# 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.

94 questions
Filter by
Sorted by
Tagged with
52 views

### For which integers $m$ does an infinite string of characters $S = c_{1} \cdot c_{2} \cdot c_{3} \cdot c_{4} \cdot c_{5} \ldots$ exist

Question: For which integers $m$ does an infinite string of characters $$S = c_{1} \cdot c_{2} \cdot c_{3} \cdot c_{4} \cdot c_{5} \ldots$$ exist such that for all $n \in \mathbb{Z}_{>0}$ there are ...
48 views

### 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 ...
• 374
58 views

### Is my logic correct? A bit string of n with more 0s than 1s

I am learning about combinatorial and bit strings. I decided to use combinatorial reasoning and wanted to see if my logic made sense. The question: How many bit strings of length n contain more 0’s ...
• 147
41 views

### 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 ...
• 419
1 vote
46 views

### Confusing definitions of Modular Group and Teichmüller space

Notations 1.$\Sigma_g$ is the Reimann surface with genus $g$ 2.$M_g$ is the space of all metrics 3.Diff($\Sigma_g$) is the diffeomorphism on $\Sigma_g$ 4.$\text{Diff}_0(\Sigma)$ is the connected ...
166 views

### 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 ...
• 591
1 vote
32 views

### Divergence of gauge kinetic coupling at the AdS boundary

This is the Einstein-Maxwell-Dilaton Gravity action: \begin{eqnarray*} S_{EM} = -\frac{1}{16 \pi G_5} \int \mathrm{d^5}x \sqrt{-g} \ [R - \frac{f(\phi)}{4}F_{MN}F^{MN} -\frac{1}{2}D_{M}\phi D^{M}\...
• 121
212 views

### 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 "...
19 views

### The connectivity of reflexive polytopes from just their vertices?

I'm working with the Kreuzer-Skarke database of 4-dimensional reflexive polyhedra. It lists almost half a billion polytopes, each represented by its vertex list and a few properties (Hodge numbers and ...
1 vote
28 views

### 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 ...
• 503
1 vote
27 views

### path integral of scalar field action on Riemann surface with boundary

In their paper 'Sewing Polyakov Amplitudes I: Sewing at a Fixed Conformal Structure' Carlip et al. start by considering the path integral $$Z_{\Sigma'}[\tilde{X}] = \int [dX]e^{-S[X]}$$ for the ...
1 vote
96 views

### 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?...
135 views

### Compactification in String Theory [closed]

It seems to me that the idea of compactification in String theory is related to the concepts of Compactification and Quotient topology in topology theory. How compactification in String theory can be ...
• 181
160 views

### 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 ...
• 581
548 views

### Exceptional Lie groups and algebras in maths and physics

By the beautiful classification theorem of complex semisimple Lie algebras, we know that there are exactly $5$ types of exceptional Lie algebras, say type $E_6,E_7,E_8,F_4$ and $G_2$. We have a ...
• 259
244 views

### 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 ...
• 1,912
176 views

### Geometric intuition for $\mathcal{L}^{-m} \oplus \mathcal{L}^{m} \rightarrow T^{2}$ Calabi-Yau threefolds

I'm having some problems to understand the geometry involved in the section 3.1 of the paper Two Dimensional Yang-Mills, Black Holes and Topological Strings. Concretely, I was wondering to know if it ...
1 vote
699 views

### 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 ...
1 vote
262 views

### How do we count the number of ways a loop can go around a torus?

As Cumrun Vafa explains in this video, he was able to calculate the number of micro-states for a black hole by counting the number of ways a loop can go around a torus. Obviously, there are infinite ...
• 169
1 vote
21 views

• 26.7k
136 views

### \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 ...
219 views

### What is a Gauge symmetry, intuitively (string theory)?

I'm writing an essay for a popular (but mathematically mature) audience on the history of mathematical physics, wherein I have a section devoted to string theory. Unfortunately, neither I (nor my ...
• 1,381
145 views

### 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 ...
1 vote
61 views

### 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
• 951
169 views

### 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 $L^*$. ...
• 131
1 vote
86 views

### 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 ...
47 views

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 $$\lim_{n\... • 446 3 votes 0 answers 1k views ### Prerequisites for Quantum Fields and Strings: A Course for Mathematicians I'm interested in learning more about the mathematical structure underneath of quantum field theory and string theory. I've taken a few courses on quantum field theory before, so am getting more ... • 351 0 votes 1 answer 33 views ### The function is considered: f: (0,\infty) \rightarrow \mathbb{R}, f(x)= \frac{\ln x}{x}, how to prove that (b_n)_{n\geq 1} has no limit? [closed] The function is considered:$$f: (0,\infty) \rightarrow \mathbb{R}, f(x)= \frac{\ln x}{x}$$to be determined a string (a_n)_{n \geq 1} so the string (b_n)_{n \geq 1}, b_n= \frac{f^{(n)}(1)}{a_n} ... 0 votes 0 answers 299 views ### What are the mathematical prerequisites for the string theory If one were to start self-studying string theory with a background only in calculus and some undergraduate linear algebra and ODE, what would the path and resources to cover to reach the string theory ... 2 votes 1 answer 196 views ### Turning an integral into a Gamma Function I have a problem with a step in a physics text book [1]. It claims that I(a,b) = \int_0^\infty dt\int_0^\infty du\, \frac{t^{a-1}u^{b-1} }{t+u}\exp \left(-\frac{tu }{t+u}\right) \end{... • 269 0 votes 0 answers 239 views ### How can num2str function cut off some digits in Matlab? I am reading the book " MATLAB: A practical introductoin programming and problem solving", written by Stormy Attaway and getting curious with the function "num2str". On page 256, the author used the ... • 735 0 votes 0 answers 84 views ### How can I prove that if a domain R is an injective module, then R is a field? [duplicate] What are the similarities between a field and a projective module that can support my question? 6 votes 1 answer 205 views ### Index of a subgroup of the Modular Group The subgroup of SL(2,\mathbb{Z}) generated by \begin{pmatrix}1&0\\1&1\end{pmatrix} and \begin{pmatrix}1&5\\0&1\end{pmatrix} has come up in a research question in string ... 1 vote 0 answers 39 views ### Confusing spinor contraction with gamma matrices in group theory I'm recently confused with spinor contracting with gamma matrices. Here is an example in String Theory on SO(8):$$\psi^{AB} \underbrace{|A\rangle\otimes|B\rangle}_{8_s\otimes 8_s}=[\underbrace{A(x)(...
• 586
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 ...