I’ll eventually watch the video, but I’ll ask now: does Costello
give a new way to compute just the one-loop beta function, or the n-loop beta function for arbitrary n? Or something else? The “exact” beta function is probably too complicated to compute by hand.
John Baez, It’s the one loop coefficient of the beta function.
To be clear, what I think is important here is not the result of the calculation, but the calculational method, which gives this a new interpretation. As a student I remember doing this calculation, wondering if this important number had any better explanation than what drops out of a slightly obscure calculation. Costello gives such an explanation, and, even better, it’s in terms of reformulating Yang-Mills on twistor space, something that fits in with the things I’ve been trying to do as “twistor unification
give a new way to compute just the one-loop beta function, or the n-loop beta function for arbitrary n? Or something else? The “exact” beta function is probably too complicated to compute by hand.
John Baez,
It’s the one loop coefficient of the beta function.
To be clear, what I think is important here is not the result of the calculation, but the calculational method, which gives this a new interpretation. As a student I remember doing this calculation, wondering if this important number had any better explanation than what drops out of a slightly obscure calculation. Costello gives such an explanation, and, even better, it’s in terms of reformulating Yang-Mills on twistor space, something that fits in with the things I’ve been trying to do as “twistor unification