This thesis is devoted to a thorough study of chiral rings in two-dimensional (0,2) theories. We first discuss properties of chiral operators in general two-dimensional (0,2) nonlinear sigma models, both in theories twistable to the A/2 or B/2 model, as well as in non-twistable theories. As a special case, we study the quantum sheaf cohomology of Grassmannians as a deformation of the usual quantum cohomology. The deformation corresponds to a (0,2) deformation of the nonabelian gauged linear sigma model whose geometric phase is associated with the Grassmannian. Combined with the classical result, the quantum ring structure is derived from the one-loop effective potential. Supersymmetric localization is also applicable in this case, which proves to be efficient in computing A/2 correlation functions. We then compute chiral operators in general (0,2) nonlinear sigma models, and apply them to the Gadde-Gukov-Putrov triality proposal, which says that certain triples of (0,2) GLSMs should RG flow to nontrivial IR fixed points. As another application, we extend previous works to construct (0,2) Toda-like mirrors to the sigma model engineering Grassmannians. / Ph. D. / This thesis studies a mathematical concept called the chiral ring, which emerges from string theory. String theory is a conjectured theory that potentially unifies the existing fundamental physical laws. It has connections with many branches of mathematics, especially geometry. Spacetime is ten-dimensional in string theory, of which four dimensions are visible, and the other six are hidden at ordinary energy levels. The chiral ring encodes many geometric properties of the hidden part of spacetime. These properties can in turn affect the visible universe even at low energies. Research on chiral rings has primarily focused on a special class of geometries which have large symmetries and so are easier to handle. In order to tackle more general scenarios, we analyze the chiral rings corresponding to theories with only half the symmetry and give several new results and applications.

京都大学 / 新制・課程博士 / 博士(農学) / 甲第25333号 / 農博第2599号 / 新制||農||1106(附属図書館) / 学位論文||R6||N5505 / DFAM / 京都大学大学院農学研究科応用生命科学専攻 / (主査)教授 小川 順, 教授 矢﨑 一史, 教授 栗原 達夫 / 学位規則第4条第1項該当 / Doctor of Agricultural Science / Kyoto University / DFAM

Chiral nematic liquid crystals or cholesteric liquid crystals (CLC) can be obtained by adding a chiral dopant into a nematic liquid crystal. Liquid crystal molecules spontaneously rotate along a long axis to form helical structures in CLC system. Both pitch size and orientation of the helical structure is determined by the boundary conditions and can be further tuned by external stimuli. Particularly, the uniform lying helical structure of CLC has attracted intensive attention due to its beam steering and diffraction abilities. Up to now, studies have worked on controlling the in-plane orientation of lying helix through surface rubbing and external stimuli. However, it remains challenging to achieve steady and uniform lying helical structure due to its higher energy, comparing with other helical configurations. Here, by varying the surface anchoring, uniform lying helical structure with long-range order is achieved as thermodynamically stable state without external support. Poly (6-(4-methoxy-azobenzene-4'-oxy) hexyl methacrylate) (PMMAZO), a liquid crystalline polymer, is deposited onto the silicon substrate to fine-tune the surface anchoring. By changing the grafting density of PMMAZO, both pitch size and orientation of lying helical structure are precisely controlled. As the grafting density increases, the enhanced titled deformation of helical structure suppresses the pitch size of CLC at the same cell thickness; as the cell thickness increases, the morphology transition from long-range order stripe to small fingerprint domain is facilitated.

