Type IIA superstring theory ($\mathcal{N}=(1,1)\text{ in ten dimensions}$)

A closed superstring theory whose left and right Ramond sector projections have opposite ten-dimensional Majorana-Weyl chiralities. It has 32 real spacetime supercharges and is nonchiral. Its massless fields form type IIA supergravity; the RR gauge potentials have odd degrees, including a one-form and a three-form.

Level matching combines two chiral massive sectors, each with 128 NS and 128 R states. The NS-NS and R-R combinations give $2(128{)}^2=32768$ bosons, and the mixed sectors give the same fermion count. Their total $2^{16}$ matches a massive uncharged long multiplet with 32 real supercharges and sixteen fermionic creation operators.

The bosons are the metric, two-form, dilaton, RR one-form and RR three-form, with physical dimensions $35+28+1+8+56=128$. Two opposite-chirality gravitinos and two dilatinos supply $2(56+8)=128$ fermionic degrees of freedom. They form the ten-dimensional type IIA supergravity multiplet. Counts refer to on-shell polarizations, not raw field components.