Thermodynamic limit of random partitions and dispersionless Toda hierarchy

We study the thermodynamic limit of random partition models for the instanton sum of 4D and 5D supersymmetric U(1) gauge theories deformed by some physical observables. The physical observables correspond to external potentials in the statistical model. The partition function is reformulated in terms of the density function of Maya diagrams. The thermodynamic limit is governed by a limit shape of Young diagrams associated with dominant terms in the partition function. The limit shape is characterized by a variational problem, which is further converted to a scalar-valued Riemann-Hilbert problem. This Riemann-Hilbert problem is solved with the aid of a complex curve, which may be thought of as the Seiberg-Witten curve of the deformed U(1) gauge theory. This solution of the Riemann-Hilbert problem is identified with a special solution of the dispersionless Toda hierarchy that satisfies a pair of generalized string equations. The generalized string equations for the 5D gauge theory are shown to be related to hidden symmetries of the statistical model. The prepotential and the Seiberg-Witten differential are also considered.Comment: latex2e using amsmath,amssymb,amsthm packages, 55 pages, no figure; (v2) typos correcte

The effectiveness of corneal cylinder masking using Polycon II lenses

The effectiveness of corneal cylinder masking using Polycon II lense

On the Baryonic Branch Root of N=2 MQCD

We investigate the brane exchange in the framework of N=2 MQCD by using a specific family of M fivebrane configurations relevant to describe the baryonic branch root. An exchange of M fivebranes is realized in the Taub-NUT geometry and controlled by the moduli parameter of the configurations. This family also provides two different descriptions of the root. These descriptions are examined carefully using the Taub-NUT geometry. It is shown that they have the same baryonic branch and are shifted each other by the brane exchange.Comment: LaTeX, 25 pages, 7 figures, references adde

Supersymmetry Flows, Semi-Symmetric Space Sine-Gordon Models And The Pohlmeyer Reduction

We study the extended supersymmetric integrable hierarchy underlying the Pohlmeyer reduction of superstring sigma models on semi-symmetric superspaces F/G. This integrable hierarchy is constructed by coupling two copies of the homogeneous integrable hierarchy associated to the loop Lie superalgebra extension f of the Lie superalgebra f of F and this is done by means of the algebraic dressing technique and a Riemann-Hilbert factorization problem. By using the Drinfeld-Sokolov procedure we construct explicitly, a set of 2D spin \pm1/2 conserved supercharges generating supersymmetry flows in the phase space of the reduced model. We introduce the bi-Hamiltonian structure of the extended homogeneous hierarchy and show that the two brackets are of the Kostant-Kirillov type on the co-adjoint orbits defined by the light-cone Lax operators L_\pm. By using the second symplectic structure, we show that these supersymmetries are Hamiltonian flows, we compute part of the supercharge algebra and find the supersymmetric field variations they induce. We also show that this second Poisson structure coincides with the canonical Lorentz-Invariant symplectic structure of the WZNW model involved in the Lagrangian formulation of the extended integrable hierarchy, namely, the semi-symmetric space sine-Gordon model (SSSSG), which is the Pohlmeyer reduced action functional for the transverse degrees of freedom of superstring sigma models on the cosets F/G. We work out in some detail the Pohlmeyer reduction of the AdS_2xS^2 and the AdS_3xS^3 superstrings and show that the new conserved supercharges can be related to the supercharges extracted from 2D superspace. In particular, for the AdS_2xS^2 example, they are formally the same.Comment: V2: Two references added, V3: Modifications in section 2.6, V4: Published versio

On Effective Superpotentials and Compactification to Three Dimensions

We study four dimensional N=2 SO/SP supersymmetric gauge theory on R^3\times S^1 deformed by a tree level superpotential. We will show that the exact superpotential can be obtained by making use of the Lax matrix of the corresponding integrable model which is the periodic Toda lattice. The connection between vacua of SO(2N) and SO(2kN-2k+2) can also be seen in this framework. Similar analysis can also be applied for SO(2N+1) and SP(2N).Comment: 18 pages, latex file, v2: typos corrected, refs adde

Nonperturbative Superpotentials and Compactification to Three Dimensions

We consider four-dimensional N=2 supersymmetric gauge theories with gauge group U(N) on R^3 x S^1, in the presence of a classical superpotential. The low-energy quantum superpotential is obtained by simply replacing the adjoint scalar superfield in the classical superpotential by the Lax matrix of the integrable system that underlies the 4d field theory. We verify in a number of examples that the vacuum structure obtained in this way matches precisely that in 4d, although the degrees of freedom that appear are quite distinct. Several features of 4d field theories, such as the possibility of lifting vacua from U(N) to U(tN), become particularly simple in this framework. It turns out that supersymmetric vacua give rise to a reduction of the integrable system which contains information about the field theory but also about the Dijkgraaf-Vafa matrix model. The relation between the matrix model and the quantum superpotential on R^3 x S^1 appears to involve a novel kind of mirror symmetry.Comment: LaTeX, 45 pages, uses AmsMath, minor correction, reference adde

