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String theories are candidates for a TOE (Theory of Everything). They provide a plausible quantum theory of gravity.
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| 2 |
Basic objects are tiny one dimensional "strings" (rather than points). Dynamics described by a two dimensional space-time world-sheet (rather than world line).
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| 3 |
Calculations involve integrating over all possible world-sheets, i.e. all 2-d surfaces embedded in some higher dimensional space (3-d, 4-d, 26-d, ....)
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| 4 |
Done numerically by a Monte Carlo integration over different triangulations of the surface, produced dynamically using the Metropolis algorithm.
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| 5 |
Current research centers on finding good discretizations of the continuum theories, and trying to find critical points with divergent correlation lengths, so the details of the discrete lattice structure become irrelevant and we can extract continuum results (c.f. lattice QCD)
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| 6 |
Interesting critical points are phase transitions between a smooth phase and a crumpled phase of the surface. The order and critical exponents of this crumpling transition are still uncertain.
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| 7 |
We have done the largest simulations so far on 2-d systems, but these are only 576 node meshes. Critical slowing down is a major problem - need better algorithms.
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| 8 |
The same techniques are used to model real fluctuating surfaces, e.g. cell membranes, lipid bilayers, phase boundaries.
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