Classical integrability in the BTZ black hole

Using the fact the BTZ black hole is a quotient of AdS_3 we show that classical string propagation in the BTZ background is integrable. We construct the flat connection and its monodromy matrix which generates the non-local charges. From examining the general behaviour of the eigen values of the monodromy matrix we determine the set of integral equations which constrain them. These equations imply that each classical solution is characterized by a density function in the complex plane. For classical solutions which correspond to geodesics and winding strings we solve for the eigen values of the monodromy matrix explicitly and show that geodesics correspond to zero density in the complex plane. We solve the integral equations for BMN and magnon like solutions and obtain their dispersion relation. Finally we show that the set of integral equations which constrain the eigen values of the monodromy matrix can be identified with the continuum limit of the Bethe equations of a twisted SL(2, R) spin chain at one loop.Comment: 45 pages, Reference added, typos corrected, discussion on geodesics improved to include all geodesic

Large Representation Recurrences in Large N Random Unitary Matrix Models

In a random unitary matrix model at large N, we study the properties of the expectation value of the character of the unitary matrix in the rank k symmetric tensor representation. We address the problem of whether the standard semiclassical technique for solving the model in the large N limit can be applied when the representation is very large, with k of order N. We find that the eigenvalues do indeed localize on an extremum of the effective potential; however, for finite but sufficiently large k/N, it is not possible to replace the discrete eigenvalue density with a continuous one. Nonetheless, the expectation value of the character has a well-defined large N limit, and when the discreteness of the eigenvalues is properly accounted for, it shows an intriguing approximate periodicity as a function of k/N.Comment: 24 pages, 11 figure

Thermodynamics of Large N Gauge Theories with Chemical Potentials in a 1/D Expansion

In order to understand thermodynamical properties of N D-branes with chemical potentials associated with R-symmetry charges, we study a one dimensional large N gauge theory (bosonic BFSS type model) as a first step. This model is obtained through a dimensional reduction of a 1+D dimensional SU(N) Yang-Mills theory and we use a 1/D expansion to investigate the phase structure. We find three phases in the \mu-T plane. We also show that all the adjoint scalars condense at large D and obtain a mass dynamically. This dynamical mass protects our model from the usual perturbative instability of massless scalars in a non-zero chemical potential. We find that the system is at least meta-stable for arbitrary large values of the chemical potentials in D \to \infty limit. We also explore the existence of similar condensation in higher dimensional gauge theories in a high temperature limit. In 2 and 3 dimensions, the condensation always happens as in one dimensional case. On the other hand, if the dimension is higher than 4, there is a critical chemical potential and the condensation happens only if the chemical potentials are below it.Comment: 37 pages, 4 figures; v2: minor corrections, references added; v3: minor corrections, to appear in JHE

The dual string sigma-model of the SU_q(3) sector

In four-dimensional N=4 super Yang-Mills (SYM) the SU(3) sub-sector spanned by purely holomorphic fields is isomorphic to the corresponding mixed one spanned by both holomorphic and antiholomorphic fields. This is no longer the case when one considers the marginally deformed N=4 SYM. The mixed SU(3) sector marginally deformed by a complex parameter beta, i.e. SU_q(3) with q=e^{2 i\pi\beta}, has been shown to be integrable at one-loop hep-th/0703150, while it is not the case for the corresponding purely holomorphic one. Moreover, the marginally deformed N=4 SYM also has a gravity dual constructed by Lunin and Maldacena in hep-th/0502086. However, the mixed SU_q(3) sector has not been studied from the supergravity point of view. Hence in this note, for the case of purely imaginary marginal $\beta$-deformations, we compute the superstring SU_q(3) \sigma-model in the fast spinning string limit and show that, for rational spinning strings, it reproduces the energy computed via Bethe equations.Comment: 20 page

Effect of Na content and hydration on the excitation spectrum of the cobaltite Na_xCoO_2 yH_2O

We report on a Raman scattering study on the superconducting cobaltite $Na_xCoO_2\cdot yH_2O$ as function of Na content and hydration (x$\approx$1/3, 3/4 and y$\approx$0, 2/3, 4/3). The observed phonon scattering and scattering continua are analyzed in terms of lattice strain due to the structural misfit and disorder. Hydration, due to the intercalation of one or two $H_2O$ layers, releases a part of this strain. Our Raman data suggest a connection between disorder on the partly occupied Na sites, the split off of the $a_{1g}$ level from the other $t_{2g}$ states of $Co^{4+}$ and superconductivity.Comment: 10 pages, 4 figures, for further information see http://www.peter-lemmens.d

