53 research outputs found
BPS Operators and Brane Geometries.
PhDIn this thesis we explore the finite N spectrum of BPS operators in four-dimensional
supersymmetric conformal field theories (CFT), which have dual AdS gravitational descriptions.
In the first part we analyze the spectrum of chiral operators in the free limit of
quiver gauge theories. We find explicit counting formulas at finite N for arbitrary quivers,
construct an orthogonal basis in the free inner product, and derive the chiral ring structure
constants. In order to deal with arbitrarily complicated quivers, we develop convenient
diagrammatic techniques: the results are expressed by associating Young diagrams and
Littlewood-Richardson coefficients to modifications of the original quiver. We develop the
notion of a "quiver character", which is a generalization of the symmetric group character,
obeying analogous orthogonality properties.
In the second part we analyze how the BPS spectrum changes at weak coupling, focusing
on the N = 4 supersymmetric Yang-Mills. We find a formal expression for the
complete set of eighth-BPS operators at finite N, and use it to derive corrections to a
near-BPS operator.
In the third part of this thesis we move on to the strong coupling regime, where
the dual gravitational description applies. The BPS spectrum on the gravity side includes
D3-branes wrapping arbitrary holomorphic surfaces, a generalization of the spherical giant
gravitons. Quantizing this moduli space gives a Hilbert space, which, via duality and nonrenormalization
theorems, should map to the space of BPS operators derived in the weak
coupling regime. We apply techniques from fuzzy geometry to study this correspondence
between D3-brane geometries, quantum states, and BPS operators in field theoryQueen Mary, University of London studentshi
Invariants of Toric Seiberg Duality
Three-branes at a given toric Calabi-Yau singularity lead to different phases
of the conformal field theory related by toric (Seiberg) duality. Using the
dimer model/brane tiling description in terms of bipartite graphs on a torus,
we find a new invariant under Seiberg duality, namely the Klein j-invariant of
the complex structure parameter in the distinguished isoradial embedding of the
dimer, determined by the physical R-charges. Additional number theoretic
invariants are described in terms of the algebraic number field of the
R-charges. We also give a new compact description of the a-maximization
procedure by introducing a generalized incidence matrix.Comment: 43 pages, 8 figures, LaTe
Beyond the Planar Limit in ABJM
In this article we consider gauge theories with a U(N)X U(N) gauge group. We
provide, for the first time, a complete set of operators built from scalar
fields that are in the bi fundamental of the two groups. Our operators
diagonalize the two point function of the free field theory at all orders in
1/N. We then use this basis to investigate non-planar anomalous dimensions in
the ABJM theory. We show that the dilatation operator reduces to a set of
decoupled harmonic oscillators, signaling integrability in a nonplanar large N
limit.Comment: v2: minor revisison
A double coset ansatz for integrability in AdS/CFT
We give a proof that the expected counting of strings attached to giant
graviton branes in AdS_5 x S^5, as constrained by the Gauss Law, matches the
dimension spanned by the expected dual operators in the gauge theory. The
counting of string-brane configurations is formulated as a graph counting
problem, which can be expressed as the number of points on a double coset
involving permutation groups. Fourier transformation on the double coset
suggests an ansatz for the diagonalization of the one-loop dilatation operator
in this sector of strings attached to giant graviton branes. The ansatz agrees
with and extends recent results which have found the dynamics of open string
excitations of giants to be given by harmonic oscillators. We prove that it
provides the conjectured diagonalization leading to harmonic oscillators.Comment: 33 pages, 3 figures; v2: references adde
On the Classification of Brane Tilings
We present a computationally efficient algorithm that can be used to generate
all possible brane tilings. Brane tilings represent the largest class of
superconformal theories with known AdS duals in 3+1 and also 2+1 dimensions and
have proved useful for describing the physics of both D3 branes and also M2
branes probing Calabi-Yau singularities. This algorithm has been implemented
and is used to generate all possible brane tilings with at most 6
superpotential terms, including consistent and inconsistent brane tilings. The
collection of inconsistent tilings found in this work form the most
comprehensive study of such objects to date.Comment: 33 pages, 12 figures, 15 table
Quivers, words and fundamentals
40 pages + Appendices, 9 figures40 pages + Appendices, 9 figure
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