5
votes
1answer
201 views

Why is $S^1\times\mathbb{R}^{n-1}$ the topology of $AdS_n$?

Anti-de Sitter $AdS_n$ may be defined by the quadric $$-(x^0)^2-(x^1)^2+\vec{x}^2=-\alpha^2\tag{1}$$ embedded in ${\mathbb{R}^{2,n-1}}$, where I write ${\vec{x}^2}$ as the squared norm ${|\vec{x}|^2}$ ...
5
votes
0answers
108 views

Why do we need non-trivial fibrations?

I am currently reading this paper. I understand how the Bloch sphere $S^2$ is presented as a geometric representation of the observables of a two-state system: $$ \alpha |0\rangle + \beta |1\rangle ...
2
votes
2answers
124 views

Zwiebach quick calculation 2.5

I am working through Zwiebach's a first course in string theory. It's been a while since I did any math (or physics!), and I am stuck on the following problem (quick calculation 2.5 in the book): ...
3
votes
5answers
168 views

Why is the world sheet of an open string a cylinder?

I went to a lecture a few weeks ago and was told the following: The world sheet of a closed string is a normal, standing cylinder. The world sheet of an open string is a cylinder on its side. This ...