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.
98 questions
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How to understand the twists physicists use in topological string theory?
I have a very hard time to understand something physicists call $A$ or $B$ twists in the context of topological string theory. A canonical reference seems to be this Witten's paper.
Let $\Sigma$ be a ...
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Solution to wave equation on a cylinder
In many texts, it is claimed that the most general solution to the wave equation
$$(\partial_{\tau}^2-\partial^{2}_{\sigma} )X(\sigma,\tau) = 0$$
where $(\sigma,\tau) \in S^1 \times \mathbb{R}$ is as ...
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Is the new series for 𝜋 a Big (or even Medium) Deal?
There's been some oohing and ahhing in the science press recently over the discovery of a new formula for $\pi$ obtained as a side effect of computing amplitudes in string theory:
$$\pi=4+\sum_{n=1}^\...
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Kahler geometry and topology in modern physics
How are tools and concepts Complex and algebraic geometry (and also algebraic topology) used in modern physics, such as in string theory? Is there any introductory text which deals with this topic (ie ...
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What is the variance of the number of occurrences of a subsequence in a random sequence.
Let $N_n$ be a random string of length $n$, where each of the $n$ characters in $S_n$ is independently chosen with uniform probability from the set $\mathcal{S} := \{s_1, \ldots, s_K\}$. Here $K$ is ...
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What was the difficulty in enumerative geometry problems before physics?
I have read the book 'Enumerative Geometry and String Theory' by Katz, and it left me with some questions. It is outlined in the text how ideas from String theory and TQFT has enriched enumerative ...
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Proving that $L_{-1}v=0$ implies $v\in V_0$ in a vertex operator algebra
The discussion of the actual problem is labelled in bold after the notoriously long definition of vertex operator algebra is given for the sake of completeness (Note: "fields" and "...
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Bijection between composition algebras over R and classical superstring theories
In the page for superstring theory, Wikipedia states:
Another approach to the number of superstring theories refers to the mathematical structure called composition algebra. In the findings of ...
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Section of the projection map [closed]
I have a CY four-fold as a hypersurface of degree $(4,3)$ in $P^3\times P^2$ and I have the projection map from this hypersurface say $X$ to $P^3$ as $\pi:X \rightarrow P^3$. Does this admit a section?...
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What does $Y(1,z)$ = id for vertex algebras mean?
I'm adding an update to this post here with my current understanding of the situation for context. I read some Wikipedia articles and two texts. I am having some trouble so I figure I would attempt to ...
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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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Is algebraic geometry actually used in string theory?
Many times I have heard string theorists say that string theory has a lot of algebraic geometry, but physicists seem to have identified complex differential geometry with algebraic geometry and ...
user746545
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String Concatenation Comparision
Let $A$ and $B$ be strings consisting of small latin alphabets.
We will say $A<B$ iff $AB$ is lexicography smaller than $BA$. ($AB$ is string concatenation of $A$ and then $B$. For example, $A="...
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Topologically, what is a 'string' from string theory?
To begin: I am not a crank. I am not sure how well-founded my titular question is, but it was interesting enough that I decided to bring it to MSE.
For context: I am an undergraduate mathematics ...
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$\begin{align}&(x\! -\! a,f_1(x),\ldots,f_r(x))\\ =\ &(x\! -\! a,f_1(a),\ldots,f_r(a))\end{align}\ $ [Ideal evaluation = mod reduction]
$\begin{align}&(x\! -\! a,f_1(x),\ldots,f_r(x))\\[.1em] =\ &(x\! -\! a,f_1(a),\ldots,f_r(a))\end{align}\ $ [Ideal evaluation = mod reduction]
I am solving Aluffi chapter 0. I am completely ...
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Riemannian compact six-dimensional manifolds Ricci-flat
Are there Real compact six-dimensional manifolds Real Ricci-flat?
It is known that Calabi-Yau manifolds exist, that is, Complex compact three-dimensional Ricci-flat, but I don't know if Real compact ...
user333046
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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$$
I want to find a set of basis vector for the dual lattice $L^*$.
...
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Limit of a string without recurence
Let the string $(x_n)_{n\geq 0}$ such that : $$\frac{1}{1}, \frac{1}{2}, \frac{1}{2}, \frac{1}{3}, \frac{1}{3}, \frac{1}{3}, \frac{1}{4}, \frac{1}{4}, \frac{1}{4}, \frac{1}{4}\cdots$$
Find $$\lim_{n\...
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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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Turning an integral into a Gamma Function
I have a problem with a step in a physics text book [1]. 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 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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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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Non-trivial fibration of $SU(3)$ over $S^1$?
In String Theory it is well known that a string can propagate on backgrounds such as a $T^2$ fibred over a circle. This fibration can be non-trivial in the following sense:
Given $T^2$ generators $J^...
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Two equivalent definitions of fibration structure on toric CY $3$-fold
I've been trying to reconcile two seemingly different definitions of what a toric space is, specifically a toric Calabi-Yau 3-fold. The first definition is from the paper Branes and Toric Geometry, by ...
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Understanding Moonshine and Heterotic E8xE8
Recently I have become familiar with the conjectured relationship of monstrous moonshine and pure $(2+1)$-dimensional quantum gravity in AdS with maximally negative cosmological constant and, it’s ...
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