Les ligands de carbènes N-hétérocycliques (NHC) qui possèdent une symétrie C1 attirent beaucoup l’attention dans la littérature. Le présent projet de recherche propose de synthétiser une nouvelle série de ligands NHC C1-symétriques avec deux groupements N-alkyles qui exploitent un relais chiral. Un protocole modulaire et efficace pour la synthèse des sels d’imidazolium chiraux qui servent comme préligands pour les NHC a été développé. Quelques-uns de ces nouveaux ligands ont été installés sur le cuivre et de l’or, créant de nouveaux complexes chiraux. Les nouveaux complexes à base de cuivre ont été évalués comme catalyseurs pour le couplage oxydatif de 2-naphthols. Les ligands C1-symmétriques ont fourni des meilleurs rendements que les ligands C2-symmétriques. Au cours de l’optimisation, des additifs ont été évalués; les additifs à base de pyridine ont fourni des énantiosélectivités modérées tandis que les additifs à base de malonate ont donné des meilleurs rendements de la réaction de couplage oxydatif. Ultérieurement, les additifs à base de malonate ont été appliqués envers l’hétérocouplage de 2-naphthols. Le partenaire de couplage qui est riche en électrons est normalement en grand excès à cause de sa tendance à dégrader. Avec le bénéfice de l’additif, les deux partenaires de couplage peuvent être utilisés dans des quantités équivalentes. La découverte de l’effet des additifs a permis le développement d’un protocole général pour l’hétérocouplage de 2-naphthols. / A new class of C1-symmetric N-heterocyclic carbene (NHC) ligands has been developed. The new ligands exploit a biaryl methyne as a chiral relay, and an N-methyl group as a reactivity controlling element. The precursors for the new ligands were synthesized via a modular scheme that allows for facile diversification. Several of the new ligands were installed onto both copper and gold, generating mono N-heterocyclic carbene transition metal complexes. The new C1-symmetric copper complexes were tested as catalysts for the synthesis of binaphthols via the oxidative coupling of electron poor 2-naphthols. The new C1-symmetric ligands afforded higher yields than their C2-symmetric counterparts. During the course of the optimization, small molecule additives were found to modulate the reactivity of the copper catalyst. Pyridine additives, such as 2-picoline, were found to induce low to moderate enantioselectivity in the oxidative coupling reaction, while diethylmalonate was found to improve the reaction yield without affecting the selectivity. The malonate additive was employed in the catalytic oxidative heterocoupling of electronically dissimilar 2-naphthols. The electron-rich coupling partner is normally added in a large excess due to its tendency to degrade. When the malonate additive is used, the coupling partners can be used in equimolar quantities. The discovery resulted in the development of a general protocol for the additive assisted aerobic oxidative heterocoupling of electronically dissimilar 2-naphthols.

<p>This thesis concerns the development and validation of methods for characterization of multi-component preparative LC systems. Measurements of competitive adsorption isotherms are performed to gain detailed information about the interactions inside the chromatography column. This information increases our understanding of the separation process and makes it possible to perform computer simulations and numerical optimizations to find optimal operating conditions.</p><p>The methods under focus are called “the tracer-pulse method”, “the inverse method”, and “the inverse method on plateaus”. They are extensions of existing methods, with new experimental and numerical procedures to enable rapid and accurate multi-component adsorption isotherm determination. In the validation it was shown that they can produce results agreeing with traditional methods and that the acquired adsorption isotherm parameters can be used in simulations to accurately predict the outcome of preparative LC separations.</p><p>The methods were used to characterize several complex LC systems and two phenomena were discovered and theoretically treated: 1) The presence of invisible deformed peaks in single-component systems. 2) Peak deformations encountered with modern chiral stationary phases, caused by strongly adsorbed eluent additives. The latter type of deformation was highly tuneable and it was possible to adjust the enantiomer peak shapes so that the peaks tailed in opposite directions with the sharp sides in between, yielding baseline resolution at remarkably high sample loads.</p><p>In a final applied study both the LC-based perturbation peak method and a biosensor method based on surface plasmon resonance (SPR) were used for the first time for detailed characterization of chiral drug-protein interactions. The fundamental properties of the two very different methods were compared and it was found that the LC method is more suitable for multi-component analysis and that the SPR method is more suitable for stronger interactions.</p>

