The dynamics of two interacting giant
Date
2011-06-10
Authors
Jefferies, Katherine Laura Elizabeth Ann
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Abstract
In this thesis, the large N limit of the anomalous dimension of operators in
N = 4 super Yang-Mills theory described by restricted Schur Polynomials
are studied. The operators studied in this thesis are labelled by Young Di-
agrams which have two columns (both long) so that the classical dimension
of these operators is O(N). At large N these two column operators mix with
each other but are decoupled from operators with n 6= 2 columns. The planar
approximation does not does not capture the large N dynamics. The dilata-
tion operator is explicitly evaluated for 2, 3, and 4 impurities. In all three
cases, for a certain limit, the dilatation operator is a discretized version of
the second derivative de ned on a lattice emerging from the Young Diagram
itself. The dilatation operator is diagonalized numerically. All eigenvalues
are an integer multiple of 8g2
Y M and there are interesting degeneracies in the
spectrum. The spectrum obtained in this thesis for the one loop anomalous
dimension operator is reproduced by a collection of harmonic oscillators. The
equivalence to harmonic oscillators generalizes giant graviton results known
for the BPS sector and further implies that the Hamiltonian de ned by the
one loop large N dilatation operator is integrable. This is an example of an
integrable dilatation operator, obtained by summing both the planar and the
non-planar diagrams.