Conformal Point Research Articles

Dynamics at and near conformal quantum critical points

We explore the dynamical behavior at and near a special class of two-dimensional quantum critical points. Each is a conformal quantum critical point (CQCP), where in the scaling limit the equal-time correlators are those of a two-dimensional conformal field theory. The critical theories include the square-lattice quantum dimer model, the quantum Lifshitz theory, and a deformed toric code model. We show that under generic perturbation the latter flows toward the ordinary Lorentz-invariant (2+1) dimensional Ising critical point, illustrating that CQCPs are generically unstable. We exploit a correspondence between the classical and quantum dynamical behavior in such systems to perform an extensive numerical study of two lines of CQCPs in a quantum eight-vertex model, or equivalently, two coupled deformed toric codes. We find that the dynamical critical exponent z remains 2 along the U(1)-symmetric quantum Lifshitz line, while it continuously varies along the line with only Z_2 symmetry. This illustrates how two CQCPs can have very different dynamical properties, despite identical equal-time ground-state correlators. Our results equally apply to the dynamics of the corresponding purely classical models.

Global monopole asymptotic solutions in Hořava gravity

In Hořava's theory of gravity coupled to a global monopole source, we seek for static, spherically symmetric spacetime, solutions for general values of λ. We obtain the explicit solutions with deficit solid angles, in the IR modified Hořava gravity model, at the IR fixed point λ = 1 and at the conformal point λ = 1/3. For the other values of 1 > λ > 0 we also find special solutions to the inhomogenous equation of the gravity model with detailed balance, and we discuss a possibility of astrophysical applications of the λ = 1/2 solution that has a deficit angle for a finite range.

Corrections to scaling for block entanglement in massive spin chains

We consider the Rényi entropiesSn in one-dimensional massive integrable models diagonalizable by means of corner transfermatrices (such as Heisenberg and Ising spin chains). By means of explicit examples andusing the relation of the corner transfer matrix with the Virasoro algebra, we showthat close to a conformally invariant critical point, when the correlation lengthξ is finite but large, the corrections to the scaling are of the unusual formξ − x/n, withx the dimension of a relevant operator in the conformal theory. This is reminiscent of theresults for gapless chains and should be valid for any massive one-dimensional model closeto a conformal critical point.

Holomorphicity and modularity in Seiberg-Witten theories with matter

We calculate the gravitational corrections to the effective action of N=2 SU(2) Seiberg-Witten theory with matter using modularity, the holomorphic anomaly equation and expected behavior at the boundaries of the moduli space. As in pure gauge theory we show that the gap condition at the dyon singularities completely fixes the gravitational corrections. We discuss the behavior of the gravitational corrections at the conformal points. We compare our results with the recursive solution of the loop equation in the matrix model approach, which provides in addition open amplitudes.

General static spherically symmetric solutions in Hořava gravity

We derive the equations describing a general static spherically symmetric configuration for the softly broken Ho\ifmmode \check{r}\else \v{r}\fi{}ava gravity introduced by A. Kehagias and K. Sfetsos with nonzero shift field and no-projectability condition. These represent ``hedgehog'' versions of black holes with radial ``hair'' arising from the shift field. For the case of the standard de Witt kinetic term ($\ensuremath{\lambda}=1$) there is an infinity of solutions that exhibit a deformed version of reparametrization invariance away from the general relativistic limit. Special solutions also arise in the anisotropic conformal point $\ensuremath{\lambda}=\frac{1}{3}$. Moreover we obtain an implicit general expression for the solutions with ${N}_{r}=0$ and generic $\ensuremath{\lambda}$. In this context we study the presence of horizons for standard matter and the related Hawking temperature, generalizing the corresponding relations in the usual static spherically symmetric case.

