Sum rules and three point functions

Sum rules constraining the R-current spectral densities are derived holographically for the case of D3-branes, M2-branes and M5-branes all at finite chemical potentials. In each of the cases the sum rule relates a certain integral of the spectral density over the frequency to terms which depend both on long distance physics, hydrodynamics and short distance physics of the theory. The terms which which depend on the short distance physics result from the presence of certain chiral primaries in the OPE of two R-currents which are turned on at finite chemical potential. Since these sum rules contain information of the OPE they provide an alternate method to obtain the structure constants of the two R-currents and the chiral primary. As a consistency check we show that the 3 point function derived from the sum rule precisely matches with that obtained using Witten diagrams.Comment: 41 page

General Form of the Color Potential Produced by Color Charges of the Quark

Constant electric charge $e$ satisfies the continuity equation $\partial_\mu j^{\mu}(x)= 0$ where $j^\mu(x)$ is the current density of the electron. However, the Yang-Mills color current density $j^{\mu a}(x)$ of the quark satisfies the equation $D_\mu[A] j^{\mu a}(x)= 0$ which is not a continuity equation ($\partial_\mu j^{\mu a}(x)\neq 0$) which implies that a color charge $q^a(t)$ of the quark is not constant but it is time dependent where $a=1,2,...8$ are color indices. In this paper we derive general form of color potential produced by color charges of the quark. We find that the general form of the color potential produced by the color charges of the quark at rest is given by \Phi^a(x) =A_0^a(t,{\bf x}) =\frac{q^b(t-\frac{r}{c})}{r}\[\frac{{\rm exp}[g\int dr \frac{Q(t-\frac{r}{c})}{r}] -1}{g \int dr \frac{Q(t-\frac{r}{c})}{r}}\]_{ab} where $dr$ integration is an indefinite integration, ~~ $Q_{ab}(\tau_0)=f^{abd}q^d(\tau_0)$, ~~$r=|{\vec x}-{\vec X}(\tau_0)|$, ~~$\tau_0=t-\frac{r}{c}$ is the retarded time, ~~$c$ is the speed of light, ~~${\vec X}(\tau_0)$ is the position of the quark at the retarded time and the repeated color indices $b,d$(=1,2,...8) are summed. For constant color charge $q^a$ we reproduce the Coulomb-like potential $\Phi^a(x)=\frac{q^a}{r}$ which is consistent with the Maxwell theory where constant electric charge $e$ produces the Coulomb potential $\Phi(x)=\frac{e}{r}$.Comment: Final version, two more sections added, 45 pages latex, accepted for publication in JHE

The a-theorem and conformal symmetry breaking in holographic RG flows

We study holographic models describing an RG flow between two fixed points driven by a relevant scalar operator. We show how to introduce a spurion field to restore Weyl invariance and compute the anomalous contribution to the generating functional in even dimensional theories. We find that the coefficient of the anomalous term is proportional to the difference of the conformal anomalies of the UV and IR fixed points, as expected from anomaly matching arguments in field theory. For any even dimensions the coefficient is positive as implied by the holographic a-theorem. For flows corresponding to spontaneous breaking of conformal invariance, we also compute the two-point functions of the energy-momentum tensor and the scalar operator and identify the dilaton mode. Surprisingly we find that in the simplest models with just one scalar field there is no dilaton pole in the two-point function of the scalar operator but a stronger singularity. We discuss the possible implications.Comment: 50 pages. v2: minor changes, added references, extended discussion. v3: we have clarified some of the calculations and assumptions, results unchanged. v4: published version in JHE

Correlators of Vertex Operators for Circular Strings with Winding Numbers in AdS5xS5

We compute semiclassically the two-point correlator of the marginal vertex operators describing the rigid circular spinning string state with one large spin and one windining number in AdS_5 and three large spins and three winding numbers in S^5. The marginality condition and the conformal invariant expression for the two-point correlator obtained by using an appropriate vertex operator are shown to be associated with the diagonal and off-diagonal Virasoro constraints respectively. We evaluate semiclassically the three-point correlator of two heavy circular string vertex operators and one zero-momentum dilaton vertex operator and discuss its relation with the derivative of the dimension of the heavy circular string state with respect to the string tension.Comment: 16 pages, LaTeX, no figure

More three-point correlators of giant magnons with finite size

In the framework of the semiclassical approach, we compute the normalized structure constants in three-point correlation functions, when two of the vertex operators correspond to heavy string states, while the third vertex corresponds to a light state. This is done for the case when the heavy string states are finite-size giant magnons with one or two angular momenta, and for two different choices of the light state, corresponding to dilaton operator and primary scalar operator. The relevant operators in the dual gauge theory are Tr(F_{\mu\nu}^2 Z^j+...) and Tr(Z^j). We first consider the case of AdS_5 x S^5 and N = 4 super Yang-Mills. Then we extend the obtained results to the gamma-deformed AdS_5 x S^5_\gamma, dual to N = 1 super Yang-Mills theory, arising as an exactly marginal deformation of N = 4 super Yang-Mills.Comment: 14 pages, no figure

