Gauge/gravity duality beyond the planar limit

PhDOne of the most exciting and successful ideas pursued in string theory is gauge/gravity duality. We consider the example of the AdS/CFT correspondence, which maps maximally supersymmetric Yang-Mills (N = 4 SYM) in four dimensions with gauge group U(N) to closed strings propagating in a background of Anti de Sitter space crossed with a sphere (AdS5 × S5). Much progress has been made understanding this duality in the planar ’t Hooft limit, where we fix the coupling of the gauge theory λ and take N large. On the gravity side the string coupling gs is proportional to 1/N for fixed λ, so in this limit we get classical string theory. In this thesis we use symmetric group methods to study the AdS/CFT correspondence exactly at finite N, without taking the planar limit. This takes the string theory into the quantum regime and allows us to probe phenomena which are non-perturbative in gs. First we enumerate the spectrum. While the spectrum is non-trivial in the planar limit, it is further complicated at finite N by the Stringy Exclusion Principle, which truncates the usual trace spectrum. We organise local operators in the gauge theory using representations of the gauge group U(N), which for heavy operators are interpreted in terms of giant graviton branes in the bulk. To do this we sort the different fields of the theory into representations of the global superconformal symmetry group using Schur- Weyl duality. We then compute two- and three-point functions of these operators exactly to all orders in N for the free theory and at one loop. We use these correlation functions to resolve certain transition probabilities for giant gravitons using CFT factorisatio

β3-Adrenergic receptor-dependent modulation of the medium afterhyperpolarization in rat hippocampal CA1 pyramidal neurons.

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this recordAction potential firing in hippocampal pyramidal neurons is regulated by generation of an afterhyperpolarization (AHP). Three phases of AHP are recognised, with the fast AHP regulating action potential firing at the onset of a burst, and the medium and slow AHPs supressing action potential firing over 100s of milliseconds and seconds respectively. Activation of β-adrenergic receptors suppresses the slow AHP by a protein kinase A-dependent pathway. However, little is known regarding modulation of the medium AHP. Application of the selective β-adrenergic receptor agonist isoproterenol suppressed both the medium and slow AHPs evoked in rat CA1 hippocampal pyramidal neurons recorded from slices maintained in organotypic culture. Suppression of the slow AHP was mimicked by intracellular application of cAMP, with the suppression of the medium AHP by isoproterenol still being evident in cAMP-dialysed cells. Suppression of both the medium and slow AHPs was antagonised by the β-adrenergic receptor antagonist propranolol. The effect of isoproterenol to suppress the medium AHP was mimicked by two β3-adrenergic receptor agonists: BRL37344 and SR58611A. The medium AHP was mediated by activation of SK and deactivation of H channels at the resting membrane potential. Suppression of the medium AHP by isoproterenol was reduced by pre-treating cells with the H-channel blocker ZD7288. These data suggest that activation of β3-adrenergic receptors inhibits H-channels, which suppresses the medium AHP in CA1 hippocampal neurons by utilising a pathway that is independent of a rise of intracellular cAMP. This finding highlights a potential new target in modulating H-channel activity, and thereby neuronal excitability

From counting to construction of BPS states in N=4 SYM

We describe a universal element in the group algebra of symmetric groups, whose characters provides the counting of quarter and eighth BPS states at weak coupling in N=4 SYM, refined according to representations of the global symmetry group. A related projector acting on the Hilbert space of the free theory is used to construct the matrix of two-point functions of the states annihilated by the one-loop dilatation operator, at finite N or in the large N limit. The matrix is given simply in terms of Clebsch-Gordan coefficients of symmetric groups and dimensions of U(N) representations. It is expected, by non-renormalization theorems, to contain observables at strong coupling. Using the stringy exclusion principle, we interpret a class of its eigenvalues and eigenvectors in terms of giant gravitons. We also give a formula for the action of the one-loop dilatation operator on the orthogonal basis of the free theory, which is manifestly covariant under the global symmetry.Comment: 41 pages + Appendices, 4 figures; v2 - refs and acknowledgments adde

Analysis of segmentation ontology reveals the similarities and differences in connectivity onto L2/3 neurons in mouse V1

Quantitatively comparing brain-wide connectivity of different types of neuron is of vital importance in understanding the function of the mammalian cortex. Here we have designed an analytical approach to examine and compare datasets from hierarchical segmentation ontologies, and applied it to long-range presynaptic connectivity onto excitatory and inhibitory neurons, mainly located in layer 2/3 (L2/3), of mouse primary visual cortex (V1). We find that the origins of long-range connections onto these two general cell classes-as well as their proportions-are quite similar, in contrast to the inputs on to a cell type in L6. These anatomical data suggest that distal inputs received by the general excitatory and inhibitory classes of neuron in L2/3 overlap considerably

Surprisingly Simple Spectra

The large N limit of the anomalous dimensions of operators in ${\cal N}=4$ super Yang-Mills theory described by restricted Schur polynomials, are studied. We focus on operators labeled by Young diagrams that 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 $n\ne 2$ columns. The planar approximation does not capture the large N dynamics. For operators built with 2, 3 or 4 impurities the dilatation operator is explicitly evaluated. In all three cases, in a certain limit, the dilatation operator is a lattice version of a second derivative, with the lattice emerging from the Young diagram itself. The one loop dilatation operator is diagonalized numerically. All eigenvalues are an integer multiple of $8g_{YM}^2$ and there are interesting degeneracies in the spectrum. The spectrum we obtain for the one loop anomalous dimension operator is reproduced by a collection of harmonic oscillators. This equivalence to harmonic oscillators generalizes giant graviton results known for the BPS sector and further implies that the Hamiltonian defined by the one loop large $N$ dilatation operator is integrable. This is an example of an integrable dilatation operator, obtained by summing both planar and non-planar diagrams.Comment: 34 page

Quivers, words and fundamentals

40 pages + Appendices, 9 figures40 pages + Appendices, 9 figure

Visualized effect of oxidation on magnetic recording fidelity in pseudo-single-domain magnetite particles

Magnetite (​Fe3O4) is an important magnetic mineral to Earth scientists, as it carries the dominant magnetic signature in rocks, and the understanding of its magnetic recording fidelity provides a critical tool in the field of palaeomagnetism. However, reliable interpretation of the recording fidelity of ​Fe3O4 particles is greatly diminished over time by progressive oxidation to less magnetic iron oxides, such as maghemite (γ-Fe2O3), with consequent alteration of remanent magnetization potentially having important geological significance. Here we use the complementary techniques of environmental transmission electron microscopy and off-axis electron holography to induce and visualize the effects of oxidation on the magnetization of individual nanoscale ​Fe3O4 particles as they transform towards γ-Fe2O3. Magnetic induction maps demonstrate a change in both strength and direction of remanent magnetization within ​Fe3O4 particles in the size range dominant in rocks, confirming that oxidation can modify the original stored magnetic information

Orthogonal Bases of Invariants in Tensor Models

Representation theory provides a suitable framework to count and classify invariants in tensor models. We show that there are two natural ways of counting invariants, one for arbitrary rank of the gauge group and a second, which is only valid for large N. We construct bases of invariant operators based on the counting, and compute correlators of their elements. The basis associated with finite N diagonalizes the two-point function of the theory and it is analogous to the restricted Schur basis used in matrix models. We comment on future lines of investigation.Comment: Two overlapping but independent results are merged to a joint work. 16 pages, 1 tabl

Flavour singlets in gauge theory as permutations

50 pages, v2: typos corrected, v3: to appear in JHEPJHEP is an open-access journal funded by SCOAP3 and licensed under CC BY 4.