Melamine-Bridged Bis(porphyrin-ZnII) Receptors: Molecular Recognition Properties

Dimeric metalloporphyrin hosts with tweezer-like structures have been synthesized by reacting the cyanuric chloride scaffold, CC, with 5-(4-aminophenyl)-10,15,20-triphenylporphyrin, P, and 5-(4-aminophenyl)-10,15,20-trimesitylporphyrin, M, to yield the homoconjugates free bases PP and MM and the heterodyad PM. Metalation with Zn(II), gives three structurally related ditopic receptors P(Zn)P(Zn), P(Zn)M(Zn), and M(Zn)M(Zn) with differential steric hindrance and conformational rigidity. The solution structure and supramolecular properties of these porphyrin dimers have been investigated as isolated molecules and in the presence of aliphatic alpha,omega-diamines of general formula H(2)N-(CH(2))(n)-NH(2) (n = 4-8) by spectroscopic and theoretical studies including multidimensional NMR, UV-vis, molecular modeling, and computational NMR methods. Binding constants in the range 4.2 x 10(6) to 3.4 x 10(7) M(-1) are observed in dichloromethane at 298 K, with a 3 orders of magnitude increase as compared to monodentate nBuNH(2), thus indicating the occurrence of a host-guest ditopic interaction. Linear correlation graphs are obtained by plotting the Soret band shift (Delta nu, cm(-1)) of the complex as a function of the diamine chain length. Combined NMR evidence and OPLS 2005 Force Field conformational analysis point to a mutual adaptation of both the binding partners in the host-guest complex, whose geometry is mainly dictated by the steric impact of the bulky substituents at the porphyrin periphery.

Role of Tryptophan 95 in substrate specificity and structural stability of Sulfolobus solfataricus alcohol dehydrogenase

A mutant of the thermostable NAD(+)-dependent (S)-stereospecific alcohol dehydrogenase from Sulfolobus solfataricus (SsADH) which has a single substitution, Trp95Leu, located at the substrate binding pocket, was fully characterized to ascertain the role of Trp95 in discriminating between chiral secondary alcohols suggested by the wild-type SsADH crystallographic structure. The Trp95Leu mutant displays no apparent activity with short-chain primary and secondary alcohols and poor activity with aromatic substrates and coenzyme. Moreover, the Trp --> Leu substitution affects the structural stability of the archaeal ADH, decreasing its thermal stability without relevant changes in secondary structure. The double mutant Trp95Leu/Asn249Tyr was also purified to assist in crystallographic analysis. This mutant exhibits higher activity but decreased affinity toward aliphatic alcohols, aldehydes as well as NAD(+) and NADH compared to the wild-type enzyme. The crystal structure of the Trp95Leu/Asn249Tyr mutant apo form, determined at 2.0 A resolution, reveals a large local rearrangement of the substrate site with dramatic consequences. The Leu95 side-chain conformation points away from the catalytic metal center and the widening of the substrate site is partially counteracted by a concomitant change of Trp117 side chain conformation. Structural changes at the active site are consistent with the reduced activity on substrates and decreased coenzyme binding.

Structure of the RNA Polymerase Core-Binding Domain of σ 54 Reveals a Likely Conformational Fracture Point

Transcription initiation by bacterial σ 54-RNA polymerase requires a conformational change of the holopolymerase–DNA complex, driven by an enhancer-binding protein. Although structures of the core polymerase and the more common σ 70 factor have been determined, little is known about the structure of the σ 54 variant. We report here the structure of an Aquifex aeolicus σ 54 domain (residues 69–198), which binds core RNA polymerase. The structure is composed of two distinct subdomains held together by a small, conserved hydrophobic interface that appears to act as a fracture point in the structure. The N-terminal, four-helical subdomain has a negative surface and conserved residues that likely contact the core polymerase, while the C-terminal, three-helical bundle has a strongly positive patch that could contact DNA. Sequence conservation indicates that these structural features are conserved and are important for the role of σ 54 in the polymerase complex.

Carrier Method for the General Evaluation and Control of Pose, Molecular Conformation, Tracking, and the Like

The four basic geometric objects of points, point pairs, circles and spheres correspond to outer product null-spaces constructed by conformal points in conformal geometric algebra. Wedging with the infinity point we get four flat objects: finite-infinity point pairs, lines, planes and the whole 5D space. We show that all these basic geometric objects have the same algebraic structure. We then develop a single general algebraic method to quantify and interpolate the relative pose of the eight different classes of objects. As an explicit example we finally apply our framework to the conformation of organic macromolecules.

GTPase activation of elongation factor EF-Tu by the ribosome during decoding

We have used single-particle reconstruction in cryo-electron microscopy to determine a structure of the Thermus thermophilus ribosome in which the ternary complex of elongation factor Tu (EF-Tu), tRNA and guanine nucleotide has been trapped on the ribosome using the antibiotic kirromycin. This represents the state in the decoding process just after codon recognition by tRNA and the resulting GTP hydrolysis by EF-Tu, but before the release of EF-Tu from the ribosome. Progress in sample purification and image processing made it possible to reach a resolution of 6.4 A. Secondary structure elements in tRNA, EF-Tu and the ribosome, and even GDP and kirromycin, could all be visualized directly. The structure reveals a complex conformational rearrangement of the tRNA in the A/T state and the interactions with the functionally important switch regions of EF-Tu crucial to GTP hydrolysis. Thus, the structure provides insights into the molecular mechanism of signalling codon recognition from the decoding centre of the 30S subunit to the GTPase centre of EF-Tu.

