/sci/ - Science & Math

[Anonymous No.11425260]

could strings in string theory form knots or links? if so, how would that change their properties?

[Anonymous No.11426085]

we can't even form knots with actual fucking string

[Anonymous No.11426669]

>>11426085
I can't strip electrons off you by tossing a ball at your fucking head so how can ionizing radiation exist.

[Anonymous No.11426711]

>>11426669
That's actually a good question. We only just touched on light shedding electrons off metals in my Gen Chem 1 class this morning. It wasn't explained very well, largely because it was only tangentially related to the topic at hand.

[Anonymous No.11426826]

>>11425260
Indeed they can. Given a link [math]L[/math], we can form a 2-fold [math]M[/math] by gluing [math]f: \coprod \partial D^2 \rightarrow K[/math] some collection of discs to it, whose world-volume is a 3-manifold classified topologically (surgery theory) by [math]L[/math] modulo ambient isotopy and Kirby moves. Just speaking in terms of the underlying TQFT, which maps [math]M[/math] to a state vector in the topological theory, the ground state [math]|L\rangle = |\operatorname{AFB}(L)\rangle[/math] formed this way define a topological vacuum labeled by link invariants [math]\operatorname{AKB}(L)[/math]; in addition, cobordant links define unitarily
equivalent ground states (in the TQFT).
In the string theory itself, the ground states in fact depend on more intricate geometric structures on [math]M[/math], such as the conformal class of the metric on it, but this is determined by much more than just the embedded links inside.

[Anonymous No.11428212]

>>11426826
nice pic.
saved.