- #1

tom.stoer

Science Advisor

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## Main Question or Discussion Point

Are there any indications in different theories or approaches to QG explaining what could possibly single out 4-dim. spacetime?

Is there an idea why string theory favours compactification of 6 dimensions?

Is there an idea why purely algebraic spin networks (w/o any dependence on triangulations of PL manifolds) should results in 4 dim.?

Has anybody thought about spin networks based on Spin(n) or SU(n) and determined a "dimension" in the low-energy limit?

Does CDT really predict 4-dim. spacetime - or does it "only" reproduce 4 dimensions based on 4-dim. triangulations?

Assume for a moment that even in QG theories we can still use differential manifolds. What about the following idea: Assume we have something like

[tex]Z \sim \sum_\text{dim}\,\sum_\text{top}\,\sum_\text{diff}\,e^{-S}[/tex]

I would like to "sum" or "integrate" over all dimensions, over all topologies (non- homeomorphic manifolds) per dimension, and over all differential structures (non-diffeomorphic manifolds). Then (regardless what S could be!) by simply "counting" manifolds the non-compact 4-dim. manifolds are singled out (continuum of non-diffeomorphic differentiable structures of R

Is there an idea why string theory favours compactification of 6 dimensions?

Is there an idea why purely algebraic spin networks (w/o any dependence on triangulations of PL manifolds) should results in 4 dim.?

Has anybody thought about spin networks based on Spin(n) or SU(n) and determined a "dimension" in the low-energy limit?

Does CDT really predict 4-dim. spacetime - or does it "only" reproduce 4 dimensions based on 4-dim. triangulations?

Assume for a moment that even in QG theories we can still use differential manifolds. What about the following idea: Assume we have something like

[tex]Z \sim \sum_\text{dim}\,\sum_\text{top}\,\sum_\text{diff}\,e^{-S}[/tex]

I would like to "sum" or "integrate" over all dimensions, over all topologies (non- homeomorphic manifolds) per dimension, and over all differential structures (non-diffeomorphic manifolds). Then (regardless what S could be!) by simply "counting" manifolds the non-compact 4-dim. manifolds are singled out (continuum of non-diffeomorphic differentiable structures of R

^{4}; Clifford Taubes).