# Tagged Questions

String theory is an research framework in particle physics that attempts to reconcile quantum mechanics and general relativity.

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### Trace identities for $\text{SO}(n)$

The Green-Schwarz mechanism in Type I string theory involves certain identities relating traces in the vector and adjoint representations of $\text{SO}(n)$ of dimension $n$ and $n(n - 1)/2$ ...
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### Complex and Kähler-manifolds

I was woundering if anyone knows any good references about Kähler and complex manifolds? I'm studying supergravity theories and for the simpelest N=1 supergravity we'll get these. Now in the course-...
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### String Theory: What to do?

This is going to be a relatively broad/open-ended question, so I apologize before hand if it is the wrong place to ask this. Anyways, I'm currently a 3rd year undergraduate starting to more seriously ...
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### CFT's vs Vertex Operator Algebras

I am trying to clear my ideas about the relation between a Conformal Field Theory (CFT) and a Vertex Operator Algebra (VOA). For me a CFT based on a (complex) vector space $H$ is a projective monoidal ...
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### How many different subsequence in Thue-Morse sequence

Consider the Thue-Morse string. Suppose it has $n$ elements. My question is: how many different substrings(or subsequence) in this string. Actually I'm interest in bound of this value. Is it smth ...
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### What is spectral flow symmetry?

I can't find much about this, and am looking into this to satisfy personal curiosity. I will like to know what spectral flow is, and what spectral flow symmetry is. I tried looking for this on ...
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### Image of ring homomorphism $\phi : \mathbb{Z}[t] \to \mathbb{Q}$?

Here is a problem I face practicing the theory of rings: Define $\phi : \mathbb{Z}[t] \to \mathbb{Q}$, a ring homomorphism (it does map $1$ to $1$). I'm trying to show that if $\phi(t)=\frac{u}{v}$...
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### Semi-infinite forms?

I am reading Vafa's paper 'Topological Mirros and Quantum Strings'(arXiv:hep-th/9111017). In this paper, the author says the Hilbert Space of a fermionic string theory corresponds to the space of semi-...
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### Physical interpretation of categorical structures related to Dirichlet Branes

In Dirichlet Branes and Mirror Symmetry by Aspinwall et al, section 5.9 discusses various questions that remain open. In particular they say: "There are many constructions from homological ...
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### (Soft Question) How active an area of research is Non-Commutative Geometry? [closed]

I am currently an undergraduate, but I am considering applying for a phd in algebraic geometry or a related field. I am quite interested in the link between non-commutative geometry and theoretical ...
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### How many bit strings of length 7 exist if the string remains unchanged if it is reversed?

How many bit strings of length 7 exist if the string remains unchanged if it is reversed ? 1 1 1 1 1 1 1 and 1 0 0 1 0 0 1 are an example that is unchanged if reversed. 0 0 0 0 0 0 0 and 0 1 1 0 1 1 ...
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### rigorous treatment of infinitesimal reparametrizations

my first post :) I am asking this directed to mathematicians or mathematical physicists since I don't like the usual physics approach. Reading some string theory books I always find that the ...
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### What is a good gentle introduction to the Virasoro algebra and its application in theoretical physics?

I am looking for an as gentle and pedagogical as possible introduction that explains the Virasoro algebra and its applications in theoretical physics; finally I am interested in its application in ...
So I'm doing a little calculus of variations on an eigenvalue problem. The goal of this is to find an upper bound for the $\omega_0$ as follows: \$\omega_0^2 \leq \frac{T_0\int_0^a\left|\frac{d\psi}{...