Stability issues with baryons in AdS/CFT

We consider baryon vertices within the gauge/gravity correspondence for a class of curved backgrounds. The holographic description based on the = 4 SYM theory for SU(N) allows classical solutions representing bound states of k-quarks with k less than or equal to N. We construct the corresponding classical configurations and perform a stability analysis. We present the details for the theory at the conformal point and at finite temperature and show that there is a critical value of k, below which there is instability. This may also arise when the baryon reaches a critical size. We also extend our treatment to magnetically charged baryon vertices.

Polyproline derivatives as chiral selectors in high performance liquid chromatography: Chromatographic and conformational studies

A proline oligopeptide-derived chiral selector (CS), containing 3,5-dimethylphenylcarbamate residues on the 4 position of the pyrrolidine rings, was bonded to a silica gel chromatographic matrix by the N-terminal group. The chromatographic behaviour of the resulting chiral stationary phase (CSP) was compared with that of a CSP containing the analogous monomeric CS and that resulting from bonding of the polyproline-derived CS by the carboxy-terminal group using several solvents as mobile phase. The CSs were also studied from the conformational point of view in solution using circular dichroism and 13C NMR. A relationship was found between the presence of an ordered conformation in the particular conditions used and increased enantioselectivity.

Modularity of Calabi-Yau varieties and conformal field theory

We study the modularity problem of Calabi-Yau varieties from the conformal field theoretic point of view. We express the modular forms associated to all 1-dimensional Calabi-Yau orbifolds in terms of products of Dedekind eta functions, which is hoped to shed light on the modularity questions for higher dimensional Calabi-Yau varieties.

Investigating by CD the molecular mechanism of elasticity of elastomeric proteins

Elastomeric proteins are widespread in the animal kingdom, and their main function is to confer elasticity and resilience to organs and tissues. Besides common functional properties, elastomeric proteins share a common sequence design. They are usually constituted by repetitive sequences with a high content of glycine residues. From a conformational point of view, all the elastomeric proteins since now analyzed show a dynamic equilibria between folded (mainly beta-turns) and extended (polyproline II and beta-strands) conformations that could be at the origin of the high entropy of the relaxed state. As a matter of fact, elastin, lamprin, abductin, as well as the PEVK domain of titin share the same conformational ensemble, thus pointing to a common molecular mechanism as the origin of elasticity. CD spectroscopy represents the proper spectroscopic technique to be used overall because of its particular sensitivity to the presence of PPII structure. Its use in the molecular studies of elastin, abductin, and lamprin as well as the recently analyzed protein resilin will be presented.

A DFT study of infrared spectrum of sphingomyelin lipid molecule with calcium cation

AbstractOne of the phospholipids, sphingomyelin (SM) is the most abundant component of mammalian membranes in brain and nervous tissues. It plays an important role for apoptosis, aging, and signal transduction with cations. Recently, Yappert and co‐workers have shown that human lens sphingomyelin and its hydrogenated derivative, dihydrosphingomyelin (DHSM) are interacted with Ca2+ ions to develop human cataracts. In this study, we investigate conformational differences between an isolated SM/DHSM molecule and Ca2+‐coordinated form by using density functional theory (DFT) calculations. B3LYP functional and 6‐31G(d,p) double‐ζ split‐valence basis set is used for geometry optimization and normal mode analysis. One of resultant conformers of SMs has hydrogen bonding between hydroxyl and phosphate group, whereas another conformer has hydrogen bonding between hydroxyl and amide group. The red shift of calculated vibrational frequencies of amide band due to Ca2+ is compared with experimental infrared spectrum. Finally, we discuss the Ca2+‐induced effects from conformational and spectroscopic point of view to compare the experimental results. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008

Obestatin conformational features: A strategy to unveil obestatin’s biological role?

Obestatin and its derivative Ob(11–23) are recently discovered peptides produced in the rat stomach. They have proven to be involved in the regulation of energy balance, inhibiting feeding, causing reductions in food intake, body weight and jejunal contraction in rodents. The G-protein coupled receptor, GPR39, was originally proposed as being an obestatin target receptor, but this remains controversial. As such, the molecular mechanism for obestatin’s effects in vivo is still uncertain. Here we report the CD and NMR conformational analysis of obestatin and Ob(11–23). Both peptides assume a regular secondary structure in the C-terminal region of the molecule. In this region, structural elements similar to other GPCR binding neuropeptides support the identity of obestatin as a new and functionally autonomous GPCR ligand. Conversely sequence and conformational specificity point to a new farmacoforic structure, on which innovative derivatives with a potential role in the treatment of obesity can be designed and synthetized.

