One-loop effective potential in M4 x T2 with and without 't Hooft flux

We review the basic notions of compactification in the presence of a background flux. In extra-dimentional models with more than five dimensions, Scherk and Schwarz boundary conditions have to satisfy 't Hooft consistency conditions. Different vacuum configurations can be obtained, depending whether trivial or non-trivial 't Hooft flux is considered. The presence of the "magnetic" background flux provide, in addition, a mechanism for producing four-dimensional chiral fermions. Particularizing to the six-dimensional case, we calculate the one-loop effective potential for a U(N) gauge theory on M4 x T2. We firstly review the well known results of the trivial 't Hooft flux case, where one-loop contributions produce the usual Hosotani dynamical symmetry breaking. Finally we applied our result for describing, for the first time, the one-loop contributions in the non-trivial 't Hooft flux case

Constructing Lifshitz solutions from AdS

Under general assumptions, we show that a gravitational theory in d+1 dimensions admitting an AdS solution can be reduced to a d-dimensional theory containing a Lifshitz solution with dynamical exponent z=2. Working in a d=4, N=2 supergravity setup, we prove that if the AdS background is N=2 supersymmetric, then the Lifshitz geometry preserves 1/4 of the supercharges, and we construct the corresponding Killing spinors. We illustrate these results in examples from supersymmetric consistent truncations of type IIB supergravity, enhancing the class of known 4-dimensional Lifshitz solutions of string theory. As a byproduct, we find a new AdS4 x S1 x T(1,1) solution of type IIB.Comment: 29 pages, no figures; v2 minor corrections, a reference adde

Lifshitz black holes in string theory

We provide the first black hole solutions with Lifshitz asymptotics found in string theory. These are expected to be dual to models enjoying anisotropic scale invariance with dynamical exponent z=2 at finite temperature. We employ a consistent truncation of type IIB supergravity to four dimensions with an arbitrary 5-dimensional Einstein manifold times a circle as internal geometry. New interesting features are found that significantly differ from previous results in phenomenological models. In particular, small black holes are shown to be thermodynamically unstable, analogously to the usual AdS-Schwarzschild black holes, and extremality is never reached. This signals a possible Hawking-Page like phase transition at low temperatures.Comment: 19 pages, 7 figures. v2 references adde

The Level of the Transcription Factor Pax6 Is Essential for Controlling the Balance between Neural Stem Cell Self-Renewal and Neurogenesis

Neural stem cell self-renewal, neurogenesis, and cell fate determination are processes that control the generation of specific classes of neurons at the correct place and time. The transcription factor Pax6 is essential for neural stem cell proliferation, multipotency, and neurogenesis in many regions of the central nervous system, including the cerebral cortex. We used Pax6 as an entry point to define the cellular networks controlling neural stem cell self-renewal and neurogenesis in stem cells of the developing mouse cerebral cortex. We identified the genomic binding locations of Pax6 in neocortical stem cells during normal development and ascertained the functional significance of genes that we found to be regulated by Pax6, finding that Pax6 positively and directly regulates cohorts of genes that promote neural stem cell self-renewal, basal progenitor cell genesis, and neurogenesis. Notably, we defined a core network regulating neocortical stem cell decision-making in which Pax6 interacts with three other regulators of neurogenesis, Neurog2, Ascl1, and Hes1. Analyses of the biological function of Pax6 in neural stem cells through phenotypic analyses of Pax6 gain- and loss-of-function mutant cortices demonstrated that the Pax6-regulated networks operating in neural stem cells are highly dosage sensitive. Increasing Pax6 levels drives the system towards neurogenesis and basal progenitor cell genesis by increasing expression of a cohort of basal progenitor cell determinants, including the key transcription factor Eomes/Tbr2, and thus towards neurogenesis at the expense of self-renewal. Removing Pax6 reduces cortical stem cell self-renewal by decreasing expression of key cell cycle regulators, resulting in excess early neurogenesis. We find that the relative levels of Pax6, Hes1, and Neurog2 are key determinants of a dynamic network that controls whether neural stem cells self-renew, generate cortical neurons, or generate basal progenitor cells, a mechanism that has marked parallels with the transcriptional control of embryonic stem cell self-renewal