The S-matrix of the Pohlmeyer-reduced AdS5 x S5 superstring

Abstract

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.