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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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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 ...
Martin.s's user avatar
4 votes
1 answer
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 ...
user720386's user avatar
0 votes
0 answers
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 ...
coolcat's user avatar
  • 147
2 votes
1 answer
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 ...
香结丁's user avatar
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1 vote
1 answer
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 ...
user avatar
4 votes
0 answers
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 ...
Hyunbok Wi's user avatar
1 vote
0 answers
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}\...
codebpr's user avatar
  • 121
2 votes
3 answers
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 "...
LeonardoOiler's user avatar
0 votes
0 answers
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 ...
Eddie V's user avatar
1 vote
0 answers
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 ...
L. E.'s user avatar
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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 ...
Davide Provasoli's user avatar
1 vote
1 answer
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?...
user333644's user avatar
0 votes
1 answer
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 ...
htr's user avatar
  • 181
4 votes
2 answers
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 ...
Kevin Njokom's user avatar
4 votes
2 answers
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 ...
Estwald's user avatar
  • 259
2 votes
1 answer
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 ...
user10478's user avatar
  • 1,912
3 votes
1 answer
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 ...
Ramiro Hum-Sah's user avatar
1 vote
0 answers
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 ...
user avatar
1 vote
1 answer
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 ...
ziv's user avatar
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1 vote
0 answers
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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="...
AquaBlaze0010's user avatar
1 vote
1 answer
111 views

$yB$ is not a prime ideal in $B.$

Let $B = \mathbb R[x,y]$ where $x^2 + y^2 = 1$ which is called the coordinate ring of the unit circle. I am trying to prove that $yB$ is not a prime ideal in $B.$ I have the following information ...
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10 votes
1 answer
1k views

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 ...
Descartes Before the Horse's user avatar
1 vote
1 answer
144 views

What this parameter in the Riemann surface metric has to do with its complex structure?

As far as I'm aware, a complex manifold $M$ is a topological manifold together with an atlas ${\cal A}$ of charts $(U_i,\varphi_i)\in{\cal A}$ such that the open sets $U_i$ cover $M$, the maps $\...
Gold's user avatar
  • 26.7k
0 votes
2 answers
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 ...
joe blacksmith's user avatar
5 votes
1 answer
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 ...
10GeV's user avatar
  • 1,381
0 votes
1 answer
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 ...
user avatar
1 vote
0 answers
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
Pluviophile's user avatar
0 votes
2 answers
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 $L^*$. ...
Awoo's user avatar
  • 131
1 vote
0 answers
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 ...
Schroedinger'sDog's user avatar
-2 votes
1 answer
47 views

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\...
sticknycu's user avatar
  • 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 ...
leob's user avatar
  • 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 $(b_n)_{n \geq 1}, b_n= \frac{f^{(n)}(1)}{a_n}$ ...
Maria Pop's user avatar
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 ...
Mohammad Nourbakhsh's user avatar
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 \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{...
Oбжорoв's user avatar
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 ...
Trần Linh's user avatar
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?
Marcos Eusébio's user avatar
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 ...
Daniel Longenecker's user avatar
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)(...
Ruairi's user avatar
  • 586
4 votes
1 answer
223 views

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 ...
soap's user avatar
  • 2,702
5 votes
1 answer
180 views

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^...
h_m's user avatar
  • 113
3 votes
0 answers
213 views

Clarification on Kac Moody algebras and the different meanings in mathematics and physics

I am confused by the way that mathematicians and physicists use the words "Kac Moody algebra", and "loop algebra", and how exactly these concepts relate to one another. I will write down what I ...
soap's user avatar
  • 2,702
1 vote
0 answers
52 views

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 ...
leastaction's user avatar
2 votes
0 answers
243 views

Grasping the idea of Virasoro Algebras in 2D Conformal field theory

I have been trying to understand the connection between Virasoro algebras and CFT. After a course in string theory, I was under the impression that the Virasoro algebra was simply the Lie algebra of ...
soap's user avatar
  • 2,702
2 votes
0 answers
183 views

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 ...
alex sharma's user avatar
0 votes
0 answers
39 views

Notation for (skew) Young Tableaux in Hubsch

I'm looking at the notation given for Young tableau in Hubsch's book "Calabi-Yau Manifolds: A Bestiary for Physicists" - see Chapter 3, p. 96. A Young tableau (for a $U(n)$ representation) is denoted ...
nonreligious's user avatar
1 vote
0 answers
81 views

How can I justify that the compact manifold in string theory must be orientable in one dimension

I am preparing a presentation on Calabi-Yau manifolds where I do not want to use advanced mathematics, but I would like to show that under some minimal assumptions in one (complex) dimension, the ...
doetoe's user avatar
  • 3,909
4 votes
1 answer
361 views

Size and shape moduli of Calabi-Yau manifolds

Let's say that Calabi-Yau manifolds are compact Kähler manifolds with a trivial canonical bundle. We know that $H^2(X,\mathcal T_X) = H^1(X,\Omega^2_X)$ is the tangent space to the deformation functor ...
doetoe's user avatar
  • 3,909
2 votes
1 answer
127 views

What is meant by the symbol $\mathbb{R}^2_{\hbar}$?

I am reading some papers in mathematical physics (https://arxiv.org/pdf/1006.0977.pdf) and I came across the following symbol $\mathbb{R}^2_{\hbar}$ I don't recognize nor could I find any background ...
Graphite's user avatar
5 votes
0 answers
282 views

Are there branches of mathematics that are unique to String Theory?

I have read that String Theory has developed “new” math but the sources do not specifically identify the math. My question: are there branches of mathematics that are unique to String Theory? By ...
Jim Johnson's user avatar
1 vote
1 answer
87 views

On the Numbers of Representations of a Number as a Sum of $2r$ Squares, Where $2r$ Does not Exceed Eighteen

I am reading the article "Mathematicians Chase Moonshine’s Shadow" [1], and want to follow up on one of its sources "On the Numbers of Representations of a Number as a Sum of $2r$ Squares, Where $2r$ ...
Valera Rozuvan's user avatar