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The Heterotic string state is a tensoring of the bosonic string left-moving state and the Type II string right-moving state. Therefore, I expect the spectrum to be: $$\begin{array}{*{20}{c}} \hline & {{\rm{Sector}}}&{{\rm{Spectrum}}}&{{\rm{Massless fields}}}& \\ \hline & {{\rm{Bosonic}} - {\rm{R}}}&{{\bf{1}}{{\bf{6}}_v} \otimes {{\bf{8}}_s} = {{\bf{8}}_v} \otimes {{\bf{8}}_v} \otimes {{\bf{8}}_s}}&?\\ \hline & {{\rm{Bosonic}} - {\rm{NS}}}&{{{\bf{8}}_v} \otimes {{\bf{8}}_v} \otimes {{\bf{8}}_v}}&?& \hline \end{array}$$

  1. However, how does one calculate the massless fields of the Type I string theory using the spectrum of the type I string theory?

  2. Furthermore, to calculate the mass spectrum of the Heterotic string, does one simply add the number operator of the bosonic string to that of the type II string and the same for the normal ordering constant? i.e. is it true that

$$\begin{array}{l} m = \sqrt {\frac{{2\pi T}}{{{c_0}}}\left( {B + {{\tilde N}_{II}} - {a_B} - {{\tilde a}_{II}}} \right)} \\ {\rm{ }} = \sqrt {\frac{{2\pi T}}{{{c_0}}}\left( {B + {{\tilde N}_{II}} - 1 - {{\tilde a}_{II}}} \right)} \end{array}$$

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  • $\begingroup$ Maybe you find this recent TRF article about heterotic string theory interesting too. $\endgroup$ – Dilaton May 18 '13 at 17:10

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