Anomalies and divergences in N=4 supergravity

The invariants in D=4, N=4 supergravity are discussed up to the three-loop order (where one expects a general R^4 structure). Because there is an anomaly in the rigid SL(2,R) symmetry of this theory, the analysis of possible restrictions on three-loop divergences due to duality needs careful treatment. We show that this anomalous symmetry is still strong enough at the three-loop order to require duality invariance of candidate counterterms. Provided one makes the additional assumption that there exists a full 16-supercharge off-shell formulation of the theory, counterterms at L \ge 2 loops would also have to be writable as full-superspace integrals. At the three-loop order such a duality-invariant full-superspace integral candidate counterterm exists, but its duality invariance is marginal in the sense that the full-superspace counter-Lagrangian is not itself duality invariant. We show that, subject to the assumption that a full off-shell quantisation formalism exists, such marginal invariants are not allowable as counterterms.Comment: 15 pages, version published in Phys. Lett.

Invariants and divergences in half-maximal supergravity theories

The invariants in half-maximal supergravity theories in D=4,5 are discussed in detail up to dimension eight (e.g. R^4). In D=4, owing to the anomaly in the rigid SL(2,R) duality symmetry, the restrictions on divergences need careful treatment. In pure N=4 supergravity, this anomalous symmetry still implies duality invariance of candidate counterterms at three loops. Provided one makes the additional assumption that there exists a full 16-supercharge off-shell formulation of the theory, counterterms at L>1 loops would also have to be writable as full-superspace integrals. At the three-loop order such a duality-invariant full-superspace integral candidate counterterm exists, but its duality invariance is marginal in the sense that the full-superspace counter-Lagrangian is not itself duality-invariant. We show that such marginal invariants are not allowable as counterterms in a 16-supercharge off-shell formalism. It is not possible to draw the same conclusion when vector multiplets are present because of the appearance of F^4 terms in the SL(2,R) anomaly. In D=5 there is no one-loop anomaly in the shift invariance of the dilaton, and we argue that this implies finiteness at two loops, again subject to the assumption that 16 supercharges can be preserved off-shell.Comment: 81 page

Genericity of Fr\'echet smooth spaces

If a separable Banach space contains an isometric copy of every separable reflexive Fr\'echet smooth Banach space, then it contains an isometric copy of every separable Banach space. The same conclusion holds if we consider separable Banach spaces with Fr\'echet smooth dual space. This improves a result of G. Godefroy and N. J. Kalton.Comment: 34 page

Food Ingredients Recognition through Multi-label Learning

Automatically constructing a food diary that tracks the ingredients consumed can help people follow a healthy diet. We tackle the problem of food ingredients recognition as a multi-label learning problem. We propose a method for adapting a highly performing state of the art CNN in order to act as a multi-label predictor for learning recipes in terms of their list of ingredients. We prove that our model is able to, given a picture, predict its list of ingredients, even if the recipe corresponding to the picture has never been seen by the model. We make public two new datasets suitable for this purpose. Furthermore, we prove that a model trained with a high variability of recipes and ingredients is able to generalize better on new data, and visualize how it specializes each of its neurons to different ingredients.Comment: 8 page

Envisioning Neighborhoods with TOD Potential (Includes demonstration CD), MTI Report 01-15

The Mineta Transportation Institute (MTI) at San José State University conducted this study to review the issues and implications involved when seeking to Envision Neighborhoods with Transit Oriented Development (TOD) Potential. The Envisioning Neighborhoods with Transit Oriented Development (TOD) Potential project seeks to introduce planners, developers, and urban analysts to information design techniques and digital computer tools that can be used to undertake and study TOD. A basic premise is that effective TOD requires thoughtful planning to be successfully integrated into the metropolitan fabric. The primary focus of this project is intra-regional comparisons, focusing on information pertaining to the relative desirability of places within a region. Context matters, so data is best understood in a comparative context. Small multiple replicate maps, charts, and digital images can be used to understand many aspects of places with TOD potential. Place comparisons can be made across space, time, and scale. The study focus is on understanding the neighborhoods surrounding transit centers and their context in terms of the character of areas within walking distance (\u3c 1/2 mile), bicycling distance (\u3c 2 miles) and five-mile driving or transit distance. These ranges of analysis include the areas where residents of possible TODs might work, shop, or prefer to go for services. This project includes a comprehensive case study application envisioning the Hayward BART Station area. Other case studies cover the Fruitvale BART in Oakland, Redwood City and Mountain View CalTrain, Campbell LRT site, and Sacramento’s 65th St. Station areas

