Open G2 Strings

We consider an open string version of the topological twist previously proposed for sigma-models with G2 target spaces. We determine the cohomology of open strings states and relate these to geometric deformations of calibrated submanifolds and to flat or anti-self-dual connections on such submanifolds. On associative three-cycles we show that the worldvolume theory is a gauge-fixed Chern-Simons theory coupled to normal deformations of the cycle. For coassociative four-cycles we find a functional that extremizes on anti-self-dual gauge fields. A brane wrapping the whole G2 induces a seven-dimensional associative Chern-Simons theory on the manifold. This theory has already been proposed by Donaldson and Thomas as the higher-dimensional generalization of real Chern-Simons theory. When the G2 manifold has the structure of a Calabi-Yau times a circle, these theories reduce to a combination of the open A-model on special Lagrangians and the open B+\bar{B}-model on holomorphic submanifolds. We also comment on possible applications of our results.Comment: 55 pages, no figure

Emergent Spacetime and Holographic CFTs

We discuss universal properties of conformal field theories with holographic duals. A central feature of these theories is the existence of a low-lying sector of operators whose correlators factorize. We demonstrate that factorization can only hold in the large central charge limit. Using conformal invariance and factorization we argue that these operators are naturally represented as fields in AdS as this makes the underlying linearity of the system manifest. In this class of CFTs the solution of the conformal bootstrap conditions can be naturally organized in structures which coincide with Witten diagrams in the bulk. The large value of the central charge suggests that the theory must include a large number of new operators not captured by the factorized sector. Consequently we may think of the AdS hologram as an effective representation of a small sector of the CFT, which is embedded inside a much larger Hilbert space corresponding to the black hole microstates.Comment: 89 pages, 8 figures, typos correcte

Auxin and cytokinin interactions regulate primary vascular patterning during root development in Arabidopsis thaliana