This thesis concerns the development and validation of methods for characterization of multi-component preparative LC systems. Measurements of competitive adsorption isotherms are performed to gain detailed information about the interactions inside the chromatography column. This information increases our understanding of the separation process and makes it possible to perform computer simulations and numerical optimizations to find optimal operating conditions. The methods under focus are called “the tracer-pulse method”, “the inverse method”, and “the inverse method on plateaus”. They are extensions of existing methods, with new experimental and numerical procedures to enable rapid and accurate multi-component adsorption isotherm determination. In the validation it was shown that they can produce results agreeing with traditional methods and that the acquired adsorption isotherm parameters can be used in simulations to accurately predict the outcome of preparative LC separations. The methods were used to characterize several complex LC systems and two phenomena were discovered and theoretically treated: 1) The presence of invisible deformed peaks in single-component systems. 2) Peak deformations encountered with modern chiral stationary phases, caused by strongly adsorbed eluent additives. The latter type of deformation was highly tuneable and it was possible to adjust the enantiomer peak shapes so that the peaks tailed in opposite directions with the sharp sides in between, yielding baseline resolution at remarkably high sample loads. In a final applied study both the LC-based perturbation peak method and a biosensor method based on surface plasmon resonance (SPR) were used for the first time for detailed characterization of chiral drug-protein interactions. The fundamental properties of the two very different methods were compared and it was found that the LC method is more suitable for multi-component analysis and that the SPR method is more suitable for stronger interactions.

En les últimes dècades, el fenomen de l’enantioselectivitat ha adquirit una importància creixent per a la indústria farmacèutica a l’hora del desenvolupament de nous fàrmacs. Això és degut a la observació d’una diferent resposta per part de l’organisme en funció de l’estereoquímica de la molècula exògena administrada, ocasionada per l’elevada estereoselectivitat dels processos fisiològics. Diferents exemples es poden trobar a la literatura a partir del desastre produït pel fàrmac anomenat talidomida, en què es va responsabilitzar la forma S de l’efecte teratogen mentre s’assignà l’acció sedant a la R. Molts altres fàrmacs quirals presenten una dicotomia d’efecte pels enantiòmers. A mode d’exemple l’anestèsic prolocaïna presenta diferències d’activitat entre enantiòmers. En aquest cas la forma de configuració S posseix majoritàriament l’acció anestèsica, mentre que la R és responsable dels efectes tòxics del fàrmac, que pot produir metahemoglobinèmia. Així, doncs, l’adiministració, i per tant la comercialització de fàrmacs enantiomèricmanet purs, simplifica aspectes farmacològics, farmacocinètics, terapèutics i toxicològics de l’acció dels fàrmacs. Altres avantatges que s’aconsegueixen amb aquest procedir són la disminució de la dosi de fàrmac requerida per a produir l’efecte desitjat i la menor variabilitat interpersonal de l’efecte produït per una determinada dosi. Degut a la importància de l’administració de fàrmacs enantiomèricament purs, en el present treball s’estudia l’aplicació de la cromatografia en contracorrent (CPC/CCC) en la separació de mescles racèmiques. La CCC/CPC és una variant de la cromatografia líquida, en la què la fase mòbil i la fase estacionària estan formades per dos líquids immiscibles entre sí. Així, s’han dissenyat i sintetitzat noves entitats quirals derivades de l’aminoàcid L-prolina. Una vegada caracteritzades, s’ha estudiat la seva aplicació en la separació de racèmics, a la vegada que s’ha estudiat el seu mecanisme d’enantioreconeixment per poder establir unes pautes a l’hora de dissenyar nous selectors quirals (SQ). D’altra banda, la CCC/CPC al tractar-se d’una tècnica que es dona entre dos líquids immiscibles. S’ha estudiat l’aplicació de nous sistemes de dissolvents menys contaminats, com es el cas de l’etoxinonafluorobutà. Així, s’han construït diferents sistemes de dissolvents que contenen el dissolvent fluorat, a l’hora que s’han utilitzat SQs fluorats. / Nowdays, the significance of the enantiomèric purity in the chiral active ingredients used in drug manufacture