The authors (Becker-Becker-Schwarz) in the book "String theory and M-theory" on pages 268-270 prove that the mass spectrum of the closed bosonic strings on a toroidally (torus $T^n$) compactified space-time has $O(n,n;\mathbb{Z})$ symmetry. After that, on page 270 they talk about the physical moduli space $\mathcal{M}_{n,n}$. I wanted to ask that what does this space mean? Not its mathematical definition. I mean what this space is and what is its purpose? Is it the Hilbert space of physical states? What is its relation to Physical states? Where does this space come from and what are its elements? Can anyone explain me in a simple language?
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