Large N conformal field theory from gauge/gravity duality
Date
2017
Authors
Hasina Tahiridimbisoa, Nirina Maurice
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Abstract
In this dissertation we exploit the Ads slash CFT correspondence to describe a system
of strings suspended between giant gravitons. The strings can be in an
excited state. The excitations of the strings can be given a particle-like description
and are known as magnons. The proposed gauge invariant operators used
to construct a complete description of this system belong to the su(2) sector
of the N = 4 SYM. Using an open spin chain description of the suspended
strings, the states of the system we consider enjoy an SU 2j2)2 symmetry. By
making use of this symmetry, we compute the all loop anomalous dimensions
of these operators. The spectrum of the dilatation operator in the su(2) sector
of the theory is reproduced in the dual gravity description. In the dual theory,
the energies of the magnons are computed using strings in a background LLM
geometry and the results are in complete agreement with the anomalous dimensions
of the operators we have considered. Using the symmetries enjoyed by our
system we achieve a complete determination - up to an overall phase - of the
reection/scattering matrix between a boundary magnon and a bulk magnon.
Thus, although the open boundary conditions of the spin chain spoil integrability. The two-loop
subleading correction to the dilatation operator is also explored. This subleading
term corresponds to a correction of the magnon energies. The computation
of this subleading term requires consideration of the giant's backreaction on
their excitations. We nd that this backreaction implies a nontrivial mixing of
the dual operators and this mixing is characterized completely.
Description
A thesis submitted to the Faculty of Science, University of the Witwatersrand, in
fulfilment of the requirements for the degree of Doctor of Philosophy
February 2017.
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Citation
Hasina Tahiridimbisoa, Nirina Maurice (2017) Large N conformal field theory from gauge/gravity duality, University of Witwatersrand, Johannesburg, <http://wiredspace.wits.ac.za/handle/10539/22731>