The Pohlmeyer reduction of the AdS5 x S5 superstring is a fermionic generalization of the relationship
between the O(3) sigma model and the sine-Gordon model. In the reduction procedure the Virasoro
constraints are solved and the resulting reduced theory is Lorentz-invariant, integrable and classically
equivalent to the superstring sigma model. Its action is that of a gauged WZW model plus an integrable
potential coupled to fermions. Furthermore, the theory is UV-finite and conjectured to be related to the
superstring at a quantum level.
This thesis begins with a review of the Pohlmeyer reduction, concentrating on its rôle in string theory.
The main focus of the thesis is an investigation into the S-matrix of the Pohlmeyer-reduced AdS5 x S5
superstring. Expanding around the trivial vacuum, a local quartic action is constructed for the 8 + 8
(bosonic and fermionic) massive asymptotic degrees of freedom. The resulting perturbative S-matrix has
the same tensorial structure and group factorization property as the light-cone gauge-fixed superstring
S-matrix. However, it does not satisfy the Yang-Baxter equation.
As a possible resolution it is proposed to consider a particular limit of the quantum-deformed (psu(2|2)xR3)-invariant
R-matrix of Beisert and Koroteev. The exact form of the corresponding S-matrix is constructed
and possible relations to the perturbative computation are explored. The on-shell symmetry
of the quantum-deformed S-matrix may be interpreted as a quantum-deformed N = 8 two-dimensional
supersymmetry. After describing the representation theory of Uq(psu(2|2)xR2) and the pole structure
of the deformed S-matrix the bootstrap programme is used to construct the S-matrix elements for the
bound states. The thesis concludes with a discussion of the current status of the Pohlmeyer reduction
and open questions.