RG flows from Spin(7), CY 4-fold and HK manifolds to AdS, Penrose limits and pp waves

We obtain explicit realizations of holographic renormalization group (RG) flows from M-theory, from E^{2,1} \times Spin(7) at UV to AdS_4 \times \tilde{S^7} (squashed S^7) at IR, from E^{2,1} \times CY4 at UV to AdS_4 \times Q^{1,1,1} at IR, and from E^{2,1} \times HK (hyperKahler) at UV to AdS_4 \times N^{0,1,0} at IR. The dual type IIA string theory configurations correspond to D2-D6 brane systems where D6 branes wrap supersymmetric four-cycles. We also study the Penrose limits and obtain the pp-wave backgrounds for the above configurations. Besides, we study some examples of non-supersymmetric and supersymmetric flows in five-dimensional gauge theories.Comment: 42 pages, 6 eps figures, typos and misprints correcte

A Massive Renormalizable Abelian Gauge Theory in 2+1 Dimensions

The standard formulation of a massive Abelian vector field in $2+1$ dimensions involves a Maxwell kinetic term plus a Chern-Simons mass term; in its place we consider a Chern-Simons kinetic term plus a Stuekelberg mass term. In this latter model, we still have a massive vector field, but now the interaction with a charged spinor field is renormalizable (as opposed to super renormalizable). By choosing an appropriate gauge fixing term, the Stuekelberg auxiliary scalar field decouples from the vector field. The one-loop spinor self energy is computed using operator regularization, a technique which respects the three dimensional character of the antisymmetric tensor $\epsilon_{\alpha\beta\gamma}$. This method is used to evaluate the vector self energy to two-loop order; it is found to vanish showing that the beta function is zero to two-loop order. The canonical structure of the model is examined using the Dirac constraint formalism.Comment: LaTeX, 17 pages, expanded reference list and discussion of relationship to previous wor

D-branes on AdS flux compactifications

We study D-branes in N=1 flux compactifications to AdS_4. We derive their supersymmetry conditions and express them in terms of background generalized calibrations. Basically because AdS has a boundary, the analysis of stability is more subtle and qualitatively different from the usual case of Minkowski compactifications. For instance, stable D-branes filling AdS_4 may wrap trivial internal cycles. Our analysis gives a geometric realization of the four-dimensional field theory approach of Freedman and collaborators. Furthermore, the one-to-one correspondence between the supersymmetry conditions of the background and the existence of generalized calibrations for D-branes is clarified and extended to any supersymmetric flux background that admits a time-like Killing vector and for which all fields are time-independent with respect to the associated time. As explicit examples, we discuss supersymmetric D-branes on IIA nearly Kaehler AdS_4 flux compactifications.Comment: 43 pages, 2 pictures, 1 table; v2: added references, color to figure and corrected typo in (6.21b

Jack superpolynomials with negative fractional parameter: clustering properties and super-Virasoro ideals

The Jack polynomials P_\lambda^{(\alpha)} at \alpha=-(k+1)/(r-1) indexed by certain (k,r,N)-admissible partitions are known to span an ideal I^{(k,r)}_N of the space of symmetric functions in N variables. The ideal I^{(k,r)}_N is invariant under the action of certain differential operators which include half the Virasoro algebra. Moreover, the Jack polynomials in I^{(k,r)}_N admit clusters of size at most k: they vanish when k+1 of their variables are identified, and they do not vanish when only k of them are identified. We generalize most of these properties to superspace using orthogonal eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland model known as Jack superpolynomials. In particular, we show that the Jack superpolynomials P_{\Lambda}^{(\alpha)} at \alpha=-(k+1)/(r-1) indexed by certain (k,r,N)-admissible superpartitions span an ideal {\mathcal I}^{(k,r)}_N of the space of symmetric polynomials in N commuting variables and N anticommuting variables. We prove that the ideal {\mathcal I}^{(k,r)}_N is stable with respect to the action of the negative-half of the super-Virasoro algebra. In addition, we show that the Jack superpolynomials in {\mathcal I}^{(k,r)}_N vanish when k+1 of their commuting variables are equal, and conjecture that they do not vanish when only k of them are identified. This allows us to conclude that the standard Jack polynomials with prescribed symmetry should satisfy similar clustering properties. Finally, we conjecture that the elements of {\mathcal I}^{(k,2)}_N provide a basis for the subspace of symmetric superpolynomials in N variables that vanish when k+1 commuting variables are set equal to each other.Comment: 36 pages; the main changes in v2 are : 1) in the introduction, we present exceptions to an often made statement concerning the clustering property of the ordinary Jack polynomials for (k,r,N)-admissible partitions (see Footnote 2); 2) Conjecture 14 is substantiated with the extensive computational evidence presented in the new appendix C; 3) the various tests supporting Conjecture 16 are reporte

