CFT4 as SO(4,2)-invariant TFT2

54 pages, 7 figures; version 2: Published version - extended discussion of CFT4/TFT2 in terms of emergent space-time; refs added; typos correctedOpen Access funded by SCOAP³ - Sponsoring Consortium for Open Access Publishing in Particle Physic

Interactions as intertwiners in 4D QFT

42 pages, 3 figures42 pages, 3 figures42 pages, 3 figuresIn a recent paper we showed that the correlators of free scalar field theory in four dimensions can be constructed from a two dimensional topological field theory based on so(4,2) equivariant maps (intertwiners). The free field result, along with results of Frenkel and Libine on equivariance properties of Feynman integrals, are developed further in this paper. We show that the coefficient of the log term in the 1-loop 4-point conformal integral is a projector in the tensor product of so(4,2) representations. We also show that the 1-loop 4-point integral can be written as a sum of four terms, each associated with the quantum equation of motion for one of the four external legs. The quantum equation of motion is shown to be related to equivariant maps involving indecomposable representations of so(4,2), a phenomenon which illuminates multiplet recombination. The harmonic expansion method for Feynman integrals is a powerful tool for arriving at these results. The generalization to other interactions and higher loops is discussed

From Matrix Models and quantum fields to Hurwitz space and the absolute Galois group

54 pages, 17 figures54 pages, 17 figures54 pages, 17 figuresWe show that correlators of the hermitian one-Matrix model with a general potential can be mapped to the counting of certain triples of permutations and hence to counting of holomorphic maps from world-sheet to sphere target with three branch points on the target. This allows the use of old matrix model results to derive new explicit formulae for a class of Hurwitz numbers. Holomorphic maps with three branch points are related, by Belyi's theorem, to curves and maps defined over algebraic numbers \bmQ. This shows that the string theory dual of the one-matrix model at generic couplings has worldsheets defined over the algebraic numbers and a target space \mP^1 (\bmQ). The absolute Galois group Gal (\bmQ / \mQ) acts on the Feynman diagrams of the 1-matrix model, which are related to Grothendieck's Dessins d'Enfants. Correlators of multi-matrix models are mapped to the counting of triples of permutations subject to equivalences defined by subgroups of the permutation groups. This is related to colorings of the edges of the Grothendieck Dessins. The colored-edge Dessins are useful as a tool for describing some known invariants of the Gal (\bmQ / \mQ) action on Grothendieck Dessins and for defining new invariants

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

Strings on Bubbling Geometries

We study gauge theory operators which take the form of a product of a trace with a Schur polynomial, and their string theory duals. These states represent strings excited on bubbling AdS geometries which are dual to the Schur polynomials. These geometries generically take the form of multiple annuli in the phase space plane. We study the coherent state wavefunction of the lattice, which labels the trace part of the operator, for a general Young tableau and their dual description on the droplet plane with a general concentric ring pattern. In addition we identify a density matrix over the coherent states on all the geometries within a fixed constraint. This density matrix may be used to calculate the entropy of a given ensemble of operators. We finally recover the BMN string spectrum along the geodesic near any circle from the ansatz of the coherent state wavefunction.Comment: 41 pages, 12 figures, published version in JHE

Minimal Model Holography for SO(2N)

A duality between the large N 't Hooft limit of the WD_N minimal model CFTs and a higher spin gravity theory on AdS3 is proposed. The gravity theory has massless spin fields of all even spins s=2,4,6,..., as well as two real scalar fields whose mass is determined by the 't Hooft parameter of the CFT. We show that, to leading order in the large N limit, the 1-loop partition function of the higher spin theory matches precisely with the CFT partition function.Comment: 21 pages, LaTe

Extracting scientific articles from a large digital archive: BioStor and the Biodiversity Heritage Library

Background: The Biodiversity Heritage Library (BHL) is a large digital archive of legacy biological literature, comprising over 31 million pages scanned from books, monographs, and journals. During the digitisation process basic metadata about the scanned items is recorded, but not article-level metadata. Given that the article is the standard unit of citation, this makes it difficult to locate cited literature in BHL. Adding the ability to easily find articles in BHL would greatly enhance the value of the archive. Description: A service was developed to locate articles in BHL based on matching article metadata to BHL metadata using approximate string matching, regular expressions, and string alignment. This article locating service is exposed as a standard OpenURL resolver on the BioStor web site http://biostor.org/openurl/. This resolver can be used on the web, or called by bibliographic tools that support OpenURL. Conclusions: BioStor provides tools for extracting, annotating, and visualising articles from the Biodiversity Heritage Library. BioStor is available from http://biostor.org

F-Theorem without Supersymmetry

The conjectured F-theorem for three-dimensional field theories states that the finite part of the free energy on S^3 decreases along RG trajectories and is stationary at the fixed points. In previous work various successful tests of this proposal were carried out for theories with {\cal N}=2 supersymmetry. In this paper we perform more general tests that do not rely on supersymmetry. We study perturbatively the RG flows produced by weakly relevant operators and show that the free energy decreases monotonically. We also consider large N field theories perturbed by relevant double trace operators, free massive field theories, and some Chern-Simons gauge theories. In all cases the free energy in the IR is smaller than in the UV, consistent with the F-theorem. We discuss other odd-dimensional Euclidean theories on S^d and provide evidence that (-1)^{(d-1)/2} \log |Z| decreases along RG flow; in the particular case d=1 this is the well-known g-theorem.Comment: 34 pages, 2 figures; v2 refs added, minor improvements; v3 refs added, improved section 4.3; v4 minor improvement

Giant Graviton Oscillators

We study the action of the dilatation operator on restricted Schur polynomials labeled by Young diagrams with p long columns or p long rows. A new version of Schur-Weyl duality provides a powerful approach to the computation and manipulation of the symmetric group operators appearing in the restricted Schur polynomials. Using this new technology, we are able to evaluate the action of the one loop dilatation operator. The result has a direct and natural connection to the Gauss Law constraint for branes with a compact world volume. We find considerable evidence that the dilatation operator reduces to a decoupled set of harmonic oscillators. This strongly suggests that integrability in N=4 super Yang-Mills theory is not just a feature of the planar limit, but extends to other large N but non-planar limits.Comment: 72 page

Effective action in a higher-spin background

We consider a free massless scalar field coupled to an infinite tower of background higher-spin gauge fields via minimal coupling to the traceless conserved currents. The set of Abelian gauge transformations is deformed to the non-Abelian group of unitary operators acting on the scalar field. The gauge invariant effective action is computed perturbatively in the external fields. The structure of the various (divergent or finite) terms is determined. In particular, the quadratic part of the logarithmically divergent (or of the finite) term is expressed in terms of curvatures and related to conformal higher-spin gravity. The generalized higher-spin Weyl anomalies are also determined. The relation with the theory of interacting higher-spin gauge fields on anti de Sitter spacetime via the holographic correspondence is discussed.Comment: 40 pages, Some errors and typos corrected, Version published in JHE