String theory is an research framework in particle physics that attempts to reconcile quantum mechanics and general relativity.

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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 $n(n - 1)/2$ ...
9
votes
2answers
1k views

Complex and Kähler-manifolds

I was woundering if anyone knows any good references about Kähler and complex manifolds? I'm studying supergravity theories and for the simpelest N=1 supergravity we'll get these. Now in the course-...
64
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4answers
11k views

String Theory: What to do?

This is going to be a relatively broad/open-ended question, so I apologize before hand if it is the wrong place to ask this. Anyways, I'm currently a 3rd year undergraduate starting to more seriously ...
7
votes
1answer
104 views

CFT's vs Vertex Operator Algebras

I am trying to clear my ideas about the relation between a Conformal Field Theory (CFT) and a Vertex Operator Algebra (VOA). For me a CFT based on a (complex) vector space $H$ is a projective monoidal ...
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0answers
27 views

How many different subsequence in Thue-Morse sequence

Consider the Thue-Morse string. Suppose it has $n$ elements. My question is: how many different substrings(or subsequence) in this string. Actually I'm interest in bound of this value. Is it smth ...
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0answers
25 views

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 ...
1
vote
1answer
113 views

Image of ring homomorphism $\phi : \mathbb{Z}[t] \to \mathbb{Q}$?

Here is a problem I face practicing the theory of rings: Define $\phi : \mathbb{Z}[t] \to \mathbb{Q}$, a ring homomorphism (it does map $1$ to $1$). I'm trying to show that if $\phi(t)=\frac{u}{v}$...
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0answers
34 views

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-...
2
votes
1answer
41 views

Polyakov action in complex coordinates

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_{\...
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0answers
55 views

Weyl transformation of geodesic distance

Consider a Riemannian manifold $M$ with a metric $g$. For two points $x,y \in M$ the geodesic distance $d(x,y)$ is defined in the usual way. I would like to know if there is a formula expressing how ...
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0answers
43 views

Are $T^2/Z_2$ orbifolds just ironed spheres?

(Note that this question is migrated from the physics SE... I apologize for the imprecise language) The only $Z_2$ symmetries I can think of the torus are reflection on plane, whose quotient should ...
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0answers
41 views

Chandrasekhar history [closed]

I have misplaced an article by Chandrasekhar from the mid 90's in which he drew an analogy between himself and his neat desk and a co-laborer 'down the hall' who was more chaotic with managing his ...
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vote
1answer
58 views

An intutive proof of 'replacing two-caps by a handle'

I am trying to understand a statement given in Polchinski Vol.1 - a torus with cross-cap can be obtained either as (g,b,c) = (0,0,3) or as (1,0,1), trading two cross-caps for a handle. Here, g is ...
1
vote
3answers
53 views

Calculating euler number of disk

I'm trying to do exercise 3.1 from Polchinski, which should be a rather easy differential geometry problem. I have to calculate the euler number defined by $$\chi = \frac{1}{4\pi}\int_{M}d^{2}\sigma ...
3
votes
1answer
102 views

Physical interpretation of categorical structures related to Dirichlet Branes

In Dirichlet Branes and Mirror Symmetry by Aspinwall et al, section 5.9 discusses various questions that remain open. In particular they say: "There are many constructions from homological ...
4
votes
0answers
109 views

(Soft Question) How active an area of research is Non-Commutative Geometry? [closed]

I am currently an undergraduate, but I am considering applying for a phd in algebraic geometry or a related field. I am quite interested in the link between non-commutative geometry and theoretical ...
1
vote
1answer
86 views

How many bit strings of length 7 exist if the string remains unchanged if it is reversed?

How many bit strings of length 7 exist if the string remains unchanged if it is reversed ? 1 1 1 1 1 1 1 and 1 0 0 1 0 0 1 are an example that is unchanged if reversed. 0 0 0 0 0 0 0 and 0 1 1 0 1 1 ...
2
votes
0answers
68 views

Polchinski 12.3.22 - superspace green's function

Forming the supersymmetric string using superfields and superspace, Polchinski claims that the function $$ G \sim \ln{\left|z_{1} - z_{2} - \theta_{1}\theta_{2}\right|^{2}} $$ satisfies the equation $$...
0
votes
1answer
242 views

String probability (with conditional prob and combinations)

I'm having trouble with the questions below, all relating to string probability. I'll write the problem and then provide my work for my (incorrect) answer. Please help me figure out what I did wrong. ...
3
votes
1answer
106 views

Why are there cubics in a Calabi-Yau manifold?

I heard from a recent talk that the "number of $n$-degree curves" in a Calabi-Yau manifold is an invariant of the space. But what does that mean? (Specifically I would like to ask the following.) ...
2
votes
2answers
366 views

What's the difference between an orbifold with a conical singularity and a conifold?

In Becker, Becker, Schwarz's book 'String Theory and M-Theory: A Modern Introduction', page 360 they explain how an orbifold of $\mathbb{C}/\mathbb{Z}_{2}$ (which is equivalent to $\mathbb{R}_{2}/\...
6
votes
0answers
150 views

Solving numerically the equation of motion of D7 brane perturbation

I want to solve this equation $$ \partial_{\rho}^{2}\phi+\frac{3}{\rho}\partial_{\rho}\phi+\left(\frac{M^{2}}{(1+\rho^{2})^{2}}-\frac{l(l+2)}{\rho^{2}}\right)\phi=0 $$ numerically. I know that ...
2
votes
0answers
94 views

Status of a question from Freeman Dyson's 1972 article

In a famous article, Freeman Dyson mentions an interesting relationship between the $\tau$ functions of number theory and the dimensions of finite-dimensional simple Lie algebras (section 2). He ...
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1answer
47 views

Strange factor multiplying the fermionic part in the NS mass-squared operator?

In the Neveu-Schwarz sector, the worldsheet fermions can be expanded as $$ \psi^I(\tau,\sigma) \sim \sum\limits_{r\in Z+1/2}b_r^Ie^{-ir(\tau-\sigma)} $$ and the total mass squared operator can then ...
2
votes
0answers
113 views

rigorous treatment of infinitesimal reparametrizations

my first post :) I am asking this directed to mathematicians or mathematical physicists since I don't like the usual physics approach. Reading some string theory books I always find that the ...
3
votes
1answer
347 views

What is a good gentle introduction to the Virasoro algebra and its application in theoretical physics?

I am looking for an as gentle and pedagogical as possible introduction that explains the Virasoro algebra and its applications in theoretical physics; finally I am interested in its application in ...
10
votes
1answer
2k views

Algebraic Geometry in String Theory?

I'm currently studying String Theory and hope to do research in this area. I have now reached a point where even with a background in Mathematics instead of Physics, I have no clue what's going on ...
1
vote
1answer
151 views

Find an upper bound for lowest eigenvalue using calculus of variations.

So I'm doing a little calculus of variations on an eigenvalue problem. The goal of this is to find an upper bound for the $\omega_0$ as follows: $\omega_0^2 \leq \frac{T_0\int_0^a\left|\frac{d\psi}{...