Graft immaturity and safety concerns in transplanted human kidney organoids

For chronic kidney disease, regeneration of lost nephrons with human kidney organoids derived from induced pluripotent stem (iPS) cells is proposed to be an attractive potential therapeutic option. It remains unclear, however, whether organoids transplanted into kidneys in vivo would be safe or functional. Here, we purified kidney organoids and transplanted them beneath the kidney capsules of immunodeficient mice to test their safety and maturity. Kidney organoid grafts survived for months after transplantation and became vascularized from host mouse endothelial cells. Nephron-like structures in grafts appeared more mature than kidney organoids in vitro, but remained immature compared with the neighboring mouse kidney tissue. Ultrastructural analysis revealed filtration barrier-like structures, capillary lumens, and tubules with brush border in the transplanted kidney organoids, which were more mature than those of the kidney organoids in vitro but not as organized as adult mammalian kidneys. Immaturity was a common feature of three separate differentiation protocols by immunofluorescence analysis and single cell RNA sequencing. Stroma of transplanted kidney organoid grafts were filled with vimentin-positive mesenchymal cells, and chondrogenesis, cystogenesis, and stromal expansion were observed in the long term. Transcription profiles showed that long-term maintenance after kidney organoid transplantation induced transcriptomic reprogramming with prominent suppression of cell-cycle-related genes and upregulation of extracellular matrix organization. Our data suggest that kidney organoids derived from iPS cells may be transplantable but strategies to improve nephron differentiation and purity are required before they can be applied in humans as a therapeutic option.11Ysciescopuskc

Comments on D-brane Interactions in PP-wave Backgrounds

We calculate the interaction potential between widely separated D-branes in PP-wave backgrounds in string theory as well as in low-energy supergravity. Timelike and spacelike orientations are qualitatively different but in both cases the effective brane tensions and RR charges take the same values as in Minkowski space in accordance with the expectations from the sigma model perturbation theory.Comment: Latex, 22 pages. Typos corrected and a reference added, final versio

Holographic Uniformization

We derive and study supergravity BPS flow equations for M5 or D3 branes wrapping a Riemann surface. They take the form of novel geometric flows intrinsically defined on the surface. Their dual field-theoretic interpretation suggests the existence of solutions interpolating between an arbitrary metric in the UV and the constant-curvature metric in the IR. We confirm this conjecture with a rigorous global existence proof.Comment: 52 pages, 3 figure

Superstrings with Intrinsic Torsion

We systematically analyse the necessary and sufficient conditions for the preservation of supersymmetry for bosonic geometries of the form R^{1,9-d} \times M_d, in the common NS-NS sector of type II string theory and also type I/heterotic string theory. The results are phrased in terms of the intrinsic torsion of G-structures and provide a comprehensive classification of static supersymmetric backgrounds in these theories. Generalised calibrations naturally appear since the geometries always admit NS or type I/heterotic fivebranes wrapping calibrated cycles. Some new solutions are presented. In particular we find d=6 examples with a fibred structure which preserve N=1,2,3 supersymmetry in type II and include compact type I/heterotic geometries.Comment: 58 pages, LaTeX; v2: New section on solutions including an example with N=3 supersymmetry and discussion of heterotic compactifications. Details on conventions and references added. v3: added an explicit example of non-integrable product structure in Appendix C; some typos fixe

D3/D7 Inflationary Model and M-theory

A proposal is made for a cosmological D3/D7 model with a constant magnetic flux along the D7 world-volume. It describes an N=2 gauge model with Fayet-Iliopoulos terms and the potential of the hybrid P-term inflation. The motion of the D3-brane towards D7 in a phase with spontaneously broken supersymmetry provides a period of slow-roll inflation in the de Sitter valley, the role of the inflaton being played by the distance between D3 and D7-branes. After tachyon condensation a supersymmetric ground state is formed: a D3/D7 bound state corresponding to an Abelian non-linear (non-commutative) instanton. In this model the existence of a non-vanishing cosmological constant is associated with the resolution of the instanton singularity. We discuss a possible embedding of this model into a compactified M-theory setup.Comment: 30 pages, 4 figures, LaTeX; v2, minor typos corrected, one reference adde

Cosmological evolution of interacting dark energy in Lorentz violation

The cosmological evolution of an interacting scalar field model in which the scalar field interacts with dark matter, radiation, and baryon via Lorentz violation is investigated. We propose a model of interaction through the effective coupling $\bar{\beta}$. Using dynamical system analysis, we study the linear dynamics of an interacting model and show that the dynamics of critical points are completely controlled by two parameters. Some results can be mentioned as follows. Firstly, the sequence of radiation, the dark matter, and the scalar field dark energy exist and baryons are sub dominant. Secondly, the model also allows the possibility of having a universe in the phantom phase with constant potential. Thirdly, the effective gravitational constant varies with respect to time through $\bar{\beta}$. In particular, we consider a simple case where $\bar{\beta}$ has a quadratic form and has a good agreement with the modified $\Lambda$CDM and quintessence models. Finally, we also calculate the first post--Newtonian parameters for our model.Comment: 14 pages, published versio