Quantum Sine(h)-Gordon Model and Classical Integrable Equations

We study a family of classical solutions of modified sinh-Gordon equation, $\partial_z\partial_{{\bar z}} \eta-\re^{2\eta}+p(z)\,p({\bar z})\ \re^{-2\eta}=0$with$p(z)=z^{2\alpha}-s^{2\alpha}$. We show that certain connection coefficients for solutions of the associated linear problem coincide with the$Q$-function of the quantum sine-Gordon$(\alpha>0)$or sinh-Gordon$(\alpha<-1)$ models.Comment: 35 pages, 3 figure

Form factors at strong coupling via a Y-system

We compute form factors in planar N=4 Super Yang-Mills at strong coupling. Namely we consider the overlap between an operator insertion and 2n gluons. Through the gauge/string duality these are given by minimal surfaces in AdS space. The surfaces end on an infinite periodic sequence of null segments at the boundary of AdS. We consider surfaces that can be embedded in AdS_3. We derive set of functional equations for the cross ratios as functions of the spectral parameter. These equations are of the form of a Y-system. The integral form of the Y-system has Thermodynamics Bethe Ansatz form. The area is given by the free energy of the TBA system or critical value of Yang-Yang functional. We consider a restricted set of operators which have small conformal dimension

Dynamical tunneling in molecules: Quantum routes to energy flow

Dynamical tunneling, introduced in the molecular context, is more than two decades old and refers to phenomena that are classically forbidden but allowed by quantum mechanics. On the other hand the phenomenon of intramolecular vibrational energy redistribution (IVR) has occupied a central place in the field of chemical physics for a much longer period of time. Although the two phenomena seem to be unrelated several studies indicate that dynamical tunneling, in terms of its mechanism and timescales, can have important implications for IVR. Examples include the observation of local mode doublets, clustering of rotational energy levels, and extremely narrow vibrational features in high resolution molecular spectra. Both the phenomena are strongly influenced by the nature of the underlying classical phase space. This work reviews the current state of understanding of dynamical tunneling from the phase space perspective and the consequences for intramolecular vibrational energy flow in polyatomic molecules.Comment: 37 pages and 23 figures (low resolution); Int. Rev. Phys. Chem. (Review to appear in Oct. 2007

Autologous neutralizing antibody responses to an HIV envelope glycan hole are not easily broadened in rabbits

Extensive studies with subtype A BG505-derived HIV Env immunogens have revealed that the dominant autologous neutralizing epitope in rabbits is located in an exposed region of the heavily glycosylated trimer that lacks potential N-linked glycosylation sites at positions 230, 241, and 289. The Env derived from B41, a subtype B virus, shares a glycan hole centered on positions 230 and 289. To test whether broader neutralization to the common glycan hole can be achieved, we immunized rabbits with B41 SOSIP alone, as well as B41 and BG505 co-immunization. We isolated autologous neutralizing antibodies (nAbs) and described their structure in complex with the B41 Env. Our data suggest that distinct autologous nAb lineages are induced by BG505 and B41 immunogens, even when both were administered together. In contrast to previously described BG505 glycan hole antibodies, the B41-specific nAbs accommodate the >97% conserved N241 glycan, which is present in B41. Single particle cryo-electron microscopy studies confirmed that B41 and BG505-specific nAbs bind to overlapping glycan hole epitopes. We then used our high-resolution data to guide mutations in the BG505 glycan hole epitope in an attempt to broaden the reactivity of a B41-specific nAb, but only recovered partial binding. Our data demonstrate that lack of cross-reactivity in glycan hole antibodies is due to amino acid differences within the epitope and our attempts to rationally design cross-reactive trimers resulted in only limited success. Thus, even for the immunodominant glycan hole shared between BG505 and B41 the prospect of designing prime-boost immunogens remains difficult

HIV envelope trimer-elicited autologous neutralizing antibodies bind a region overlapping the N332 glycan supersite

To date, immunization studies of rabbits with the BG505 SOSIP.664 HIV envelope glycoprotein trimers have revealed the 241/289 glycan hole as the dominant neutralizing antibody epitope. Here, we isolated monoclonal antibodies from a rabbit that did not exhibit glycan hole–dependent autologous serum neutralization. The antibodies did not compete with a previously isolated glycan hole–specific antibody but did compete with N332 glycan supersite broadly neutralizing antibodies. A 3.5-Å cryoEM structure of one of the antibodies in complex with the BG505 SOSIP.v5.2 trimer demonstrated that while the epitope recognized overlapped the N332 glycan supersite by contacting the GDIR motif at the base of V3, primary contacts were located in the variable V1 loop. These data suggest that strain-specific responses to V1 may interfere with broadly neutralizing responses to the N332 glycan supersite and vaccine immunogens may require engineering to minimize these off-target responses or steer them toward a more desirable pathway

Series Solution and Minimal Surfaces in AdS

According to the Alday-Maldacena program the strong coupling limit of Super Yang-Mills scattering amplitudes is given by minimal area surfaces in AdS spacetime with a boundary consisting of a momentum space polygon. The string equations in AdS systematically reduce to coupled Toda type equations whose Euclidean classical solutions are then of direct relevance. While in the simplest case of AdS_3 exact solutions were known from earlier studies of the sinh-Gordon equation, there exist at present no similar exact forms for the generalized Toda equations related to AdS_d with d>=4. In this paper we develop a series method for the solution to those equations and evaluate their contribution to the finite piece of the worldsheet area. For the known sinh-Gordon case the method is seen to give results in excellent agreement with the exact answer.Comment: 19 pages, no figures; references added, one note adde

