# 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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### D-brane gauge theories

Reading Yang-Hui He's review on quiver gauge theories, I read that D-brane gauge theories manifest as a natural description of symplectic quotients and their resolutions in geometric invariant theory....
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### Violin String PDE Modeling

I have this exercise in my differential equations book... If you pluck a violin string, and then finger the string, fixing it precisely in the middle, the tone increases by one octave. In ...
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### Prerequisites for Quantum Fields and Strings: A Course for Mathematicians

I'm interested in learning more about the mathematical structure underneath of quantum field theory and string theory. I've taken a few courses on quantum field theory before, so am getting more ...
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### The function is considered: $f: (0,\infty) \rightarrow \mathbb{R}, f(x)= \frac{\ln x}{x}$, how to prove that $(b_n)_{n\geq 1}$ has no limit? [closed]

The function is considered: $$f: (0,\infty) \rightarrow \mathbb{R}, f(x)= \frac{\ln x}{x}$$ to be determined a string $(a_n)_{n \geq 1}$ so the string $(b_n)_{n \geq 1}, b_n= \frac{f^{(n)}(1)}{a_n}$ ...
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### What are the mathematical prerequisites for the string theory

If one were to start self-studying string theory with a background only in calculus and some undergraduate linear algebra and ODE, what would the path and resources to cover to reach the string theory ...
109 views

### Turning an integral into a Gamma Function

I have a problem with a step in a physics text book . It claims that \begin{equation} I(a,b) = \int_0^\infty dt\int_0^\infty du\, \frac{t^{a-1}u^{b-1} }{t+u}\exp \left(-\frac{tu }{t+u}\right) \end{...
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### How can num2str function cut off some digits in Matlab?

I am reading the book " MATLAB: A practical introductoin programming and problem solving", written by Stormy Attaway and getting curious with the function "num2str". On page 256, the author used the ...
63 views

### How can I prove that if a domain $R$ is an injective module, then $R$ is a field? [duplicate]

What are the similarities between a field and a projective module that can support my question?
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### Index of a subgroup of the Modular Group

The subgroup of $SL(2,\mathbb{Z})$ generated by $\begin{pmatrix}1&0\\1&1\end{pmatrix}$ and $\begin{pmatrix}1&5\\0&1\end{pmatrix}$ has come up in a research question in string ...
1 vote
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### Confusing spinor contraction with gamma matrices in group theory

I'm recently confused with spinor contracting with gamma matrices. Here is an example in String Theory on SO(8): \psi^{AB} \underbrace{|A\rangle\otimes|B\rangle}_{8_s\otimes 8_s}=[\underbrace{A(x)(...
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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 vote
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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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### 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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I've recently been learning about moduli spaces of instantons on $\mathbb{C}^{2}=\mathbb{R}^{4}$. From what I can gather, one can consider the framed moduli space of torsion-free sheaves on $\mathbb{... 1 vote 1 answer 27 views ### The group$O(n,n,\mathbb{Z})$and its properties. While reading "String Theory" by Becker$^2$, Schwarz I encountered a group called$O(n,m,\mathbb{Z})\$, which is a group of symmetries of the bosonic/heterotic strings compactified on a torus. I would ... 