Tarun Chitra
|
Registered User
|
Previous: Undergrad in Mathematics (BA) and Engineering Physics (BS) at Cornell. Did research in Generalized Complex Geometry/String Theory.
Currently: Scientific Associate at D. E. Shaw Research Currently Reading (06/14/11): Principles of Algebraic Geometry — Griffiths and Harris Biological Physics – Phillip Nelson |
|
Mar 23 |
comment |
What are the uses of the homotopy groups of spheres? Note that this propagator is usually formulated in terms of a sum over Euler characters (since the intuition behind this limit is that a sum over Feynman diagrams turns into a sum over closed connected surfaces). The authors themselves liken this to a 'sum over high-dimensional spheres.' This is likely ill-posed, but one might be able to view this process as the construction of an infinite sequence of $\mathsf{SU}(N)$-structures that asymptotically has some sort of $S^{\infty}$-bundle-like structure that resembles this whole process. I would love to learn if someone has already done this! |
|
Mar 23 |
comment |
What are the uses of the homotopy groups of spheres? I'm not sure if this ends up having a connection to the homotopy groups on spheres, but part of the AdS/CFT correspondence is the idea (due to t'Hooft) that String Theories can be viewed as "large-N" Gauge Theories with gauge group $\mathsf{SU}(N)$ [0]. As mentioned in reference [0], the idea is to turn YM fields into a set of $\mathsf{SU}(N)$ fields and thehn take a "limit" (probably ill-defined) of $N\uparrow \infty$. In the paper they show that the propagator of theory depends on 'large-N sphere topology of spheres.' [0] Section 1.2 of hep-th:9905111 |