Weak coupling large-N transitions at finite baryon density

We study thermodynamics of free SU(N) gauge theory with a large number of colours and flavours on a three-sphere, in the presence of a baryon number chemical potential. Reducing the system to a holomorphic large-N matrix integral, paying specific attention to theories with scalar flavours (squarks), we identify novel third-order deconfining phase transitions as a function of the chemical potential. These transitions in the complex large-N saddle point configurations are interpreted as "melting" of baryons into (s)quarks. They are triggered by the exponentially large (~ exp(N)) degeneracy of light baryon-like states, which include ordinary baryons, adjoint-baryons and baryons made from different spherical harmonics of flavour fields on the three-sphere. The phase diagram of theories with scalar flavours terminates at a phase boundary where baryon number diverges, representing the onset of Bose condensation of squarks.Comment: 38 pages, 7 figure

Spinning strings and integrable spin chains in the AdS/CFT correspondence

In this introductory review we discuss dynamical tests of the AdS_5 x S^5 string/N=4 super Yang-Mills duality. After a brief introduction to AdS/CFT we argue that semiclassical string energies yield information on the quantum spectrum of the string in the limit of large angular momenta on the S^5. The energies of the folded and circular spinning string solutions rotating on a S^3 within the S^5 are derived, which yield all loop predictions for the dual gauge theory scaling dimensions. These follow from the eigenvalues of the dilatation operator of N=4 super Yang-Mills in a minimal SU(2) subsector and we display its reformulation in terms of a Heisenberg s=1/2 spin chain along with the coordinate Bethe ansatz for its explicit diagonalization. In order to make contact to the spinning string energies we then study the thermodynamic limit of the one-loop gauge theory Bethe equations and demonstrate the matching with the folded and closed string result at this loop order. Finally the known gauge theory results at higher-loop orders are reviewed and the associated long-range spin chain Bethe ansatz is introduced, leading to an asymptotic all-loop conjecture for the gauge theory Bethe equations. This uncovers discrepancies at the three-loop order between gauge theory scaling dimensions and string theory energies and the implications of this are discussed. Along the way we comment on further developments and generalizations of the subject and point to the relevant literature.Comment: 40 pages, invited contribution to Living Reviews in Relativity. v2: improvements in the text and references adde

Histological validation of diagnoses of thyroid cancer among adults in the registries of Belarus and the Ukraine

In order to evaluate the diagnostic reliability of the thyroid cancers listed in adult registries from the Ukraine and Belarus, a histological review was organised of 327 randomly selected thyroid carcinoma cases diagnosed between 1960 and 1999. A final diagnosis was reached at a 5-day consensus conference by six pathologists who met around a multiheaded microscope. The study concluded with a comparison between the final diagnosis and the initial diagnosis. The pathologists agreed with the initial diagnosis of malignancy in 286 cases (88%). A final diagnosis of papillary, follicular or medullary thyroid carcinoma was reached in 86, 4, and 6% of the cases respectively. In 2.8% of the cases reviewed, diagnostic discrepancies persisted. The percentage of agreement between the final diagnosis and the initial diagnosis was 93%, with a weighted κ-statistic of 0.61 (confidence interval 95% (CI 95%): [0.45-0.77]). In all, 89% of the 286 confirmed cancer cases were in agreement for the type of cancer, with a κ-statistic of 0.56 (CI95%: [0.43-0.69]). The level of agreement differed according to cancer categories, with concordance rates of 94, 40 and 33% for papillary, follicular and medullary thyroid carcinomas respectively. The low prevalence of follicular thyroid carcinomas in the adult population studied calls for further exploration. The discrepancies and classification difficulties encountered were analysed. © 2003 Cancer Research UK

Lymphoepithelioma-like carcinoma of the vulva, an underrecognized entity? Case report with a single inguinal micrometastasis detected by sentinel node technique

This report describes an unusual EBV-negative lymphoepithelioma-like carcinoma of the vulva in a 73-year-old patient. The lesion was localised at the right minor labium and was resected by partial vulvectomy. A synchronous sentinel lymph node biopsy revealed a single micrometastasis in the right inguinal region, which prompted local radiotherapy. Follow-up nine months later showed only slight vulvar atrophy, without signs of local recurrence or distant metastases

Identification of a large rearrangement in CYLD as a cause of familial cylindromatosis

Pathogenic mutations in CYLD can be identified in patients affected with Brooke-Spiegler syndrome, (Familial) Cylindromatosis or multiple familial trichoepithelioma. To date, only technologies which are able to identify small point mutations in CYLD, such as sequence and WAVE analysis, were used. Here we describe the identification of a larger rearrangement identified by Quantitative PCR analysis of CYLD, indicating that a combination of these technologies is necessary when searching for pathogenic mutations in CYLD