# Questions tagged [string-theory]

For questions about string theory, which is a research framework in theoretical physics and mathematical physics that attempts to unify quantum theories and general relativity.

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### Equivalence of the Dirac representation of the Lorentz algebra and its conjugate in even dimensions

In Polchinski's String Theory, Appendix B.1 we look at the smallest irreps of the Clifford algebra in even-dimensional spacetimes $d=2k+2$. In (B.1.16) he defines two operators from the gamma matrices ...
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### Levenshtein Distance vs Damerau Levenstein vs Optimal String Alignment Distance

Could anyone explain the differences between Levenshtein Distance vs Damerau Levenstein vs Optimal String Alignment Distance? And the Math behind calculating distance between the strings
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### Find a dual lattice basis for lattice $e_1 = \sqrt 2 \hat e_x, \ e_2 = -\frac{1}{\sqrt 2} \hat e_x + \sqrt{\frac{3}{2}}\hat e_y$

Given the basis vector of a lattice $L$: $$e_1 = \sqrt 2 \hat e_x, \ e_2 = -\frac{1}{\sqrt 2} \hat e_x + \sqrt{\frac{3}{2}}\hat e_y$$ I want to find a set of basis vector for the dual lattice $L^*$. ...
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### Origin and source of this quote pertaining to the Monster group

I asked an almost exact question on History of Science and Mathematics SE. I vaguely remember reading a quote/listening to a statement by (I think) John Conway which I can paraphrase as follows: "I ...
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### How Quintic 3-fold is a Calabi–Yau manifold and has non vanishing Ricci scalar?

It’s well known that quintic 3-fold is a Calabi-Yau manifold in the complex projective space $\mathbb{CP}^{n+1}$ , see for instance: https://en.m.wikipedia.org/wiki/Quintic_threefold Now the main ...
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### Unitarity of a representation in the physics literature (in particular in CFT)

In many places in the physics literature, and specifically in conformal field theory, a representation of the Virasoro algebra is defined to be unitary when $L_n^\dagger = L_{-n}$. For example in the ...
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### $1+2+3+4+5+\dotsb =\frac{-1}{12}$ Is this true in real domain? Can you tell where this series is used? [duplicate]

In our sequence and series class, my teacher wrote this series and asked if it makes any sense. We all were saying "this makes no sense at all." But when I Googled it, the whole world knows it. So ...
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### Sphere fibrations over Riemann surfaces

In a physics application, there's a 5-dimensional space which consists of a fibration of $S^3$ over a genus-$g$ Riemann surface $\Sigma_g$. In fact this nontrivial fibration is part of a bigger where ...
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### Riemann zeta-function regularization in string theory

First of all let me say that I am a physicist and therefore it is sometimes hard for me to understand some mathematical steps... Now, I've been trying to obtain the well known result for the zeta ...
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### A basis with rational entries for the Niemeier lattices

The Niemeier lattices are defined to be the 24 even, self-dual lattices in 24 dimensions. Can anyone provide me with explicit bases for them, such that all the entries of the bases are rational ...
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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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### 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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### 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-...
Let $\Sigma$ be a compact $2$-manifold with riemannian metric $g$ and $f:\Sigma \to \mathbf{R}^n$ given locally by $f_1(x_1,x_2),\dots,f_n(x_1,x_2)$. Define  S(f,g) = -\frac{1}{2\pi\alpha'}\int_{\...