Using the Internet to Envision Neighborhoods with Transit Oriented Development Potential, MTI Report 01-24

The Mineta Transportation Institute (MTI) at San José State University conducted this study to review the issues and implications involved in Using the Internet to Envision Neighborhoods with Transit-Oriented Development Potential. SUMMARY OF PROBLEM: The Using the Internet to Envision Neighborhoods with Transit-Oriented Development Potential project seeks to provide guidelines and examples to facilitate use of the Internet to envision places with TOD potential, building on the envisioning techniques developed and presented in MTI Report 01-15, Envisioning Neighborhoods with Transit-Oriented Development Potential. RECOMMENDATIONS: These recommendations are made in terms of general style and approach, because the Internet is evolving so rapidly that currently available program are likely to change soon. The envisioning neighborhoods principles presented in MTI Report 01-15 are useful for Internet applications. These principles are: Use small replicate maps, charts, images, and tables to facilitate comparisons across space, time, and scale, because data are best understood in a comparative context. The suggested solution for analyzing the transit-oriented development potential of neighborhoods is twofold: First, use the evolving digital information tools (especially the Internet) and information design principles to find, filter, transform, model, and synthesize neighborhood data. Second, use small replicate maps, charts, digital images, and tables to facilitate comparisons across space, time, and scale, presenting the resulting information in a form useful for understanding conditions, making decisions, and taking action

Superconformal invariance from N=2 supersymmetry Ward identities

We algebraically prove the cancellation of the β function at all order of perturbation theory of Script N = 2 supersymmetric gauge theories with a vanishing one-loop β function. The proof generalises that recently given for the Script N = 4 case. It uses the consistent Slavnov-Taylor identities of the shadow dependent formulation. We also demonstrate the cancellation at all orders of the anomalous dimensions of vector and hypermultiplet ½BPS operators

Classification of BPS instantons in N=4 D=4 supergravity

This talk is based on the recent work in collaboration with M. Azreg-A\"{\i}nou and G. Cl\'ement devoted to extremal instantons in the one-vector truncation of the Euclidean $\mathcal{N}=4,\, D=4$ theory. Extremal solutions satisfying the no-force condition can be associated with null geodesic curves in the homogeneous target space of the three-dimensional sigma model arising in toroidal reduction of the four-dimensional theory. Here we (preliminarily) discuss the case of two vector fields sufficient to find all relevant metrics in the full $\mathcal{N}=4,\, D=4$ theory. Classification of instanton solutions is given along the following lines. The first is their possible asymptotic structure: asymptotically locally flat (ALF), asymptotically locally Euclidean (ALE) and ALF or ALE with the dilaton growing at infinity. The second is the algebraic characterization of matrix generators according to their rank and the nature of the charge vectors in an associated Lorentzian space. Finally, solutions are distinguished by the number of independent harmonic functions with unequal charges (up to four).Comment: Submitted to Proceedings of "Quantum Theory and Symmetries" (QTS-7), Prague, August 7-13, 201

Counterterms vs. Dualities

We investigate and clarify the mutual compatibility of the higher order corrections arising in supergravity and string theory effective actions and the non-linear duality symmetries of these theories. Starting from a conventional tree level action leading to duality invariant equations of motion, we show how to accommodate duality invariant counterterms given as functionals of both electric and magnetic fields in a perturbative expansion, and to deduce from them a non-polynomial bona fide action satisfying the Gaillard-Zumino constraint. There exists a corresponding consistency constraint in the non-covariant Henneaux-Teitelboim formalism which ensures that one can always restore diffeomorphism invariance by perturbatively solving this functional identity. We illustrate how this procedure works for the R^2 \nabla F \nabla F and F^4 counterterms in Maxwell theory.Comment: 15 page

Reconstruction of N=1 supersymmetry from topological symmetry

The scalar and vector topological Yang-Mills symmetries on Calabi-Yau manifolds geometrically define consistent sectors of Yang-Mills D=4,6 N=1 supersymmetry, which fully determine the supersymmetric actions up to twist. For a CY_2 manifold, both N=1,D=4 Wess and Zumino and superYang-Mills theory can be reconstructed in this way. A superpotential can be introduced for the matter sector, as well as the Fayet-Iliopoulos mechanism. For a CY_3 manifold, the N=1, D=6 Yang-Mills theory is also obtained, in a twisted form. Putting these results together with those already known for the D=4,8 N=2 cases, we conclude that all Yang--Mills supersymmetries with 4, 8 and 16 generators are determined from topological symmetry on special manifolds.Comment: 13 page