Three-dimensional Black Holes and Liouville Field Theory

A quantization of (2+1)-dimensional gravity with negative cosmological constant is presented and quantum aspects of the (2+1)-dimensional black holes are studied thereby. The quantization consists of two procedures. One is related with quantization of the asymptotic Virasoro symmetry. A notion of the Virasoro deformation of 3-geometry is introduced. For a given black hole, the deformation of the exterior of the outer horizon is identified with a product of appropriate coadjoint orbits of the Virasoro groups $\hat{diff S^1}_{\pm}$. Its quantization provides unitary irreducible representations of the Virasoro algebra, in which state of the black hole becomes primary. To make the quantization complete, holonomies, the global degrees of freedom, are taken into account. By an identification of these topological operators with zero modes of the Liouville field, the aforementioned unitary representations reveal, as far as $c \gg 1$, as the Hilbert space of this two-dimensional conformal field theory. This conformal field theory, living on the cylinder at infinity of the black hole and having continuous spectrums, can recognize the outer horizon only as a it one-dimensional object in $SL_2({\bf R})$ and realize it as insertions of the corresponding vertex operator. Therefore it can not be a conformal field theory on the horizon. Two possible descriptions of the horizon conformal field theory are proposed.Comment: 39 pages, LaTeX, 8 figures are added. Section 4.3 is revised and enlarged to include the case of conical singularities. Several typos are corrected. References are adde

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

Factorization of Seiberg-Witten Curves and Compactification to Three Dimensions

We continue our study of nonperturbative superpotentials of four-dimensional N=2 supersymmetric gauge theories with gauge group U(N) on R^3 x S^1, broken to N=1 due to a classical superpotential. In a previous paper, hep-th/0304061, we discussed how the low-energy quantum superpotential can be obtained by substituting the Lax matrix of the underlying integrable system directly into the classical superpotential. In this paper we prove algebraically that this recipe yields the correct factorization of the Seiberg-Witten curves, which is an important check of the conjecture. We will also give an independent proof using the algebraic-geometrical interpretation of the underlying integrable system.Comment: laTeX, 14 pages, uses AMSmat

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

Keratin 13 is a more specific marker of conjunctival epithelium than keratin 19

PurposeTo evaluate the expression patterns of cytokeratin (K) 12, 13, and 19 in normal epithelium of the human ocular surface to determine whether K13 could be used as a marker for conjunctival epithelium.MethodsTotal RNA was isolated from the human conjunctiva and central cornea. Those transcripts that had threefolds or higher expression levels in the conjunctiva than the cornea were identified using microarray technique. Expression levels of three known signature genes and of two conjunctival genes, K13 and K19 were confirmed by using quantitative real-time PCR (qRT-PCR). Protein expression of K12, K13, and K19 was confirmed by immunostaining with specific antibodies on histologic sections of human sclerocornea that contained the conjunctiva, limbus, and cornea and on impression cytology (IC) specimens of the cornea and conjunctiva from normal donors. Double staining of K13/K12 and K19/K12 on histologic sections and IC specimens was performed.ResultsThere were 337 transcripts that were preferentially expressed in the conjunctiva. K13 and K19 were among the top twenty transcripts in the conjunctiva and this preferential expression pattern of K13 and K19 was confirmed by qRT-PCR. Immunohistochemical studies showed that K13 was expressed at the posterior limbal epithelium and conjunctival epithelium but was totally absent in the cornea. K12 was expressed in the corneal and anterior limbal epithelia except for the basal layer and was absent from the conjunctiva. In contrast, K19 was detected in the corneal, limbal and conjunctival epithelia. Immunostaining of the IC specimens showed K12(+) epithelial cells in the corneal region, K13(+) cells in the conjunctival area, and K19(+) cells in the corneal and conjunctival specimens. Expression of K13 and K12 on the ocular surface was mutually exclusive on both the histologic and IC samples using double immunostaining.ConclusionsK13 is more specific to the conjunctival epithelial cells than K19 and potentially could be used as a marker to identify conjunctival epithelial cells in limbal stem cell deficiency

The Whitham Deformation of the Dijkgraaf-Vafa Theory

We discuss the Whitham deformation of the effective superpotential in the Dijkgraaf-Vafa (DV) theory. It amounts to discussing the Whitham deformation of an underlying (hyper)elliptic curve. Taking the elliptic case for simplicity we derive the Whitham equation for the period, which governs flowings of branch points on the Riemann surface. By studying the hodograph solution to the Whitham equation it is shown that the effective superpotential in the DV theory is realized by many different meromorphic differentials. Depending on which meromorphic differential to take, the effective superpotential undergoes different deformations. This aspect of the DV theory is discussed in detail by taking the N=1^* theory. We give a physical interpretation of the deformation parameters.Comment: 35pages, 1 figure; v2: one section added to give a physical interpretation of the deformation parameters, one reference added, minor corrections; v4: minor correction

Fatal bacteremia due to immotile Vibrio cholerae serogroup O21 in Vientiane, Laos – a case report

<p>Abstract</p> <p>Background</p> <p>Human infections with non-O1, non-O139 <it>V. cholerae </it>have been described from Laos. Elsewhere, non cholera-toxin producing, non-O1, non-O139 <it>V. cholerae </it>have been described from blood cultures and ascitic fluid, although they are exceedingly rare isolates.</p> <p>Case presentation</p> <p>We describe a farmer who died with <it>Vibrio cholerae </it>O21 bacteremia and peritonitis in Vientiane, Laos, after eating partially cooked apple snails (<it>Pomacea canaliculata</it>) and mussels (<it>Ligumia </it>species). The cultured <it>V. cholerae </it>were non-motile. PCR detected <it>ompW </it>and <it>toxR </it>gene regions but not the <it>ctxA, ompU, omp K </it>and <it>TCP </it>gene regions. Although the organisms lacked flagellae on scanning electron microscopy, they possessed the <it>Vibrio </it>flagellin <it>flaA </it>gene.</p> <p>Conclusion</p> <p>Severe bacteremic non-O1, non-O139 <it>V. cholerae </it>is reported from Laos. The organisms were unusual in being non-motile. They possessed the <it>Vibrio </it>flagellin <it>flaA </it>gene. Further research to determine the reasons for the non-motility and virulence is required.</p

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

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