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some guy named Nakanishi claims to have proven that 2-d string theories are inconsistent:

question:

answer: Eric Says:

Kevin,

The main reason for string theory being considered the ‘leading’ (really, the only) contender for a theory of everything is that it is presently the only known way to consistently combine gravity with quantum mechanics. String theory only works because of number of nearly miraculous anomaly cancellations. It is because of this that it is studied, despite the fact that it has not yet been possible to make definitive experimental predictions.

Back to the drawing board? # N. Nakanishi Says:

January 29th, 2008 at 10:59 pm

Eric,

I believe the anomaly cancellation in superstring is a meaningful condition only if the corresponding QFT has gravitational anomaly. The existence of gravitational anomaly in QFT was claimed by Alvarez-Gaume and Witten (Nucl. Phys. B 234 (1984) 269), but their reasoning contained a serious mistake: They were not aware of the fundamental difference between T-product quantities and T*-product ones. Both coincide for chiral current but not for energy-momentum tensor, because the expression for the latter contains time differentiation. The genuine anomaly must be considered for T-product quantities, but what they considered are T*-product ones,

because only T*-product quantities can be calculated by Feynman integrals and path integrals. I have explicitly shown in the 2dimensional case that what they called gravitational anomaly arises from the difference between T-product and T*-product. Thus,

at least in the 2-dimensional case, the gravitational anomaly in the genuine sense is non-existent in QFT. It is quite likely that the same is true in the 10-dimensional case.

B. Schroer completely agreed with me.

For details, see Abe and Nakanishi, Prog. Theor. Phys. 115 (2006) 1151 or arXiv hep-th/0503172 v2.

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# Nakanishi proves 2-d string theories inconsistent(?)

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