Holes in the Glycan Shield of the Native HIV Envelope Are a Target of Trimer-Elicited Neutralizing Antibodies

A major advance in the search for an HIV vaccine has been the development of a near-native Envelope trimer (BG505 SOSIP.664) that can induce robust autologous Tier 2 neutralization. Here, potently neutralizing monoclonal antibodies (nAbs) from rabbits immunized with BG505 SOSIP.664 are shown to recognize an immunodominant region of gp120 centered on residue 241. Residue 241 occupies a hole in the glycan defenses of the BG505 isolate, with fewer than 3% of global isolates lacking a glycan site at this position. However, at least one conserved glycan site is missing in 89% of viruses, suggesting the presence of glycan holes in most HIV isolates. Serum evidence is consistent with targeting of holes in natural infection. The immunogenic nature of breaches in the glycan shield has been under-appreciated in previous attempts to understand autologous neutralizing antibody responses and has important potential consequences for HIV vaccine design

Antibodies from rabbits immunized with HIV-1 clade B SOSIP trimers can neutralize multiple clade B viruses by destabilizing the envelope glycoprotein

The high HIV-1 viral diversity is a formidable hurdle for the development of an HIV-1 vaccine. Elicitation of broadly neutralizing antibodies (bNAbs) would offer a solution, but so far immunization strategies have failed to elicit bNAbs efficiently. To overcome the obstacles, it is important to understand the immune responses elicited by current HIV-1 envelope glycoprotein (Env) immunogens. To gain more insight, we characterized monoclonal antibodies (mAbs) isolated from rabbits immunized with Env SOSIP trimers based on the clade B isolate AMC008. Four rabbits that were immunized three times with AMC008 trimer developed robust autologous and sporadic low-titer heterologous neutralizing responses. Seventeen AMC008 trimer-reactive mAbs were isolated using antigen-specific single B cell sorting. Four of these mAbs neutralized the autologous AMC008 virus and several other clade B viruses. When visualized by electron microscopy, the complex of the neutralizing mAbs with the AMC008 trimer showed binding to the gp41 subunit with unusual approach angles and we observed that their neutralization ability depended on their capacity to induce Env trimer dissociation. Thus, AMC008 SOSIP trimer immunization induced clade B neutralizing mAbs with unusual approach angles with neutralizing effects that involve trimer destabilization. Optimizing these responses might provide an avenue to the induction of trimer dissociating bNAbs. IMPORTANCE Roughly 32 million people have died as a consequence of HIV-1 infection since the start of the epidemic and still 1.7 million people get infected with HIV-1 annually. Therefore, a vaccine to prevent HIV-1 infection is urgently needed. Current HIV-1 immunogens are not able to elicit the broad immune responses needed to provide protection against the large variation of HIV-1 strains circulating globally. A better understanding of the humoral immune responses elicited by immunization with state-of-the-art HIV-1 immunogens should facilitate the design of improved HIV-1 vaccine candidates. We identified antibodies with the ability to neutralize multiple HIV-1 viruses by destabilization of the envelope glycoprotein. Their weak but consistent cross-neutralization ability indicates the potential of this epitope to elicit broad responses. The trimer-destabilizing effect of the neutralizing mAbs combined with detailed characterization of the neutralization epitope can be used to shape the next generation of HIV-1 immunogens to elicit improved humoral responses after vaccination

Correlation function of null polygonal Wilson loops with local operators

We consider the correlator of a light-like polygonal Wilson loop with n cusps with a local operator (like the dilaton or the chiral primary scalar) in planar N =4 super Yang-Mills theory. As a consequence of conformal symmetry, the main part of such correlator is a function F of 3n-11 conformal ratios. The first non-trivial case is n=4 when F depends on just one conformal ratio \zeta. This makes the corresponding correlator one of the simplest non-trivial observables that one would like to compute for generic values of the `t Hooft coupling \lambda. We compute F(\zeta,\lambda) at leading order in both the strong coupling regime (using semiclassical AdS5 x S5 string theory) and the weak coupling regime (using perturbative gauge theory). Some results are also obtained for polygonal Wilson loops with more than four edges. Furthermore, we also discuss a connection to the relation between a correlator of local operators at null-separated positions and cusped Wilson loop suggested in arXiv:1007.3243.Comment: 36 pages, 2 figure

Dynamics and transport near quantum-critical points

The physics of non-zero temperature dynamics and transport near quantum-critical points is discussed by a detailed study of the O(N)-symmetric, relativistic, quantum field theory of a N-component scalar field in $d$ spatial dimensions. A great deal of insight is gained from a simple, exact solution of the long-time dynamics for the N=1 d=1 case: this model describes the critical point of the Ising chain in a transverse field, and the dynamics in all the distinct, limiting, physical regions of its finite temperature phase diagram is obtained. The N=3, d=1 model describes insulating, gapped, spin chain compounds: the exact, low temperature value of the spin diffusivity is computed, and compared with NMR experiments. The N=3, d=2,3 models describe Heisenberg antiferromagnets with collinear N\'{e}el correlations, and experimental realizations of quantum-critical behavior in these systems are discussed. Finally, the N=2, d=2 model describes the superfluid-insulator transition in lattice boson systems: the frequency and temperature dependence of the the conductivity at the quantum-critical coupling is described and implications for experiments in two-dimensional thin films and inversion layers are noted.Comment: Lectures presented at the NATO Advanced Study Institute on "Dynamical properties of unconventional magnetic systems", Geilo, Norway, April 2-12, 1997, edited by A. Skjeltorp and D. Sherrington, Kluwer Academic, to be published. 46 page