is well recognized. In addition, the strict regulations established by health authorities on the commercialisation of chiral drugs, has led to the requirement for analytical and preparative methods for enantioseparation. Although diverse procedures exist, chromatographic techniques are amongst the most used to resolve mixtures of enantiomers at a preparative level. In the present doctoral thesis we intend to study the enantioselectivity phenomena of L-proline derivatives as chiral selectors in countercurrent chromatography (CCC) using diferent solvent systems. CCC is an effective separation technique base don the differences in partitioning of solutes in a sample between two non-miscible solvents or solutions that constitute the solvent system. Therefore, the mobile and the stationary phases in the chromatographic process are liquids. The absence of a solid support opens a whole range of possibilities to apply alternative elution modes alternatives to the classic one. The exchange between mobile phase and stationary phase during the separation, that CCC only involves the change of a valve position, allows the dual and mutidual mode. Also, the application of ph-zone refining, a kind of displacement chromatography that involve the addition of a displacement agent in the mobile phase, has been evaluated in order to improve the separation of ionizable racemates. Finally, the evaluation of the enantioselectivite capacity of fluorinated solvents and chiral selectors has been tested in CCC and in liquid membranes.

La thèse est consacrée à la développement de méthodes efficaces pour la synthèse d'une nouvelle classe d'intrinsèquement chiral calix[4]arènes contenant du phosphore, phosphines et acides phosphoriques avec une certaine disposition mutuelle des groupes fonctionnels sur le bord inférieur du macrocycle, avec un potentiel activité catalytique. La façon optimale fot la synthèse de calix[4]arènes contenant du phosphore par la substitution progressive des hydroxyles phénoliques a été développé afin de concevoir des intrinsèquement chiral calix[4]arènes avec des types de remplacement ABHH et ABCH au bord inférieur du macrocycle. En utilisant ces techniques, la synthèse de la six catalyseurs et efficaces avec chiralité planaire a été réalisée. En utilisant des études de diffraction des rayons X a permis d'étudier la localisation spatiale des groupes fonctionnels. L'utilisation de la réaction de Mitsunobu autorisé à fournir une synthèse de la nouvelle "poche" -comme ligands - calix[4]arènes portant des fragments ferrocényle-phosphines chirales. L'efficacité des nouveaux ligands phosphine synthétisés a été confirmé par l'exemple du modèle de réaction Tsuji-Trost. intéressante dépendance du niveau de sélectivité de la taille du cation de métal de base ajoutée, en raison de l'effet de ligand de chélation du supramoléculaire a été observée. Calix[4]arènes acides phosphoriques a d'abord été appliqués comme organocatalyseurs la série de réactions modèles: aza-Diels-Alder, aza-Mukayiama réaction asymétrique et réaction d'ouverture d'époxydes anneau. Il a été constaté que la plupart des composés synthétisés présentent un degré notable de activitydue catalytique à des caractéristiques de chiralité interne. / The thesis is devoted to the developing of effective methods for the synthesis of new class of inherently chiral phosphorus-containing calix[4]arenes, phosphines and phosphoric acids with a certain mutual arrangement of functional groups on the lower rim of the macrocycle, with potential catalytic activity. The optimal way fot the synthesis of phosphorus-containing calix[4]arenes by the stepwise substitution of the phenolic hydroxyls was developed in order to design inherently chiral calix[4]arenes with ABHH and ABCH replacement types at the lower rim of the macrocycle. By using these techniques, synthesis of six analogues of known and effective catalysts with planar chirality was performed. Using X-ray diffraction studies allowed to investigate spatial location of functional groups. Using of Mitsunobu reaction allowed to provide synthesis of the new "pocket"-like ligands - calix[4]arenes bearing chiral ferrocenyl-phosphines moieties. The effectiveness of the synthesized new phosphine ligands was confirmed by the example of the model Tsuji-Trost reaction. Interesting dependence of the selectivity level on the metal cation size of added base, due to chelation effect of supramolecular ligand was observed. Calix[4]arenes phosphoric acids was first applied as organocatalysts the series of model reactions: aza-Diels-Alder reaction, aza-Mukaiyama asymmetric reaction and epoxides ring opening reaction. It was found that most of the synthesized compounds exhibit a noticeable level of catalytic activitydue to features of internal chirality.