The evolution of vascular tissues was a critical innovation in the colonization of land by plants. We investigated how vascular tissues, in particular xylem, are patterned in the root of the model plant Arabidopsis. The vascular tissues of the Arabidopsis root tip are consistently patterned as a xylem axis flanked by procambial cells, with phloem poles developing perpendicular to the xylem axis. Cytokinin signalling inhibits the specification of protoxylem; the AHP6 gene inhibits cytokinin signalling at the protoxylem position during normal vascular development. We sought to understand the factors regulating AHP6 expression in the root tip. Cytokinin signalling is known to flank the xylem axis; we discovered a complementary domain of auxin signalling throughout the xylem axis. Based on this, we showed that auxin upregulates AHP6, creating a domain of low cytokinin signalling, and also acts to specify protoxylem. We used a combination of mutants and pharmacological treatments to investigate how mutually exclusive auxin and cytokinin signalling domains are maintained in the Arabidopsis stele. We discovered a feedback loop between the hormones, in which cytokinin activates auxin exporters, while auxin represses cytokinin signalling. The mutual inhibition between auxin and cytokinin regulates the extent of their domains during vascular patterning. We turned to computational simulations to investigate the sufficiency, stability, and dynamics of this network. Our simulations confirmed that the network is sufficient to maintain the hormone domains during vascular patterning, but also revealed a role for auxin importers, which we confirmed through experiments. While cytokinin is frequently thought to form gradients guiding developmental processes in the Arabidopsis shoot and root, we showed that an informative cytokinin gradient cannot form on the scale of these tissues via diffusion. While auxin is patterned through the activity of polarly localised transporters, there is no evidence for similar transport of cytokinin. Nevertheless, our findings highlight the need for a cytokinin patterning mechanism, such as directed cytokinin transport or patterning of the cytokinin perception machinery, since diffusion cannot form the observed cytokinin patterns. Finally, we discovered a potential link between the auxin-cytokinin feedback loop in the root tip and the initiation of lateral roots. Since our experimental data are equivocal on whether or not PIN1 is polarly localised in the procambium, we investigated both possibilities in our computational model. We discovered that polar localisation of PIN1 results in a regular flux of auxin towards the centre of the stele and back out via the xylem axis. This circuit privileges pericycle cells flanking the xylem axis to accumulate auxin if they experience a brief activation of an auxin importer; activation of the importer AUX1 in the xylem-pole pericycle cells is one of the earliest steps in lateral root initiation. Altogether, my thesis reveals a key role for mutually inhibitory auxin-cytokinin interactions in vascular development and links these findings to other developmental contexts. This work also demonstrates how the combination of experimental & computational approaches enables us to critically evaluate our models and develop more general insights.Johtosolukon evoluutio oli tärkeä askel kasvien siirtyessä vedestä maalle. Tutkimme, miten juuren johtosolukot muodostuvat mallikasvissa Arabidopsisissa, eli lituruohossa. Johtosolukot lituruohon juuren kärjessä ovat ksyleemi (puu), nila ja esijälsi. Ksyleemisolut sijaitsevat säännönmukaisesti rivissä juuren keskellä ja esijälsi ksyleemi- ja nilasolujen välissä. Sytokiniinisignalointi estää alkuksyleemin määrittelyn. Juuren kehittyessä, AHP6-geeni normaalisti ehkäisee sytokiniinisignalointia alkuksyleemissä. Kysyimme, mitkä tekijät säätelevät AHP6:n ilmentymistä juuren kärjessä. Sytokiniinisignaloinnin alue on ksyleemin rivin viereisissä soluissa ja me havaitsimme, että auksiinisignalointi on ksyleemin rivissä. Näin ollen, auksiinisignalointi ja sytokiniinisignalointi ovat toisensa poissulkevia juuren poikkileikkauksessa. Osoitimme, että auksiini edistää AHP6:n ilmentymistä ja alkuksyleemin määrittymistä. Sytokiniinisignalointia ei tapahdu AHP6:n ilmentymisen alueella. Tutkimme mutanttien ja lääkkeiden avulla miten auksiini- ja sytokiniinisignaloinnin toisensa poissulkevat alueet ylläpidetään litruohon juuren kärjessä. Havaitsimme takaisinkytkennän, joka säätelee kasvihormonien ilmentymisalueita. Sytokiniini lisää auksiinin poistamista soluista, kun taas auksiini ehkäisee sytokiniinisignalointia edistämällä AHP6:a. Siten auksiinin ja sytokiniinin molemminpuolinen estäminen säätelee näiden kasvihormonien ilmentymisalueita johtosolukon muodostuessa. Käytimme tietokonesimulaatioita tutkiaksemme geneettisen verkon vakautta, riittävyyttä ja dynamiikkaa. Simulaatiomme vahvistivat, että verkko on riittävä ylläpitämään kasvihormonien alueita johtosolukon muodostuessa. Simulaatiot osoittivat myös, että auksiinin tuonti soluihin vaikuttaa johtosolukon kehitykseen, ja vahvistimme tuonnin merkityksen kokeilla. Lisäksi, vaikka on ehdotettu että sytokiniinin gradientit ohjaavat kehitystä lituruohon varsissa ja juurissa, osoitimme, että sytokiniinin gradientti ei voi muodostua näiden solukoiden mittakaavassa diffuusiolla. Auksiinin liikkuminen tapahtuu polaarisilla kuljetusjärjestelmillä, mutta sytokiniinin kuljetusjärjestelmiä ei vielä ole selvitetty. Tuloksemme osoittavat, että havaittujen sytokiniinikuvioiden muodostuminen vaativat mekanismin, esimerkiksi suunnattu sytokiniinin kuljetus tai erilainen sytokiniinisignalointi eri soluissa, koska havaitut sytokiniin kuviot eivät voi muodustua ainoastaan diffuusiolla. Havaitsimme myös, että auksiini-sytokiniini takaisinkytkentä juuren kärjessä voisi mahdollisesti vaikuttaa versojuurien kehityksen initiaatioon. Koetuloksemme eivät selvästi osoita, onko PIN1-proteiinin (joka poistaa auksiinin soluista) sijainti esijälsisoluissa polaarinen vai ei. Siksi tutkimme molempia mahdollisuuksia simulaatioilla, ja havaitsimme, että kuljetusjärjestelmän polaarinen sijainti aiheuttaa ensin säännöllistä virtausta juuren keskukseen ja sitten pois ksyleemin kautta. Virtaus suosii auksiinin kertymistä lieriökettosoluihin ksyleemin vieressä, jos auksiinipitoisuus näissä soluissa nousee lyhyesti. Tässä väitöskirjassa on kerrottu, että auksiinin ja sytokiniinin molemminpuolinen estäminen on tärkeä tekijä johtosolukon muodostumiselle ja että se vaikuttaa myös muihin kehitysprosesseihin. Havainnollistimme myös, että kokeelliset ja laskennalliset menetelmät yhdessä auttavat mallien arvioinnissa ja oivalluksien tekemisessä

