic and fermionic subspaces $\mathcal{H}_0$ and $\mathcal{H}_1$ respectively. Define a new ...