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Results tagged with topology
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user 251344
In mathematics, topology examines the properties of space (such as connectedness and compactness) that are preserved under continuous deformations, such as stretching and bending, but not tearing or gluing.
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67
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Misconception about closed string worldsheet definition
.$$
The problem is that some books define $\Sigma$ as the set $\mathbb{R} \times [0,π]$ (Becker & Becker), or $\mathbb{R} \times [0,2π]$ (Polchinski) and most of the books claim that $\Sigma$ has the topology …
- 1,330
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1
answer
66
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What does really mean to glue the endpoints of a closed string?
I'm almost all string theory standard textbooks such as Polchinski, Barton Zwiebach's book, etc. It is stated that the Worldsheet (or parameter space) flor the closed string is such that the points $( …
- 1,330
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answers
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Reason to consider only compact world-sheets in string theory
Generally speaking, the "sum over world-sheets" in string theory involves summing over all possible topologies of compact, orientable and connected, as Polchinski says in page $100$ of his first volum …
- 1,330
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On what space of maps is Polyakov path integral actually defined?
has the following passage:
The Polyakov action leads to well-defined transition amplitudes, obtained by
integration over the space $\text{Met}(\Sigma)$ of all positive metrics on $\Sigma$ for a given topology …
- 1,330