Conformal Field Theories in Fractional Dimensions

We study the conformal bootstrap in fractional space-time dimensions, obtaining rigorous bounds on operator dimensions. Our results show strong evidence that there is a family of unitary CFTs connecting the 2D Ising model, the 3D Ising model, and the free scalar theory in 4D. We give numerical predictions for the leading operator dimensions and central charge in this family at different values of D and compare these to calculations of phi^4 theory in the epsilon-expansion.Comment: 11 pages, 4 figures - references updated - one affiliation modifie

Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents

We use the conformal bootstrap to perform a precision study of the operator spectrum of the critical 3d Ising model. We conjecture that the 3d Ising spectrum minimizes the central charge c in the space of unitary solutions to crossing symmetry. Because extremal solutions to crossing symmetry are uniquely determined, we are able to precisely reconstruct the first several Z2-even operator dimensions and their OPE coefficients. We observe that a sharp transition in the operator spectrum occurs at the 3d Ising dimension Delta_sigma=0.518154(15), and find strong numerical evidence that operators decouple from the spectrum as one approaches the 3d Ising point. We compare this behavior to the analogous situation in 2d, where the disappearance of operators can be understood in terms of degenerate Virasoro representations.Comment: 55 pages, many figures; v2 - refs and comments added, to appear in a special issue of J.Stat.Phys. in memory of Kenneth Wilso

Theoretical approaches to understanding root vascular patterning: a consensus between recent models

The root vascular tissues provide an excellent system for studying organ patterning, as the specification of these tissues signals a transition from radial symmetry to bisymmetric patterns. The patterning process is controlled by the combined action of hormonal signaling/transport pathways, transcription factors, and miRNA that operate through a series of non-linear pathways to drive pattern formation collectively. With the discovery of multiple components and feedback loops controlling patterning, it has become increasingly difficult to understand how these interactions act in unison to determine pattern formation in multicellular tissues. Three independent mathematical models of root vascular patterning have been formulated in the last few years, providing an excellent example of how theoretical approaches can complement experimental studies to provide new insights into complex systems. In many aspects these models support each other; however, each study also provides its own novel findings and unique viewpoints. Here we reconcile these models by identifying the commonalities and exploring the differences between them by testing how transferable findings are between models. New simulations herein support the hypothesis that an asymmetry in auxin input can direct the formation of vascular pattern. We show that the xylem axis can act as a sole source of cytokinin and specify the correct pattern, but also that broader patterns of cytokinin production are also able to pattern the root. By comparing the three modelling approaches, we gain further insight into vascular patterning and identify several key areas for experimental investigatio

Black Hole Bound States in AdS(3) x S**2

We systematically construct the geometries dual to the 1+1 dimensional (0, 4) conformal field theories that arise in the low-energy description of wrapped M5-branes in S1 × CY3 compactifications of M-theory. This includes a large number of multicentered black hole bound states asymptotic to AdS3 × S2. In addition, we find many geometries that develop multiple, mutually decoupled AdS3 × S2 throats. We argue there is a useful one to one correspondence between the connected components of the space of solutions and particular limits of type IIA attractor flow trees. We point out that there is a thermodynamic instability of small supersymmetric BTZ black holes to localization on the S2, a supersymmetric and exactly solvable analog of the well known AdS-Schwarzschild localization instability, and identify this with the "Entropy Enigma" in four dimensions. We discuss the phase transition this suggests, and initiate the CFT interpretation of these results.Physic