Starting with a SUSY $E_8$ x $E_8$ heterotic partition function:

$ Z = - \frac{1}{8} \sum Z^8_x Z_4[^s_{s'}] Z_8[^t_{t'}] Z_8[^u_{u'}] $

where the sum is over all spin structures $s,t,u,s',t',u' = 0, 1$.

I can go to a lattice formulation of this partition function:

$$ Z = Z^8_x (V_4 + S_4) \times (R_8 + S_8) \times (R_8 + S_8) $$

Where $V,S,R$ are the partition sums of the corresponding lattices.

How does the last part (gauge representation) define which of the fermions/bosons I get in the $(R_8 \otimes S_8)$ representation?

How can I get from the partition function to a particle of the QFT using the massless part of the partition function? If I choose corresponding vectors in the three lattices how can I see the properties of the particles?

This post imported from StackExchange Physics at 2015-12-08 22:39 (UTC), posted by SE-user LOQ