Quantum states to brane geometries via fuzzy moduli spaces of giant gravitons

Eighth-BPS local operators in N=4 SYM are dual to quantum states arising from the quantization of a moduli space of giant gravitons in AdS5xS5. Earlier results on the quantization of this moduli space give a Hilbert space of multiple harmonic oscillators in 3 dimensions. We use these results, along with techniques from fuzzy geometry, to develop a map between quantum states and brane geometries. In particular there is a map between the oscillator states and points in a discretization of the base space in the toric fibration of the moduli space. We obtain a geometrical decomposition of the space of BPS states with labels consisting of U(3) representations along with U(N) Young diagrams and associated group theoretic multiplicities. Factorization properties in the counting of BPS states lead to predictions for BPS world-volume excitations of specific brane geometries. Some of our results suggest an intriguing complementarity between localisation in the moduli space of branes and localisation in space-time.Comment: 69 pages, 6 figures. v2: references adde

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

Correlation functions and representation bases in free N=4 Super Yang-Mills

We study exact correlation functions of N=4 SYM at zero coupling. It has been known that it is convenient to label local gauge invariant operators by irreducible representations of symmetric groups/Brauer algebras. We first review the construction of representation bases from the viewpoint of the enhanced symmetry structure of the free theory. We present a basis of multi-matrix models using elements of Brauer algebras, generalising our previous construction for two matrices. We will compute multi-point functions of the basis with the exact N-dependence. In particular we study three-point functions of a class of BPS operators, and we find that they are given by a branching rule of the Brauer algebra. The three-point functions take a factorised form if representations on the operators satisfy a relation.Comment: 28 pages, typos correcte

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