Torelli Group: Understanding the Non-Trivial Diffeomorphisms of String Theory

[Darth Sidious]

Hello,

While reading the lectures of Luest and Theisen on string
theory I encountered the Torelli group. They are very vague
about it (the discussion is at pages 118-119) but they say
that it correspond to twists arround trivial cycles so the
homology basis is unchanged but these transformations
are non-trivial diffeomorphisms nevertheless.

I searched the Web for some drawing describing these
twists but I couldn't find them. Would some kind soul
explain them to me? I *think* that they should be like the
Dehn twists but I'm not sure about that.

There's some other interesting piece of information in
Luest & Theisen about the moduli space of genus g Riemann
surfaces. It seems that this moduli space gets quite
complicated for genus g > 3. I think g=3 is the state
of the art in computing superstring amplitudes (I have no
idea about bosonic string amplitudes). I therefore think it's
necessary to go at least to g=4 to see if there's something
qualitatively different there.

 

[thomas_larsson_01@hotmail.com]

http://arxiv.org/find/hep-th,grp_math/1/ti:+Torelli/0/1/0/all/0/1