Quantum aspects of Pohlmeyer-reduced AdS5 x S5 superstring

Abstract

The AdS5 ×S5 superstring action is constructed by the Green-Schwarz formalism. For quantization it is necessary to eliminate unphysical degrees of freedom from the action by solving the Virasoro constraints and fixing the fermionic kappa-symmetry, which can be achieved by the Pohlmeyer reduction preserving the two-dimensional Lorentz invariance and the integrability. The resulting system is a gauged Wess-Zumino-Witten (gWZW) model deformed with a certain integrable potential and two-dimensional fermions. This thesis explores the quantum relation between the AdS5 × S5 superstring theory and the deformed gWZW model by evaluating the reduced theory quantum partition functions for respective classical string configurations. To understand the quantum relation between the original string theory and the reduced theory, the one-loop computation in the reduced theory is first studied for homogeneous and inhomogeneous string configurations localized in subspaces. For these classical backgrounds we demonstrate that the reduced theory partition function is exactly the same as the string theory one, then they are equivalent at one-loop level. Next we investigate the two-loop relation between the original string theory the reduced theory. The two-loop computation in the reduced theory is performed by considering the long folded string localized in AdS3. We show that the nontrivial finite terms of the two-loop partition functions of the two theories match, exhibiting the same patterns of the bosonic contributions and fermionic contributions. This is a strong indication that the AdS5 × S5 GS string and its reduced form are closely related at the quantum level.