The continuum limit of aN−1(2)a_{N-1}^{(2)} spin chains

Building on our previous work for $a_2^{(2)}$ and $a_3^{(2)}$ we explore systematically the continuum limit of gapless $a_{N-1}^{(2)}$ vertex models and spin chains. We find the existence of three possible regimes. Regimes I and II for $a_{2n-1}^{(2)}$ are related with $a_{2n-1}^{(2)}$ Toda, and described by $n$ compact bosons. Regime I for $a_{2n}^{(2)}$ is related with $a_{2n}^{(2)}$ Toda and involves $n$ compact bosons, while regime II is related instead with $B^{(1)}(0,n)$ super Toda, and involves in addition a single Majorana fermion. The most interesting is regime III, where {\sl non-compact} degrees of freedom appear, generalising the emergence of the Euclidean black hole CFT in the $a_{2}^{(2)}$ case. For $a_{2n}^{(2)}$ we find a continuum limit made of $n$ compact and $n$ non-compact bosons, while for $a_{2n-1}^{(2)}$ we find $n$ compact and $n-1$ non-compact bosons. We also find deep relations between $a_{N-1}^{(2)}$ in regime III and the gauged WZW models $SO(N)/SO(N-1)$.Comment: 43 pages, 4 figure

A new look at the collapse of two-dimensional polymers

We study the collapse of two-dimensional polymers, via an O($n$) model on the square lattice that allows for dilution, bending rigidity and short-range monomer attractions. This model contains two candidates for the theta point, $\Theta_{\rm BN}$ and $\Theta_{\rm DS}$, both exactly solvable. The relative stability of these points, and the question of which one describes the `generic' theta point, have been the source of a long-standing debate. Moreover, the analytically predicted exponents of $\Theta_{\rm BN}$ have never been convincingly observed in numerical simulations. In the present paper, we shed a new light on this confusing situation. We show in particular that the continuum limit of $\Theta_{\rm BN}$ is an unusual conformal field theory, made in fact of a simple dense polymer decorated with {\sl non-compact degrees of freedom}. This implies in particular that the critical exponents take continuous rather than discrete values, and that corrections to scaling lead to an unusual integral form. Furthermore, discrete states may emerge from the continuum, but the latter are only normalizable---and hence observable---for appropriate values of the model's parameters. We check these findings numerically. We also probe the non-compact degrees of freedom in various ways, and establish that they are related to fluctuations of the density of monomers. Finally, we construct a field theoretic model of the vicinity of $\Theta_{\rm BN}$ and examine the flow along the multicritical line between $\Theta_{\rm BN}$ and $\Theta_{\rm DS}$.Comment: v2 : references adde

Non compact continuum limit of two coupled Potts models

We study two $Q$-state Potts models coupled by the product of their energy operators, in the regime $2 < Q \le 4$ where the coupling is relevant. A particular choice of weights on the square lattice is shown to be equivalent to the integrable $a_3^{(2)}$ vertex model. It corresponds to a selfdual system of two antiferromagnetic Potts models, coupled ferromagnetically. We derive the Bethe Ansatz equations and study them numerically for two arbitrary twist angles. The continuum limit is shown to involve two compact bosons and one non compact boson, with discrete states emerging from the continuum at appropriate twists. The non compact boson entails strong logarithmic corrections to the finite-size behaviour of the scaling levels, the understanding of which allows us to correct an earlier proposal for some of the critical exponents. In particular, we infer the full set of magnetic scaling dimensions (watermelon operators) of the Potts model.Comment: 33 pages, 10 figures v2: reference added, minor typo corrected v3: revised version for publication in JSTAT: section 3.1 added, some technical content moved to appendi

Non compact conformal field theory and the a_2^{(2)} (Izergin-Korepin) model in regime III

The so-called regime III of the a_2^{(2)} Izergin-Korepin 19-vertex model has defied understanding for many years. We show in this paper that its continuum limit involves in fact a non compact conformal field theory (the so-called Witten Euclidian black hole CFT), which leads to a continuous spectrum of critical exponents, as well as very strong corrections to scaling. Detailed numerical evidence based on the Bethe ansatz analysis is presented, involving in particular the observation of discrete states in the spectrum, in full agreement with the string theory prediction for the black hole CFT. Our results have important consequences for the physics of the O(n) model, which will be discussed elsewhere.Comment: 57 pages, 19 figures; v2: reference adde

Thiourea-catalysed ring opening of episulfonium ions with indole derivatives by means of stabilizing non-covalent interactions

