Factorizations of Elements in Noncommutative Rings: A Survey

We survey results on factorizations of non zero-divisors into atoms (irreducible elements) in noncommutative rings. The point of view in this survey is motivated by the commutative theory of non-unique factorizations. Topics covered include unique factorization up to order and similarity, 2-firs, and modular LCM domains, as well as UFRs and UFDs in the sense of Chatters and Jordan and generalizations thereof. We recall arithmetical invariants for the study of non-unique factorizations, and give transfer results for arithmetical invariants in matrix rings, rings of triangular matrices, and classical maximal orders as well as classical hereditary orders in central simple algebras over global fields.Comment: 50 pages, comments welcom

A Soluble String Theory of Hadrons

We consider Penrose limits of the Klebanov-Strassler and Maldacena-Nunez holographic duals to N =1 supersymmetric Yang-Mills. By focusing in on the IR region we obtain exactly solvable string theory models. These represent the nonrelativistic motion and low-lying excitations of heavy hadrons with mass proportional to a large global charge. We argue that these hadrons, both physically and mathematically, take the form of heavy nonrelativistic strings; we term them "annulons." A simple toy model of a string boosted along a compact circle allows us considerable insight into their properties. We also calculate the Wilson loop carrying large global charge and show the effect of confinement is quadratic, not linear, in the string tension.Comment: 40 pages, 1 figure; v2: typos correcte

Baldness/delocalization in intersecting brane systems

Marginally bound systems of two types of branes are considered, such as the prototypical case of Dp+4 branes and Dp branes. As the transverse separation between the two types of branes goes to zero, different behaviour occurs in the supergravity solutions depending on p; no-hair theorems result for p<=1 only. Within the framework of the AdS/CFT correspondence, these supergravity no-hair results are understood as dual manifestations of the Coleman-Mermin-Wagner theorem. Furthermore, the rates of delocalization for p<=1 are matched in a scaling analysis. Talk given at ``Strings '99''; based on hep-th/9903213 with D. Marolf.Comment: LaTeX, 10 pages, 1 figure; contribution to Strings'99 proceeding

Semiclassical quantization of Rotating Strings in Pilch-Warner geometry

Some of the recent important developments in understanding string/ gauge dualities are based on the idea of highly symmetric motion of ``string solitons'' in $AdS_5\times S^5$ geometry originally suggested by Gubser, Klebanov and Polyakov. In this paper we study symmetric motion of certain string configurations in so called Pilch-Warner geometry. The two-form field $A_2$ breaks down the supersymmetry to $\mathcal{N}=1$ but for the string configurations considered in this paper the classical values of the energy and the spin are the same as for string in $AdS\times S^5$. Although trivial at classical level, the presence of NS-NS antisymmetric field couples the fluctuation modes that indicates changes in the quantum corrections to the energy spectrum. We compare our results with those obtained in the case of pp-wave limit in hep-th/0206045.Comment: 31 pages, no figures, v2 - a few typos correcte

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

Can holography reproduce the QCD Wilson line?

Recently a remarkable agreement was found between lattice simulations of long Wilson lines and behavior of the Nambu Goto string in flat space-time. However, the latter fails to fit the short distance behavior since it admits a tachyonic mode for a string shorter than a critical length. In this paper we examine the question of whether a classical holographic Wilson line can reproduce the lattice results for Wilson lines of any length. We determine the condition on the the gravitational background to admit a Coulombic potential at short distances. We analyze the system using three different renormalization schemes. We perform an explicit best fit comparison of the lattice results with the holographic models based on near extremal D3 and D4 branes, non-critical near extremal AdS6 model and the Klebanov Strassler model. We find that all the holographic models examined admit after renormalization a constant term in the potential. We argue that the curves of the lattice simulation also have such a constant term and we discuss its physical interpretation

Branes and fluxes in special holonomy manifolds and cascading field theories

We conduct a study of holographic RG flows whose UV is a theory in 2+1 dimensions decoupled from gravity, and the IR is the N=6,8 superconformal fixed point of ABJM. The solutions we consider are constructed by warping the M-theory background whose eight spatial dimensions are manifolds of special holonomies sp(1) times sp(1) and spin(7). Our main example for the spin(7) holonomy manifold is the A8 geometry originally constructed by Cvetic, Gibbons, Lu, and Pope. On the gravity side, our constructions generalize the earlier construction of RG flow where the UV was N=3 Yang-Mills-Chern-Simons matter system and are simpler in a number of ways. Through careful consideration of Page, Maxwell, and brane charges, we identify the discrete and continuous parameters characterizing each system. We then determine the range of the discrete data, corresponding to the flux/rank for which the supersymmetry is unbroken, and estimate the dynamical supersymmetry breaking scale as a function of these data. We then point out the similarity between the physics of supersymmetry breaking between our system and the system considered by Maldacena and Nastase. We also describe the condition for unbroken supersymmetry on class of construction based on a different class of spin(7) manifolds known as B8 spaces whose IR is different from that of ABJM and exhibit some interesting features.Comment: 51 pages, 12 figures. Update in quantization of G4 on B8 in equations (5.12) and (5.13

Screening effects on meson masses from holography

We study the spectra of scalar and vector mesons in four dimensional strongly coupled SQCD-like theories in the Veneziano limit. The gauge theories describe the low energy dynamics of intersecting D3 and D7-branes on the singular and deformed conifold and their strong coupling regime can be explored by means of dual fully backreacted supergravity backgrounds. The mesons we focus on are dual to fluctuations of the worldvolume gauge field on a probe D7-brane in these backgrounds. As we will comment in detail, the general occurrence of various UV pathologies in the D3-D7 set-ups under study, forces us to adapt the standard holographic recipes to theories with intrinsic cutoffs. Just as for QED, the low energy spectra for mesonic-like bound states will be consistent and largely independent of the UV cutoffs. We will study in detail how these spectra vary with the number of the fundamental sea flavors and their mass.Comment: 30 pages + appendices, 10 figures; v2: subsection 3.3.3 and some comments adde

Intracerebroventricular Administration of Neuropeptide Y Induces Hepatic Insulin Resistance via Sympathetic Innervation

OBJECTIVE—We recently showed that intracerebroventricular infusion of neuropeptide Y (NPY) hampers inhibition of endogenous glucose production (EGP) by insulin in mice. The downstream mechanisms responsible for these effects of NPY remain to be elucidated. Therefore, the aim of this study was to establish whether intracerebroventricular NPY administration modulates the suppressive action of insulin on EGP via hepatic sympathetic or parasympathetic innervation

Effects of amantadine on circulating neurotransmitters in healthy subjects

Considering that glutamatergic axons innervate the C1(Ad) medullary nuclei, which are responsible for the excitation of the peripheral adrenal glands, we decided to investigate catecholamines (noradrenaline, adrenaline and dopamine) plus indolamines (plasma serotonin and platelet serotonin) at the blood level, before and after a small oral dose of amantadine, a selective NMDA antagonist. We found that the drug provoked a selective enhancement of noradrenaline plus a minimization of adrenaline, dopamine, plasma serotonin and platelet serotonin circulating levels. Significant enhancement of diastolic blood pressure plus reduction of systolic blood pressure and heart rate paralleled the circulating parameter changes. The above findings allow us to postulate that the drug was able to enhance the peripheral neural sympathetic activity. Minimization of both adrenal sympathetic and parasympathetic activities was also registered after the amantadine challenge. The above findings supported the postulation that this drug should be a powerful therapeutic tool for treating diseases affected by adrenal sympathetic hyperactivity