Structural Compromise of Disallowed Conformations in Peptide and Protein Structures

Using a data set of 454 crystal structures of peptides and 80 crystal structures of non-homologous proteins solved at ultra high resolution of 1.2 A or better we have analyzed the occurrence of disallowed Ramachandran (phi, psi) angles. Out of 1492 and 13508 non-glycyl residues in peptides and proteins respectively 12 and 76 residues in the two datasets adopt clearly disallowed combinations of Ramachandran angles. These examples include a number of conformational points which are far away from any of the allowed regions in the Ramachandran map. According to the Ramachandran map a given (phi, psi) combination is considered disallowed when two non-bonded atoms in a system of two-linked peptide units with ideal geometry are prohibitively proximal in space. However, analysis of the disallowed conformations in peptide and protein structures reveals that none of the observations of disallowed conformations in the crystal structures correspond to a short contact between non-bonded atoms. A further analysis of deviations of bond lengths and angles, from the ideal peptide geometry, at the residue positions of disallowed conformations in the crystal structures suggest that individual bond lengths and angles are all within acceptable limits. Thus, it appears that the rare tolerance of disallowed conformations is possible by gentle and acceptable deviations in a number of bond lengths and angles, from ideal geometry, over a series of bonds resulting in a net gross effect of acceptable non-bonded inter-atomic distances.

SuperconformalRcharges and dyon multiplicities inN=2gauge theories

$\mathcal{N}=(2,2)$ theories in $1+1\mathrm{D}$ exhibit a direct correspondence between the $R$ charges of chiral operators at a conformal point and the multiplicities of Bogomol'nyi-Prasad-Sommerfield (BPS) kinks in a massive deformation, as shown by Cecotti and Vafa. We obtain an analogous relation in $3+1\mathrm{D}$ for $\mathcal{N}=2$ gauge theories that are massive perturbations of Argyres-Douglas fixed points, utilizing the geometric engineering approach to $\mathcal{N}=2$ vacua within IIB string theory. In this case the scaling dimensions of a certain subset of chiral operators at the UV fixed point are related to the multiplicities of BPS dyons. When the Argyres-Douglas superconformal field theory is realized at the root of a baryonic Higgs branch, this translation from $1+1\mathrm{D}$ to $3+1\mathrm{D}$ can be understood physically from the relation between the bulk dynamics and the $\mathcal{N}=(2,2)$ world-sheet dynamics of vortices in the baryonic Higgs phase. Under a relevant perturbation, the BPS kink multiplicity on the vortex world sheet translates to that of the bulk dyonic states. The latter viewpoint suggests the $3+1\mathrm{D}$ version of the Cecotti-Vafa relation may hold more generally, and simple tests provide evidence in favor of this for more generic choices of the baryonic root.

Entanglement Entropy of 2D Conformal Quantum Critical Points: Hearing the Shape of a Quantum Drum

The entanglement entropy of a pure quantum state of a bipartite system A union or logical sumB is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. In one dimension, the entanglement of critical ground states diverges logarithmically in the subsystem size, with a universal coefficient that for conformally invariant critical points is related to the central charge of the conformal field theory. We find that the entanglement entropy of a standard class of z=2 conformal quantum critical points in two spatial dimensions, in addition to a nonuniversal "area law" contribution linear in the size of the AB boundary, generically has a universal logarithmically divergent correction, which is completely determined by the geometry of the partition and by the central charge of the field theory that describes the critical wave function.

Kaluza-Klein holography

We construct a holographic map between asymptotically AdS_5 x S^5 solutions of 10d supergravity and vacuum expectation values of gauge invariant operators of the dual QFT. The ingredients that enter in the construction are (i) gauge invariant variables so that the KK reduction is independent of any choice of gauge fixing; (ii) the non-linear KK reduction map from 10 to 5 dimensions (constructed perturbatively in the number of fields); (iii) application of holographic renormalization. A non-trivial role in the last step is played by extremal couplings. This map allows one to reliably compute vevs of operators dual to any KK fields. As an application we consider a Coulomb branch solution and compute the first two non-trivial vevs, involving operators of dimension 2 and 4, and reproduce the field theory result, in agreement with non-renormalization theorems. This constitutes the first quantitative test of the gravity/gauge theory duality away from the conformal point involving a vev of an operator dual to a KK field (which is not one of the gauged supergravity fields).