Six and seven loop Konishi from Luscher corrections

In the present paper we derive six and seven loop formulas for the anomalous dimension of the Konishi operator in N=4 SYM from string theory using the technique of Luscher corrections. We derive analytically the integrand using the worldsheet S-matrix and evaluate the resulting integral and infinite sum using a combination of high precision numerical integration and asymptotic expansion. We use this high precision numerical result to fit the integer coefficients of zeta values in the final analytical answer. The presented six and seven loop results can be used as a cross-check with FiNLIE on the string theory side, or with direct gauge theory computations. The seven loop level is the theoretical limit of this Luscher approach as at eight loops double-wrapping corrections will appear.Comment: 18 pages, typos correcte

Finite volume form factors in the presence of integrable defects

We developed the theory of finite volume form factors in the presence of integrable defects. These finite volume form factors are expressed in terms of the infinite volume form factors and the finite volume density of states and incorporate all polynomial corrections in the inverse of the volume. We tested our results, in the defect Lee-Yang model, against numerical data obtained by truncated conformal space approach (TCSA), which we improved by renormalization group methods adopted to the defect case. To perform these checks we determined the infinite volume defect form factors in the Lee-Yang model exactly, including their vacuum expectation values. We used these data to calculate the two point functions, which we compared, at short distance, to defect CFT. We also derived explicit expressions for the exact finite volume one point functions, which we checked numerically. In all of these comparisons excellent agreement was found.Comment: pdflatex, 34 pages, many figure

Geometry of W-algebras from the affine Lie algebra point of view

To classify the classical field theories with W-symmetry one has to classify the symplectic leaves of the corresponding W-algebra, which are the intersection of the defining constraint and the coadjoint orbit of the affine Lie algebra if the W-algebra in question is obtained by reducing a WZNW model. The fields that survive the reduction will obey non-linear Poisson bracket (or commutator) relations in general. For example the Toda models are well-known theories which possess such a non-linear W-symmetry and many features of these models can only be understood if one investigates the reduction procedure. In this paper we analyze the SL(n,R) case from which the so-called W_n-algebras can be obtained. One advantage of the reduction viewpoint is that it gives a constructive way to classify the symplectic leaves of the W-algebra which we had done in the n=2 case which will correspond to the coadjoint orbits of the Virasoro algebra and for n=3 which case gives rise to the Zamolodchikov algebra. Our method in principle is capable of constructing explicit representatives on each leaf. Another attractive feature of this approach is the fact that the global nature of the W-transformations can be explicitly described. The reduction method also enables one to determine the ``classical highest weight (h. w.) states'' which are the stable minima of the energy on a W-leaf. These are important as only to those leaves can a highest weight representation space of the W-algebra be associated which contains a ``classical h. w. state''.Comment: 17 pages, LaTeX, revised 1. and 7. chapter

Scaling function in AdS/CFT from the O(6) sigma model

Asymptotic behavior of the anomalous dimensions of Wilson operators with high spin and twist is governed in planar N=4 SYM theory by the scaling function which coincides at strong coupling with the energy density of a two-dimensional bosonic O(6) sigma model. We calculate this function by combining the two-loop correction to the energy density for the O(n) model with two-loop correction to the mass gap determined by the all-loop Bethe ansatz in N=4 SYM theory. The result is in agreement with the prediction coming from the thermodynamical limit of the quantum string Bethe ansatz equations, but disagrees with the two-loop stringy corrections to the folded spinning string solution.Comment: 25 pages, 2 figure

Exactly solvable model of the 2D electrical double layer

We consider equilibrium statistical mechanics of a simplified model for the ideal conductor electrode in an interface contact with a classical semi-infinite electrolyte, modeled by the two-dimensional Coulomb gas of pointlike $\pm$ unit charges in the stability-against-collapse regime of reduced inverse temperatures $0\le \beta<2$. If there is a potential difference between the bulk interior of the electrolyte and the grounded interface, the electrolyte region close to the interface (known as the electrical double layer) carries some nonzero surface charge density. The model is mappable onto an integrable semi-infinite sine-Gordon theory with Dirichlet boundary conditions. The exact form-factor and boundary state information gained from the mapping provide asymptotic forms of the charge and number density profiles of electrolyte particles at large distances from the interface. The result for the asymptotic behavior of the induced electric potential, related to the charge density via the Poisson equation, confirms the validity of the concept of renormalized charge and the corresponding saturation hypothesis. It is documented on the non-perturbative result for the asymptotic density profile at a strictly nonzero $\beta$ that the Debye-H\"uckel $\beta\to 0$ limit is a delicate issue.Comment: 14 page

TBA, NLO Luscher correction, and double wrapping in twisted AdS/CFT

The ground-state energy of integrably-twisted theories is analyzed in finite volume. We derive the leading and next-to-leading order (NLO) L\"uscher-type corrections for large volumes of the vacuum energy for integrable theories with twisted boundary conditions and twisted S-matrix. We then derive the twisted thermodynamic Bethe ansatz (TBA) equations to describe exactly the ground state, from which we obtain an untwisted Y-system. The two approaches are compared by expanding the TBA equations to NLO, and exact agreement is found. We give explicit results for the O(4) model and for the three-parameter family of $\gamma$-deformed (non-supersymmetric) planar AdS/CFT model, where the ground-state energy can be nontrivial and can acquire finite-size corrections. The NLO corrections, which correspond to double-wrapping diagrams, are explicitly evaluated for the latter model at six loops.Comment: 42 pages, 2 figures, v2: references added, v3: minor correction