N=1 G_2 SYM theory and Compactification to Three Dimensions

We study four dimensional N=2 G_2 supersymmetric gauge theory on R^3\times S^1 deformed by a tree level superpotential. We will show that the exact superpotential can be obtained by making use of the Lax matrix of the corresponding integrable model which is the periodic Toda lattice based on the dual of the affine G_2 Lie algebra. At extrema of the superpotential the Seiberg-Witten curve typically factorizes, and we study the algebraic equations underlying this factorization. For U(N) theories the factorization was closely related to the geometrical engineering of such gauge theories and to matrix model descriptions, but here we will find that the geometrical interpretation is more mysterious. Along the way we give a method to compute the gauge theory resolvent and a suitable set of one-forms on the Seiberg-Witten curve. We will also find evidence that the low-energy dynamics of G_2 gauge theories can effectively be described in terms of an auxiliary hyperelliptic curve.Comment: 27 pages, late

Non-holomorphic terms in N=2 SUSY Wilsonian actions and RG equation

In this paper we first investigate the Ansatz of one of the present authors for K(\Psi,\bar\Psi), the adimensional modular invariant non-holomorphic correction to the Wilsonian effective Lagrangian of an N=2 globally supersymmetric gauge theory. The renormalisation group beta-function of the theory crucially allows us to express K(\Psi,\bar\Psi) in a form that easily generalises to the case in which the theory is coupled to N_F hypermultiplets in the fundamental representation of the gauge group. This function satisfies an equation which should be viewed as a fully non-perturbative ``non-chiral superconformal Ward identity". We also determine its renormalisation group equation. Furthermore, as a first step towards checking the validity of this Ansatz, we compute the contribution to K(\Psi,\bar\Psi) from instantons of winding number k=1 and k=2. As a by-product of our analysis we check a non-renormalisation theorem for N_F=4.Comment: 39 pages, LaTex file, no figure

Prolyl Isomerase Pin1 Regulates Mouse Embryonic Fibroblast Differentiation into Adipose Cells

isomerase, Pin1, regulates insulin signal transduction. Pin1 reduces responses to insulin stimulation by binding CRTC2 (CREB-regulated transcriptional co-activator 2) and PPARγ (peroxisome prolifereator- activated receptor γ), but conversely enhances insulin signaling by binding IRS-1 (insulin receptor substrate-1), Akt kinase, and Smad3. Therefore, it is still unclear whether Pin1 inhibits or enhances adipose cell differentiation. mice was restored by increasing expression of Pin1. We found that Pin1 binds to phosphoThr172- and phosphoSer271-Pro sites in CREB suppress the activity in COS-7 cells.Pin1 enhanced the uptake of triglycerides and the differentiation of MEF cells into adipose cells in response to insulin stimulation. Results of this study suggest that Pin1 down-regulation could be a potential approach in obesity-related dysfunctions, such as high blood pressure, diabetes, non-alcoholic steatohepatitis

Comparison of DNA extraction kits for PCR-DGGE analysis of human intestinal microbial communities from fecal specimens

<p>Abstract</p> <p>Background</p> <p>The influence of diet on intestinal microflora has been investigated mainly using conventional microbiological approaches. Although these studies have advanced knowledge on human intestinal microflora, it is imperative that new methods are applied to facilitate scientific progress. Culture-independent molecular fingerprinting method of Polymerase Chain Reaction and Denaturing Gradient Gel Electrophoresis (PCR-DGGE) has been used to study microbial communities in a variety of environmental samples. However, these protocols must be optimized prior to their application in order to enhance the quality and accuracy of downstream analyses. In this study, the relative efficacy of four commercial DNA extraction kits (Mobio Ultra Clean^®Fecal DNA Isolation Kit, M; QIAamp^®DNA Stool Mini Kit, Q; FastDNA^®SPIN Kit, FSp; FastDNA^®SPIN Kit for Soil, FSo) were evaluated. Further, PCR-DGGE technique was also assessed for its feasibility in detecting differences in human intestinal bacterial fingerprint profiles.</p> <p>Method</p> <p>Total DNA was extracted from varying weights of human fecal specimens using four different kits, followed by PCR amplification of bacterial 16S rRNA genes, and DGGE separation of the amplicons.</p> <p>Results</p> <p>Regardless of kit, maximum DNA yield was obtained using 10 to 50 mg (wet wt) of fecal specimens and similar DGGE profiles were obtained. However, kits FSp and FSo extracted significantly larger amounts of DNA per g dry fecal specimens and produced more bands on their DGGE profiles than kits M and Q due to their use of bead-containing lysing matrix and vigorous shaking step. DGGE of 16S rRNA gene PCR products was suitable for capturing the profiles of human intestinal microbial community and enabled rapid comparative assessment of inter- and intra-subject differences.</p> <p>Conclusion</p> <p>We conclude that extraction kits that incorporated bead-containing lysing matrix and vigorous shaking produced high quality DNA from human fecal specimens (10 to 50 mg, wet wt) that can be resolved as bacterial community fingerprints using PCR-DGGE technique. Subsequently, PCR-DGGE technique can be applied for studying variations in human intestinal microbial communities.</p