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.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:556563 |
| Date | January 2012 |
| Creators | Hoare, Benjamin David |
| Contributors | Tseytlin, Arkady |
| Publisher | Imperial College London |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/10044/1/9760 |
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