|dc.contributor.author||Garner, David P. R||
|dc.identifier.citation||Garner, D.P.R. 2015. Combinatorics and Gauge-String Duality. Queen Mary University of London.||en_US
|dc.description.abstract||This thesis exhibits a range of applications of combinatoric methods to string theory.
The concepts and techniques used in the counting of ribbon graphs, the theory of finite
groups, and the construction of cell complexes can give powerful methods and interesting
insights into the nature of gauge-string duality, the limits of CFT factorisation,
and the topology of worldsheet moduli space.
The first part presents a candidate space-time theory of the Belyi string with
a holographic extension to three-dimensional Euclidean gravity. This is a model of
gauge-string duality in which the correlators of the Gaussian Hermitian matrix model
are identfied with sums over worldsheet embeddings onto the 2-sphere target space.
We show that the matrix model can be reformulated on the sphere by using su(2)
representation couplings, and that the analogues of Feynman diagrams in this model
can be holographically extended to 3-manifolds within the Ponzano-Regge model.
The second part explores the limits of large N factorisation in conformal field
theory and the dual interpretation in supergravity. By considering exact finite N
correlators of single and multi-trace half-BPS operators in N = 4 super Yang-Mills
theory in four dimensions, we can explicitly nd the exact threshold of the operator
dimensions at which the correlators fail to factorise. In the dual supergravity, this is
the energy regime at which quantum correlations between distinct gravitons become
The third part develops a cell decomposition of the moduli space of punctured
Riemann surfaces. The cells are specified by a particular family of ribbon graphs, and
we show that these graphs correspond to equivalence classes of permutation tuples
arising from branched coverings of the Riemann sphere. This description yields efficient
computational approaches for understanding the topology of moduli space||en_US
|dc.publisher||Queen Mary University of London||en_US
|dc.title||Combinatorics and Gauge-String Duality.||en_US
|dc.rights.holder||The copyright of this thesis rests with the author and no quotation from it or information derived from it may be published without the prior written consent of the author||