Trivial solutions of generalized supergravity vs non-abelian T-duality anomaly

The equations that follow from kappa symmetry of the type II Green-Schwarz string are a certain deformation, by a Killing vector field $K$, of the type II supergravity equations. We analyze under what conditions solutions of these `generalized' supergravity equations are trivial in the sense that they solve also the standard supergravity equations. We argue that for this to happen $K$ must be null and satisfy $dK=i_KH$ with $H=dB$ the NSNS three-form field strength. Non-trivial examples are provided by symmetric pp-wave solutions. We then analyze the consequences for non-abelian T-duality and the closely related homogenous Yang-Baxter sigma models. When one performs non-abelian T-duality of a string sigma model on a non-unimodular (sub)algebra one generates a non-vanishing $K$ proportional to the trace of the structure constants. This is expected to lead to an anomaly but we show that when $K$ satisfies the same conditions the anomaly in fact goes away leading to more possibilities for non-anomalous non-abelian T-duality.Comment: 11 pages; v2: Important clarifications in sec 5 and projections fixed there. References added. v3: Typos fixed and eq. (5.13) with the general form of the anomaly in terms of K and X adde

Constraining integrable AdS/CFT with factorized scattering

We consider (warped) AdS string backgrounds which allow for a GKP spinning string/null cusp solution. Integrability implies that the worldsheet S-matrix should factorize, which in turn constrains the form of the warp factor as a function of the coordinates of the internal space. This constraint is argued to rule out integrability for all supersymmetric AdS7 and AdS6 backgrounds as well as AdS5 Gaiotto-Maldacena backgrounds and a few highly supersymmetric AdS4 and AdS3 backgrounds.Comment: 19 pages; v2: Further clarifications in sec 4 and 5. Published versio

Classifying integrable symmetric space strings via factorized scattering

All symmetric space $AdS_n$ solutions of type II supergravity have recently been found for $n>2$. For the supersymmetric solutions (and their T-duals) it is known that the Green-Schwarz string is classically integrable. We complete the classification by ruling out integrability for the remaining non-supersymmetric solutions. This is achieved by showing that tree-level scattering on the worldsheet of a GKP or BMN string fails to factorize for these cases.Comment: 17 pages; v2: Improvements to sec 1, results now summarized in Tab 1. Matches published versio

On integrability of strings on symmetric spaces

In the absence of NSNS three-form flux the bosonic string on a symmetric space is described by a symmetric space coset sigma-model. Such models are known to be classically integrable. We show that the integrability extends also to cases with non-zero NSNS flux (respecting the isometries) provided that the flux satisfies a condition of the form H_{abc}H^{cde}~R_{ab}^{de}. We then turn our attention to the type II Green-Schwarz superstring on a symmetric space. We prove that if the space preserves some supersymmetry there exists a truncation of the full superspace to a supercoset space and derive the general form of the superisometry algebra. In the case of vanishing NSNS flux the corresponding supercoset sigma-model for the string is known to be integrable. We prove that the integrability extends to the full string by augmenting the supercoset Lax connection with terms involving the fermions which are not captured by the supercoset model. The construction is carried out to quadratic order in these fermions. This proves the integrability of strings on symmetric spaces supported by RR flux which preserve any non-zero amount of supersymmetry. Finally we also construct Lax connections for some supercoset models with non-zero NSNS flux describing strings in AdS(2,3) x S(2,3) x S(2,3) x T(2,3,4) backgrounds preserving eight supersymmetries.Comment: 34 pages; v3: Minor clarifications, matches published version; v4: Missing local Lorentz transformation added in eqs. (2.14), (2.15) and (4.64

Diatoms: an amazing resource

Diatoms are unicellular microscopic algae with cell walls consisting of silicon dioxide with a small amount of water. The cell wall consists of two halves, like a box with a lid. The cell wall (frustule) has a specific pattern of tiny pores, each pattern is species-specific. The pores allow exchange of nutrients and waste products. Diatoms are found everywhere where it is moist and enough light: in the ocean, on the sea floor, lakes, in and on ice, and even on cave walls. Sometimes they form long filaments by adding cell after cell in a thread up to 3 m length. They form the basis of the food web and are eaten by everything from the size of microscopic ciliates to whales. They photosynthesize but are also able to uptake small organic molecules. Thus, they can survive in darkness without forming resting stages. Diatoms contain chlorophylls a, c1, c2, and, in addition, different carotenoids such as fucoxanthin, which give them a brownish color. They store energy in the form of oil (lipids) and the carbohydrate chrysolaminarin. Frustules have one to three layers of nanopores, which can be used in several industrial applications. For example, this frustule material can be used to increase the efficiency of solar panels due to the structures light trapping property. The structure also blocks UV light efficiently, which can be utilized in e.g. sunscreens and plastics. Due to the materials nanoporosity it also takes up and releases chemical substances efficiently, which can be utilized in a lot of different applications. The oil produced by diatoms is excellent for use in fish feed production or even food supplements due to the content of polyunsaturated fatty acids. In our prototype facility we are constantly exploring new ways for how to convert our findings into valuable products. Energy storage, UV resistant paint and plastic, cosmetics, feed, fertilizers…Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech