## Brane states and group representation theory

##### Date

2014-01-14

##### Authors

Nokwara, Nkululeko

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##### Abstract

A complete understanding of quantum gravity remains an open problem. However, the
AdS/CFT correspondence which relates quantum eld theories that enjoy conformal
symmetry to theories of (quantum) gravity is proving to be a useful tool in shedding
light on this formidable problem. Recently developed group representation theoretic
methods have proved useful in understanding the large N; but non-planar limit of N = 4
supersymmetric Yang-Mills theory. In this work, we study operators that are dual
to excited giant gravitons, which corresponds to a sector of N = 4 super Yang-Mills
theory that is described by a large N; but non-planar limit. After a brief review of
the work done in the su (2) sector, we compute the spectrum of anomalous dimensions
in the su (2) sector of the Leigh-Strassler deformed theory. The result resembles the
spectrum of a shifted harmonic oscillator. We then explain how to construct restricted
Schur polynomials built using both fermionic and bosonic elds which transform in the
adjoint of the gauge group U (N) : We show that these operators diagonalise the free
eld two point function to all orders in 1=N: As an application of our new operators,
we study the action of the one-loop dilatation operator in the su (2,3) sector in a large
N; but non-planar limit of N = 4 super Yang-Mills theory. As in the su (2) case, the
resulting spectrum matches the spectrum of a set of decoupled oscillators. Finally, in
an appendix, we study the action of the one-loop dilatation operator in an sl (2) sector
of N = 4 super Yang-Mills theory. Again, the resulting spectrum matches that of a
set of harmonic oscillators. In all these cases, we nd that the action of the dilatation
operator is diagonalised by a double coset ansatz.

##### 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.
3rd October 2013.