Cette thèse comporte deux parties indépendantes. La première étude présente les premiers exemples de métallation de la structure azobenzène par les réactifs organométalliques polaires. Largement utilisés en tant que colorants, les azobenzènes trouvent actuellement de nombreuses applications dans le domaine des matériaux en raison de leur facile photoisomerisation E/Z. Il est montré que les bases organométalliques polaires classiques (n-BuLi, n-BuLi/TMEDA, n-BuLi/t-BuOK, TMPMgCl.LiCl, LDA) ne métallent pas l’azobenzène parent mais réduisent plutôt la liaison N=N. Cependant la métallation est possible avec le tétraméthylpipéridure de lithium si un groupement directeur de métallation tel que le méthoxy (OMe), diéthylamide (CONEt2) ou fluoro (F) est présent sur l’azobenzène. La réaction permet un accès original et direct à de nouveaux azobenzènes substitués. L’objectif de la deuxième partie est la synthèse de dérivés biaryliques chiraux en l’absence de métaux de transition (Pd, Ni…). Les biaryles chiraux sont présents dans de nombreuses molécules biologiquement actives et peuvent être utilisés comme ligands pour la catalyse asymétrique. La substitution nucléophile aromatique des acides naphtoïques en présence de ligands chiraux a été étudiée. Une optimisation fine des conditions réactionnelles (choix du solvant, température, structure du ligand…) a permis de préparer des 1,1’-binaphtalènes, 1,2’-binaphtalènes et phénylnaphtalènes avec de bons rendements et excès énantiomériques (jusqu’à 89% ee). La substitution nucléophile aromatique atroposélective de dérivés d’acides naphtoïques de type naphtyloxazolines et naphtoates est également décrite. / This thesis is divided into two independant parts. The first part describes for the first time the chemoselective lithiation of azobenzenes. Azobenzenes derivatives are widely used as dyes and more recently have been applied to the preparation of photoresponsive molecular switches and materials by taking advantage of the N=N bond E/Z photoisomerization. Whereas standard polar organometallics (n-BuLi, n-BuLi/TMEDA, n-BuLi/t-BuOK, TMPMgCl.LiCl, LDA) reduce the N=N bond of the parent compound, aromatic HLi permutation occurs with LTMP when a suitable director of lithiation (OMe, CONEt2, F) is present in the benzene residue of the azo compound. The method allows a direct access to new substituted azobenzenes.Axially chiral biaryls, which are found in many biologically active natural products, are conventionally used as ligands for asymmetric catalysis. The purpose of the second part is to develop a new method for the preparation of axially chiral biaryls in the absence of transition metals (Pd, Ni…). To tackle that goal, nucleophilic aromatic substitution reactions on unprotected naphthoic acids were performed in the presence of chiral ligands. A careful optimization of the reaction parameters (choice of the solvent, temperature, structure of the ligand…) allowed to prepare chiral 1,1’- binaphthalenes 1,2’- binaphthalenes and phenylnaphthalenes in good yields and enantiomeric excesses (up to 89% ee). The atroposelective SNAr reaction of naphthyloxazoline and naphthoate derivatives was also reported.

