The distinguished guests of giants
Date
2016
Authors
Mathwin, Christopher Richard
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Abstract
The convenient pictorial descriptions of the half-BPS and near-BPS sectors of the AdS=CFT equivalent
theories of N = 4, D = 4 super Yang-Mills and D = 10 Type IIB superstring theory on AdS5 S5 are
exploited in this thesis by using Schur polynomials labelled by Young diagrams as a basis for the gauge
invariant operators in the eld theory.
We use a \Fourier transform" on these operators to construct asymptotic eigenstates of the dilatation
operator, the spectrum of which agrees precisely with the rst two leading order terms in the smallcoupling
expansion of the exact result determined by symmetry. Motivated by the geometric description
of the systems of open strings with magnon excitations to which the operators are dual, we propose
a simple and minimal all-loop expression that interpolates between anomalous dimensions computed
in the gauge theory and energies computed in the string theory. The connection to the string theory
result provides the insight necessary to understand the interpretation of our Gauss graphs in the magnon
language. Symmetry determines the two-body scattering matrix for the magnons up to a phase, and it
is demonstrated that integrability is spoiled by the boundary conditions on the open strings.
The Schur polynomial construction is then applied to the study of closed strings on a class of half-
BPS excitations of the AdS5 S5 background. The string theory predictions for the magnon energies
are again reproduced by calculating the anomalous dimensions of particular linear combinations of our
operators. Group theoretic quantities which can be read o the Young diagram labels provide the correct
modi cation of terms in the dilatation action to account for the energies of magnons at di erent radii on
the LLM plane. The representation theory implies a natural splitting of the full symmetry group - the
distinction between what is the background and what is the excitation is accomplished in the choice of
the subgroup and representations used to construct the operator.
Connecting the descriptions utilised in obtaining these results is expected to allow the construction of
operators dual to general open string con gurations on the class of backgrounds considered.
Description
A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, 2016.