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Why is it hard to give a lattice definition of string theory?

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In Polyakov's book, he explains that one possible way to compute the propagator for a point particle is to compute the lattice sum $\sum_{P_{x,x'}}\exp(-m_0L[P_{x,x'}])$, where the sum goes over all paths between $x$ and $x'$. One then needs to compute this sum and choose the bare mass so that there's a good continuum limit.

Polyakov then goes on to say that this doesn't work for string theory. I skimmed the literature and couldn't find any explanation of this fact. Naively I would think that in order to find the propagator, you could just compute the sum $\sum_{W_{C,C'}}\exp(-T_0 A[W_{C,C'}])$, where the sum is over worldsheets that end on the curves $C$ and $C'$. What goes wrong? Is this just a hard sum to do?


This post imported from StackExchange Physics at 2015-11-08 10:05 (UTC), posted by SE-user Matthew

asked Aug 11, 2013 in Theoretical Physics by Matthew (320 points) [ revision history ]
edited Nov 8, 2015 by Dilaton

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