Correlation functions of three heavy operators - the AdS contribution

We consider operators in N=4 SYM theory which are dual, at strong coupling, to classical strings rotating in S^5. Three point correlation functions of such operators factorize into a universal contribution coming from the AdS part of the string sigma model and a state-dependent S^5 contribution. Consequently a similar factorization arises for the OPE coefficients. In this paper we evaluate the AdS universal factor of the OPE coefficients which is explicitly expressed just in terms of the anomalous dimensions of the three operators.Comment: 49 pages, 3 figures; v.2 references corrected; v3: corrected discussion in section 5, results unchange

The spatio-temporal relationship between concurrent lesion and brain atrophy changes in early multiple sclerosis: A post-hoc analysis of the REFLEXION study

BACKGROUND: White matter (WM) lesions and brain atrophy are present early in multiple sclerosis (MS). However, their spatio-temporal relationship remains unclear. METHODS: Yearly magnetic resonance images were analysed in 387 patients with a first clinical demyelinating event (FCDE) from the 5-year REFLEXION study. Patients received early (from baseline; N = 258; ET) or delayed treatment (from month-24; N = 129; DT) with subcutaneous interferon beta-1a. FSL-SIENA/VIENA were used to provide yearly percentage volume change of brain (PBVC) and ventricles (PVVC). Yearly total lesion volume change (TLVC) was determined by a semi-automated method. Using linear mixed models and voxel-wise analyses, we firstly investigated the overall relationship between TLVC and PBVC and between TLVC and PVVC in the same follow-up period. Analyses were then separately performed for: the untreated period of DT patients (first two years), the first year of treatment (year 1 for ET and year 3 for DT), and a period where patients had received at least 1 year of treatment (stable treatment; ET: years 2, 3, 4, and 5; DT: years 4 and 5). RESULTS: Whole brain: across the whole study period, lower TLVC was related to faster atrophy (PBVC: B = 0.046, SE = 0.013, p < 0.001; PVVC: B = −0.466, SE = 0.118, p < 0.001). Within the untreated period of DT patients, lower TLVC was related to faster atrophy (PBVC: B = 0.072, SE = 0.029, p = 0.013; PVVC: B = −0.917, SE = 0.306, p = 0.003). A similar relationship was found within the first year of treatment of ET patients (PBVC: B = 0.081, SE = 0.027, p = 0.003; PVVC: B = −1.08, SE = 0.284, p < 0.001), consistent with resolving oedema and pseudo-atrophy. Voxel-wise: overall, higher TLVC was related to faster ventricular enlargement. Lower TLVC was related to faster widespread atrophy in year 1 in both ET (first year of treatment) and DT (untreated) patients. In the second untreated year of DT patients and within the stable treatment period of ET patients (year 4), faster periventricular and occipital lobe atrophy was associated with higher TLVC. CONCLUSIONS: WM lesion changes and atrophy occurred simultaneously in early MS. Spatio-temporal correspondence of these two processes involved mostly the periventricular area. Within the first year of the study, in both treatment groups, faster atrophy was linked to lower lesion volume changes, consistent with higher shrinking and disappearing lesion activity. This might reflect the pseudo-atrophy phenomenon that is probably related to the therapy driven (only in ET patients, as they received treatment from baseline) and “natural” (both ET and DT patients entered the study after a FCDE) resolution of oedema. In an untreated period and later on during stable treatment, (real) atrophy was related to higher lesion volume changes, consistent with increased new and enlarging lesion activity

Protein disulfide-isomerase interacts with a substrate protein at all stages along its folding pathway

In contrast to molecular chaperones that couple protein folding to ATP hydrolysis, protein disulfide-isomerase (PDI) catalyzes protein folding coupled to formation of disulfide bonds (oxidative folding). However, we do not know how PDI distinguishes folded, partly-folded and unfolded protein substrates. As a model intermediate in an oxidative folding pathway, we prepared a two-disulfide mutant of basic pancreatic trypsin inhibitor (BPTI) and showed by NMR that it is partly-folded and highly dynamic. NMR studies show that it binds to PDI at the same site that binds peptide ligands, with rapid binding and dissociation kinetics; surface plasmon resonance shows its interaction with PDI has a Kd of ca. 10−5 M. For comparison, we characterized the interactions of PDI with native BPTI and fully-unfolded BPTI. Interestingly, PDI does bind native BPTI, but binding is quantitatively weaker than with partly-folded and unfolded BPTI. Hence PDI recognizes and binds substrates via permanently or transiently unfolded regions. This is the first study of PDI's interaction with a partly-folded protein, and the first to analyze this folding catalyst's changing interactions with substrates along an oxidative folding pathway. We have identified key features that make PDI an effective catalyst of oxidative protein folding – differential affinity, rapid ligand exchange and conformational flexibility

On correlation functions of operators dual to classical spinning string states

We explore how to compute, classically at strong coupling, correlation functions of local operators corresponding to classical spinning string states. The picture we obtain is of `fattened' Witten diagrams, the evaluation of which turns out to be surprisingly subtle and requires a modification of the naive classical action due to a necessary projection onto appropriate wave functions. We examine string solutions which compute the simplest case of a two-point function and reproduce the right scaling with the anomalous dimensions corresponding to the energies of the associated spinning string solutions. We also describe, under some simplifying assumptions, how the spacetime dependence of a conformal three-point correlation function arises in this setup.Comment: 27 pages, 3 figures; v2: references and comments added