What I had in mind was starting at our point in moduli space and moving to the nearby point where the cosmological constant is zero. If I'm not mistaken, the theory there has exact superconformal symmetry?
It certainly doesn't have to be true; there are infinite moduli spaces of SUSY theories that arise from string theory, and only very special points on these are superconformal. (I assume you mean the low-energy field theory; no perturbative string theory is conformal, because there's always the string scale.)
It does sound Banksian, though, since he suggests (for reasons I don't completely understand) that our vacuum is a small perturbation of an isolated supersymmetric theory with zero cosmological constant (i.e. one with no associated moduli space). I guess such a point probably is superconformal?
But you also get enhanced gauged symmetry at a self T-dual point in string theory... a similarity I'd never thought of before. It doesn't mean they're necessarily connected, but that would be pretty crazy (in a good way) if they were!
Well, what is certainly true is that if you have a duality acting on one variable and you consider a flow in that variable, any self-dual point is a fixed point of the flow. So if for some reason cosmology (or some other abstract flow on the moduli space) was changing some radius and only that radius, the self T-dual point would be a fixed point (not necessarily an attractive one). But since string constructions depend on many more variables, it's not so clear to me what relationship self-dual points and fixed points of some flow should have. I guess self-dual points should probably still be fixed points, but the more directions you have to go in on your moduli space, the more likely it is that the fixed point is only a saddle and you will get driven away from it. (The trouble is that the subspace where you flow into a saddle generally has a lower dimension.)
Given what Ooguri and Vafa have to say about the geometry of the string theory moduli space, it seems unlikely that any picture of simply flowing along the moduli space to the right vacuum would make sense. They even suggest that geodesic flow might be ergodic.
Faraggi seems to be motivated more by some strange reformulation of quantum mechanics than by the idea of some flow driving to the fixed point, though.
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timeasmymeasure
no subject
Date: 2007-04-10 04:25 am (UTC)It certainly doesn't have to be true; there are infinite moduli spaces of SUSY theories that arise from string theory, and only very special points on these are superconformal. (I assume you mean the low-energy field theory; no perturbative string theory is conformal, because there's always the string scale.)
It does sound Banksian, though, since he suggests (for reasons I don't completely understand) that our vacuum is a small perturbation of an isolated supersymmetric theory with zero cosmological constant (i.e. one with no associated moduli space). I guess such a point probably is superconformal?
But you also get enhanced gauged symmetry at a self T-dual point in string theory... a similarity I'd never thought of before. It doesn't mean they're necessarily connected, but that would be pretty crazy (in a good way) if they were!
Well, what is certainly true is that if you have a duality acting on one variable and you consider a flow in that variable, any self-dual point is a fixed point of the flow. So if for some reason cosmology (or some other abstract flow on the moduli space) was changing some radius and only that radius, the self T-dual point would be a fixed point (not necessarily an attractive one). But since string constructions depend on many more variables, it's not so clear to me what relationship self-dual points and fixed points of some flow should have. I guess self-dual points should probably still be fixed points, but the more directions you have to go in on your moduli space, the more likely it is that the fixed point is only a saddle and you will get driven away from it. (The trouble is that the subspace where you flow into a saddle generally has a lower dimension.)
Given what Ooguri and Vafa have to say about the geometry of the string theory moduli space, it seems unlikely that any picture of simply flowing along the moduli space to the right vacuum would make sense. They even suggest that geodesic flow might be ergodic.
Faraggi seems to be motivated more by some strange reformulation of quantum mechanics than by the idea of some flow driving to the fixed point, though.