Development of approaches for investigating the distribution of toxoplasma gondii infection in natural populations of animals and humans

Toxoplasma gondii is a globally distributed protozoan parasite that infects humans and a wide variety of warm-blooded animals. Although there are many surveys for T. gondii infection in mammals, little is known about the detailed distribution in localised natural populations. In this study we investigated host genotype and spatial location in relation to T. gondii infection and genotypes. We collected wood mice (Apodemus sylvaticus) from 4 sampling sites within a localised peri-aquatic woodland ecosystem which is relatively free of cats. Mice were genotyped using standard A. sylvaticus microsatellite markers and T. gondii and its genotypes were detected using 5 specific PCR based markers: SAG1, SAG2, SAG3, B1 and GRA6 directly from infected tissue. Of 126 wood mice collected, 44 samples gave positive reactions with T. gondii specific markers giving an infection rate of 34.92% (95% CI: 27.14%-43.59%). A total of 24/76 (31.58%, 95% CI: 22.19%-42.74%) males and 20/50 (40%, 95% CI: 27.59%-53.84%) female mice were found to be positive for T. gondii with no significant difference (P = 0.353). Juvenile, young adults and adults were infected at similar prevalences, respectively, 7/17 (41.18%), 27/65 (41.54%) and 10/44 (22.72%) with no significant age-prevalence effect (P = 0.23). Detailed analysis of the RFLP patterns and the DNA sequences for the SAG2, SAG3 and GRA6 loci showed a range of genotypes but, surprisingly, suggested that 30/44 (68.2%) infected mice had multiple genotypes (mixed infections) present. Results of genetic analysis of the mice showed that the collection consists of four genetically distinct populations. There was a significant difference in T. gondii infection in the different mouse genotypically derived populations (P=0.035) but not between geographically defined populations based on sampling location (P=0.29). In a parallel study, DNA was successfully collected from 88 human lung tissue samples. All samples showed successful amplification of the human α-tubulin gene and were used for T. gondii DNA detection. We used commonly used PCR markers (B1, SAG1, SAG2, SAG3, GRA6, APICO, L358, PK1, SAG1-Su, BTUB, alt.SAG2, c22-8 and c29-2), histological and immunohistochemical staining to confirm the presence of the parasite. All 88 tested samples were confirmed to be positive for T. gondii with markers B1, SAG1, SAG2 3’, SAG2 5’ and SAG3, giving a prevalence of 100% (95% CI: 95.82%-100%). From all successfully genotyped samples, 34 had single infection on all loci and 42 were of mixed infection on one or more loci with all three genotypes present. Type II genotype was the most predominant, followed by Type I and Type III. We detected 11 unusual genotypes. Immunohistochemistry was performed on 76 of the 88 tissue sections using commercial polyclonal antibodies produced in rabbits. All 76 sections were confirmed to be positive for T. gondii. A surprisingly high number of patients (96.05%) showed evidence of an active form of infection, as defined by the presence of tachyzoites or infected alveolar macrophages (or other cell types). Only three subjects (3.95%) had the dormant cyst stage as the only stage present. All 76 tissue sections were successfully stained with haematoxylin and eosin and observed under the light microscope. The presence of structures consistent with infection by the parasite was confirmed in 67 samples. All these patients are at risk of reactivation of chronic infection, leading to toxoplasmic encephalitis or pulmonary toxoplasmosis; which can complicate and delay their treatment or lead to death

The Bajnok-Janik formula and wrapping corrections

We write down the simplified TBA equations of the $AdS_5 \times S^5$ string sigma-model for minimal energy twist-two operators in the sl(2) sector of the model. By using the linearized version of these TBA equations it is shown that the wrapping corrected Bethe equations for these states are identical, up to O(g^8), to the Bethe equations calculated in the generalized L\"uscher approach (Bajnok-Janik formula). Applications of the Bajnok-Janik formula to relativistic integrable models, the nonlinear O(n) sigma models for n=2,3,4 and the SU(n) principal sigma models, are also discussed.Comment: Latex, 22 pages, published versio

Casimir effect in the boundary state formalism

Casimir effect in the planar setting is described using the boundary state formalism, for general partially reflecting boundaries. It is expressed in terms of the low-energy degrees of freedom, which provides a large distance expansion valid for general interacting field theories provided there is a non-vanishing mass gap. The expansion is written in terms of the scattering amplitudes, and needs no ultraviolet renormalization. We also discuss the case when the quantum field has a nontrivial vacuum configuration.Comment: 11 pages. Proceedings contribution of talk given at the Workshop on Quantum Field Theory under the Influence of External Conditions (QFEXT07), University of Leipzig, September 16-21, 2007. To appear in J. Phys.