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0:00:00 Introduction
0:01:05 [Talk: What Every Physicist Should Know About String Theory by Edward Witten]
0:02:46 Anyone who has studied physics is familiar with the fact that while physics - like history - does not precisely repeat itself,
0:03:13 Quantum gravity
0:07:11 If we introduce the "canonical momentum"
0:08:46 So we have found an exactly soluble theory of quantum gravity in one dimension that describes a spin
0:09:55 Just to make things more familiar,
0:12:26 For a given T,
0:13:57 Thus the complete path integral for our problem - integrating over all metrics get
0:14:47 So we have interpreted a free particle in D-dimensional spacetime in terms of 1-dimensional quantum gravity.
0:15:35 Now to do the quantum gravity path integral,
0:16:22 To integrate over the paths, we just observe that if we specify the positions y1.
0:18:00 We have arrived at one of nature's rhymes:
0:19:17 There is actually a much more perfect rhyme if we repeat this in two dimensions,
0:20:42 But now we notice that the obvious analog of the action function that we used for the particle,
0:21:30 Some very pretty 19th century mathematics now comes into play
0:23:01 To underscore how a two-manifold is understood as a generalization of a Feynman graph,
0:23:51 Now I come to a deeper rhyme:
0:26:34 Operators in quantum mechanics
0:27:36 But in conformal field theory, there is an operator-state correspondence,
0:28:31 The operator-state correspondence arises from a 19th century relation between two pictures that are conformally equivalent:
0:30:53 The next step is to explain why this type of theory does not have ultraviolet divergences.
0:33:07 It is true that, as I said, a Riemann surface can be described by parameters that
0:35:03 Instead of giving a general explanation of this,
0:36:04 Going to string theory means replacing the classical one-loop diagram
0:36:09 Going to string theory means replacing the classical one-loop diagram with its stringy counterpart,
0:36:18 19th century mathematicians showed that every torus is conformally equivalent to a parallelogram in the plane with opposite sides identified
0:36:33 But to explain the idea without extraneous details,
0:38:54 I have explained a special case, but this is a general story.
0:39:39 I want to use the remaining time to explain, at least partly,
0:40:17 We could have used in this construction a different 2d conformal field theory
0:41:09 When we get away from a semiclassical limit, the Lagrangian is not so useful
0:42:04 Many other nonclassical things can happen.
0:42:20 We can say that from this point of view,
0:43:06 This is not a complete explanation of the sense in which,
