Principal Chiral Model without and with WZ term: Symmetries and Poisson-Lie T-Duality

Duality properties of the $SU(2)$ Principal Chiral Model are investigated starting from a one-parameter family of its equivalent Hamiltonian descriptions generated by a non-Abelian deformation of the cotangent space $T^*SU(2) \simeq SU(2) \ltimes \mathbb{R}^3$. The corresponding dual models are obtained through $O(3,3)$ duality transformations and result to be defined on the group $SB(2,\mathbb{C})$, which is the Poisson-Lie dual of $SU(2)$ in the Iwasawa decomposition of the Drinfel'd double $SL(2,\mathbb{C})=SU(2) \bowtie SB(2,\mathbb{C})$.These dual models provide an explicit realization of Poisson-Lie T-duality. A doubled generalized parent action is then built on the tangent space $TSL(2,\mathbb{C})$. Furthermore, a generalization of the $SU(2)$ PCM with a WZ term is shortly discussed.Comment: 25 pages, Contribution to the Proceedings of Corfu Summer Institute 2019 "Schools and Workshops on Elementary Particle Physics and Gravity

Jacobi sigma models

We introduce a two-dimensional sigma model on surfaces with boundary and target space a Jacobi manifold. The model yields a topological open string theory. In the Hamiltonian approach first class constraints are derived, which generate gauge invariance of the model under diffeomorphisms. By introducing a metric term, a non-topological sigma model is obtained, yielding a Polyakov action with metric and B-field, whose target space is a Jacobi manifold.Comment: 21 pages. Latex2e. Minor changes, references adde

Dissecting the heritable risk of breast cancer:From statistical methods to susceptibility genes

Decades of research have shown that rare highly penetrant mutations can promote tumorigenesis, but it is still unclear whether variants observed at high-frequency in the broader population could modulate the risk of developing cancer. Genome-wide Association Studies (GWAS) have generated a wealth of data linking single nucleotide polymorphisms (SNPs) to increased cancer risk, but the effect of these mutations are usually subtle, leaving most of cancer heritability unexplained. Understanding the role of high-frequency mutations in cancer can provide new intervention points for early diagnostics, patient stratification and treatment in malignancies with high prevalence, such as breast cancer. Here we review state-of-the-art methods to study cancer heritability using GWAS data and provide an updated map of breast cancer susceptibility loci at the SNP and gene level

The Effective Theory of Quantum Black Holes

We explore the quantum nature of black holes by introducing an effective framework that takes into account deviations from the classical results. The approach is based on introducing quantum corrections to the classical Schwarzschild geometry in a way that is consistent with the physical scales of the black hole and its classical symmetries. This is achieved by organizing the quantum corrections in inverse powers of a physical distance. By solving the system in a self-consistent way we show that the derived physical quantities, such as event horizons, temperature and entropy can be expressed in a well defined expansion in the inverse powers of the black hole mass. The approach captures the general form of the quantum corrections to black hole physics without requiring to commit to a specific model of quantum gravity.Comment: Revised version, added references, refined text and added explanatory footnote. 23 pages, 13 figure

Poisson-Lie T-Duality of WZW Model via Current Algebra Deformation

Poisson-Lie T-duality of the Wess-Zumino-Witten (WZW) model having the group manifold of $SU(2)$ as target space is investigated. The whole construction relies on the deformation of the affine current algebra of the model, the semi-direct sum $\mathfrak{su}(2)(\mathbb{R}) \, \dot{\oplus} \, \mathfrak{a}$, to the fully semisimple Kac-Moody algebra $\mathfrak{sl}(2,\mathbb{C})(\mathbb{R})$. A two-parameter family of models with $SL(2,\mathbb{C})$ as target phase space is obtained so that Poisson-Lie T-duality is realised as an $O(3,3)$ rotation in the phase space. The dual family shares the same phase space but its configuration space is $SB(2,\mathbb{C})$, the Poisson-Lie dual of the group $SU(2)$. A parent action with doubled degrees of freedom on $SL(2,\mathbb{C})$ is defined, together with its Hamiltonian description.Comment: 46 page

Foreword for Visualized Cancer Medicine: The era for dynamic visuals is here

We have seen in many circumstances of cancer research and clinical practice that the process itself is more critical and valuable than the result. For better presenting the natural movements of studied subject as well as the processes of medical intervention in treating patient, we proudly launch Visualized Cancer Medicine as a peer-reviewed publication platform covering all relevant topics in which videos play a critical role for presenting the results or the procedures. We appreciate the constant supports from our rigorous authors, dedicating editorial staff members, creative informative technology engineers, and enthusiastic readers. We hope that our small step of establishing Visualized Cancer Medicine for better scientific presentation would foster giant leaps of our understanding on cancer, which would subsequently benefit human being in many ways

N=1 Matter from Fractional Branes

We study a bound state of fractional D3-branes localized inside the world-volume of fractional D7-branes on the orbifold C^3/Z_2 x Z_2. We determine the open string spectrum that leads to N=1 U(N1)xU(N2)xU(N3)xU(N4) gauge theory with matter having the number of D7-branes as a flavor index. We derive the linearized boundary action of the D7-brane on this orbifold using the boundary state formalism and we discuss the tadpole cancellation. After computing the asymptotic expression of the supergravity solution the anomalies of the gauge theory are reproduced.Comment: LaTeX 20 pages, 1 figure, small changes and references adde

Fragility Fractures of the Acetabulum: Current Concepts for Improving Patients’ Outcomes

The incidence of fragility fractures of the acetabulum (FFA) is constantly increasing. Generally, these fractures are related to a fall on the greater trochanter involving the anterior column. The management of FFA is extremely difficult considering both patients’ comorbidities and poor bone quality. Both non-operative and several operative treatment protocols are available, and the choice among them is still ambiguous. The proposed surgical techniques for FFA [namely open reduction and internal fixation (ORIF), percutaneous fixation and total hip arthroplasty (THA)] are associated with a high complication rate. The treatment with the higher early mortality is the ORIF + THA, while the one with the lowest is the non-operative. However, at longer follow-up, this difference dreadfully change is becoming the opposite. Frequently ORIF, percutaneous fixation, and non-operative treatment need a subsequent re-operation through a THA. This latter could be extremely difficult, because of poor bone quality, acetabular mal union/non-union, bone gaps and hardware retention. However, the outcomes of each of the proposed treatment are mostly poor and controverted; therefore, a comprehensive patient evaluation and an accurate fracture description are required to appropriately manage acetabular fracture in the elderly