The interplay of thermodynamic properties of strongly interacting matter and its emission of photons is investigated. For this purpose the Lagrangian of the quark meson model (in the literature also dubbed "linear sigma model" or "linear sigma model with quarks") is extended by an electromagnetic sector. Based on this extended Lagrangian both the grand-canonical potential and the generating functional of correlation functions are calculated in a consistent manner. From the former, the phase structure and various thermodynamical properties are determined. Especially, the dependence of certain landmarks (critical point, intersections of the phase boundary with the coordinate axes, etc.) of the phase diagram with respect to the model parameters is investigated in detail. With the help of the generating functional in turn, the photon propagator can be computed whose imaginary part is connected to the emission rate of photons. The leading order of the result with respect to the number of participating particles and the power of the quark-meson coupling is expressed in terms of tree level diagrams, which are calculated likewise. On this basis, the photon emissivity with respect to temperature, chemical potential and photon frequency is calculated and analyzed addressing various questions. The dependence of the particle masses with respect to temperature and chemical potential leaves notable imprints on the emissivities of the individual production processes. Especially a first-order phase transition can easily be identified, since, there, the emissivity may jump - depending on the temperature - by a factor of about ten. Contrarily, within our analysis, we do not find signatures in the photon emissivities that specifically mark a critical end point. Moreover, it is investigated on which parameters the photon emission rate depends in the low- and high-frequency regions. With these results the behavior of the emissivity with respect to temperature and chemical potential can be understood and many peculiarities of the emissivities can be explained. / Das Zusammenspiel der thermodynamischen Eigenschaften von stark wechselwirkender Materie und deren Emission von Photonen wird untersucht. Dazu wird die Lagrangedichte des Quark-Meson-Modells (auch: Linear-Sigma-Modell oder Linear-Sigma-Modell mit Quarks) um einen elektromagnetischen Sektor erweitert. Aus der so erweiterten Lagrangedichte werden auf konsistente Weise sowohl das großkanonische Potential als auch das erzeugende Funktional der Korrelationsfunktionen ermittelt. Aus ersterem werden die Phasenstruktur des Modells sowie zahlreiche thermodynamische Eigenschaften berechnet. Insbesondere wird die Abhänigkeit einiger Orientierungspunkte (kritischer Punkt, Schnittpunkte der Phasengrenze mit den Koordinatenachsen usw.) des Phasendiagramms von den Modellparametern detailiert untersucht. Mit Hilfe des erzeugenden Funktionals wiederum kann der Photonenpropagator bestimmt werden, dessen Imaginärteil mit der Emissionsrate von Photonen zusammenhängt. Die führende Ordnung in einer Entwicklung nach der Anzahl der beteiligten Teilchen und der Potenz der Quark-Meson-Kopplung lässt sich durch Baumgraphen-Diagramme darstellen, die ebenfalls berechnet werden. Auf dieser Basis wird die Photon-Emissivität in Abhängigkeit von Temperatur, chemischem Potential und Photon-Frequenz berechnet und unter verschiedenen Gesichtspunkten analysiert. Die Abhängigkeit der Teilchenmassen von Temperatur und chemischem Potential hinterlässt teilweise ausgeprägte Signaturen in den Emissivitäten der einzelnen sub-Prozesse. Insbesondere ein Phasenübergang erster Ordnung zeigt sich deutlich, da an diesem die Emissivität - abhänging von der Temperatur - um einen Faktor der Größenordnung zehn springen kann. Jedoch finden wir im Rahmen dieser Analyse keine spezifischen Signaturen in den Photonen-Emissivitäten, die einen kritischen Punkt auszeichnen. Des weiteren wird untersucht von welchen Parametern die Photonen-Emissionsrate in den Bereichen niedriger oder hoher Photonen-Frequenzen abhängt. Mit diesen Ergebnissen kann das Verhalten der Emissivität in Abhängigkeit von Temperatur und chemischem Potential gut verstanden und zahlreiche Auffälligkeiten in den Emissivitäten erklärt werden.