Semiclassical Quantisation of Finite-Gap Strings

Understand

We perform a first principle semiclassical quantisation of the general finite-gap solution to the equations of a string moving on R x S^3.

• The derivation is only formal as we do not regularise divergent sums over stability angles.
• Moreover, with regards to the AdS/CFT correspondence the result is incomplete as the fluctuations orthogonal to this subspace in AdS_5 x S^5 are not taken into account.
• Nevertheless, the calculation serves the purpose of understanding how the moduli of the algebraic curve gets quantised semiclassically, purely from the point of view of finite-gap integration and with no input from the gauge theory side.