Small organic and metal-containing molecules (molecular mass <1,000) can catalyse synthetically useful reactions with the high levels of stereoselectivity typically associated with macromolecular enzymatic catalysts. Whereas enzymes are generally understood to accelerate reactions and impart selectivity as they stabilize specific transition structures through networks of cooperative interactions, enantioselectivity with chiral, small-molecule catalysts is rationalized typically by the steric destabilization of all but one dominant pathway. However, it is increasingly apparent that stabilizing effects also play an important role in small-molecule catalysis, although the mechanistic characterization of such systems is rare. Here, we show that arylpyrrolidino amido thiourea catalysts catalyse the enantioselective nucleophilic ring opening of episulfonium ions by indoles. Evidence is provided for the selective transition-state stabilization of the major pathway by the thiourea catalyst in the rate- and selectivity-determining step. Enantioselectivity is achieved through a network of attractive anion binding, cation-π and hydrogen-bond interactions between the catalyst and the reacting components in the transition-structure assembly.Chemistry and Chemical Biolog

Asymmetric Ion-Pairing Catalysis

Chemistry and Chemical Biolog

Transition-State Charge Stabilization through Multiple Non-covalent Interactions in the Guanidinium-Catalyzed Enantioselective Claisen Rearrangement

The mechanism by which chiral arylpyrrole-substituted guanidinium ions promote the Claisen rearrangement of O-allyl α-ketoesters and induce enantioselectivity was investigated by experimental and computational methods. In addition to stabilization of the developing negative charge on the oxallyl fragment of the rearrangement transition state by hydrogen-bond donation, evidence was obtained for a secondary attractive interaction between the π-system of a catalyst aromatic substituent and the cationic allyl fragment. Across a series of substituted arylpyrrole derivatives, enantioselectivity was observed to vary predictably according to this proposal. This mechanistic analysis led to the development of a new p-dimethylaminophenyl-substituted catalyst, which afforded improvements in enantioselectivity relative to the parent phenyl catalyst for a representative set of substrates.Chemistry and Chemical Biolog

Chiral Sulfinamidourea and Strong Brønsted Acid–Cocatalyzed Enantioselective Povarov Reaction to Access Tetrahydroquinolines

This protocol describes a method for the laboratory synthesis of enantiomerically enriched, chiral tetrahydroisoquinolines through the application of a chiral sulfinamido urea catalyst for the Povarov reaction. Tetrahydroisoquinolines are bicyclic organic frameworks present in a wide assortment of natural and synthetic biologically important compounds including ​martinelline, ​scoulerine and ​tubocurarine. The methodology involves the [4+2] cycloaddition of a N-arylimines with electron-rich olefins such as vinyl lactams and dihydropyrroles in the presence of a two-catalyst system consisting of an achiral strong Brønsted acid (​o-nitrobenzenesulfonic acid), together with the chiral sulfinamido urea derivative 1. The anion-binding properties of the ​urea lead to the association of the ion pair that results from protonation of the imine substrate. Cycloaddition is followed by spontaneous proton loss with re-aromatization to provide the tetrahydroisoquinoline products in highly enantio-enriched form.Chemistry and Chemical Biolog

Structural Analysis of Spiro β-Lactone Proteasome Inhibitors

Spiro β-lactone-based proteasome inhibitors were discovered in the context of an asymmetric catalytic total synthesis of the natural product (+)-lactacystin (1). Lactone 4 was found to be a potent inhibitor of the 26S proteasome, while its C-6 epimer (5) displayed weak activity. Crystallographic studies of the two analogues covalently bound to the 20S proteasome permitted characterization of the important stabilizing interactions between each inhibitor and the proteasome’s key catalytic N-terminal threonine residue. This structural data support the hypothesis that the discrepancy in potency between 4 and 5 may be due to differences in the hydrolytic stabilities of the resulting acyl enzyme complexes.Chemistry and Chemical Biolog

Thiourea-Catalyzed Enantioselective Iso-Pictet-Spengler Reactions

A one-pot condensation of isotryptamines and aldehydes that affords enantiomerically enriched 4-substituted tetrahydro-$\gamma$-carbolines is reported. The reaction is induced by a chiral thiourea/benzoic acid dual catalyst system. Purification of the N-Boc-protected products by trituration or crystallization provides the optically pure tetrahydro-$\gamma$-carboline derivatives in a scalable and highly practical procedure.Chemistry and Chemical Biolog