Peak reduction technique in commutative algebra

The "peak reduction" method is a powerful combinatorial technique with applications in many different areas of mathematics as well as theoretical computer science. It was introduced by Whitehead, a famous topologist and group theorist, who used it to solve an important algorithmic problem concerning automorphisms of a free group. Since then, this method was used to solve numerous problems in group theory, topology, combinatorics, and probably in some other areas as well. In this paper, we give a survey of what seems to be the first applications of the peak reduction technique in commutative algebra and affine algebraic geometry.Comment: survey; 10 page

Effects of common pesticides on prostaglandin D2 (PGD2) inhibition in SC5 mouse sertoli cells, evidence of binding at the cox-2 active site, and implications for endocrine disruption

Background: There are concerns that diminished prostaglandin action in fetal life could increase the risk of congenital malformations. Many endocrine-disrupting chemicals have been found to suppress prostaglandin synthesis, but to our knowledge, pesticides have never been tested for these effects. Objectives: We assessed the ability of pesticides that are commonly used in the European Union to suppress prostaglandin D2 (PGD2) synthesis. Methods: Changes in PGD2 secretion in juvenile mouse Sertoli cells (SC5 cells) were measured using an ELISA. Coincubation with arachidonic acid (AA) was conducted to determine the site of action in the PGD2 synthetic pathway. Molecular modeling studies were performed to assess whether pesticides identified as PGD2-active could serve as ligands of the cyclooxygenase-2 (COX-2) binding pocket. Results: The pesticides boscalid, chlorpropham, cypermethrin, cyprodinil, fenhexamid, fludioxonil, imazalil (enilconazole), imidacloprid, iprodione, linuron, methiocarb, o-phenylphenol, pirimiphos- methyl, pyrimethanil, and tebuconazole suppressed PGD2 production. Strikingly, some of these substances—o-phenylphenol, cypermethrin, cyprodinil, linuron, and imazalil (enilconazole)— showed potencies (IC50) in the range between 175 and 1,500 nM, similar to those of analgesics intended to block COX enzymes. Supplementation with AA failed to reverse this effect, suggesting that the sites of action of these pesticides are COX enzymes. The molecular modeling studies revealed that the COX-2 binding pocket can accommodate most of the pesticides shown to suppress PGD2 synthesis. Some of these pesticides are also capable of antagonizing the androgen receptor. Conclusions: Chemicals with structural features more varied than previously thought can suppress PGD2 synthesis. Our findings signal a need for in vivo studies to establish the extent of endocrinedisrupting effects that might arise from simultaneous interference with PGD2 signaling and androgen action

Hydrodynamics of fundamental matter

First and second order transport coefficients are calculated for the strongly coupled N=4 SYM plasma coupled to massless fundamental matter in the Veneziano limit. The results, including among others the value of the bulk viscosity and some relaxation times, are presented at next-to-leading order in the flavor contribution. The bulk viscosity is found to saturate Buchel's bound. This result is also captured by an effective single-scalar five-dimensional holographic dual in the Chamblin-Reall class and it is suggested to hold, in the limit of small deformations, for generic plasmas with gravity duals, whenever the leading conformality breaking effects are driven by marginally (ir)relevant operators. This proposal is then extended to other relations for hydrodynamic coefficients, which are conjectured to be universal for every non-conformal plasma with a dual Chamblin-Reall-like description. Our analysis extends to any strongly coupled gauge theory describing the low energy dynamics of Nc>>1 D3-branes at the tip of a generic Calabi-Yau cone. The fundamental fields are added by means of 1<<Nf<<Nc homogeneously smeared D7-branes.Comment: 24 pages. V2: Important improvements in the discussion of the results in section 1. References adde

D-brane potentials in the warped resolved conifold and natural inflation

In this paper we obtain a model of Natural Inflation from string theory with a Planckian decay constant. We investigate D-brane dynamics in the background of the warped resolved conifold (WRC) throat approximation of Type IIB string compactifications on Calabi-Yau manifolds. When we glue the throat to a compact bulk Calabi-Yau, we generate a D-brane potential which is a solution to the Laplace equation on the resolved conifold. We can exactly solve this equation, including dependence on the angular coordinates. The solutions are valid down to the tip of the resolved conifold, which is not the case for the more commonly used deformed conifold. This allows us to exploit the effect of the warping, which is strongest at the tip. We inflate near the tip using an angular coordinate of a D5-brane in the WRC which has a discrete shift symmetry, and feels a cosine potential, giving us a model of Natural Inflation, from which it is possible to get a Planckian decay constant whilst maintaining control over the backreaction. This is because the decay constant for a wrapped brane contains powers of the warp factor, and so can be made large, while the wrapping parameter can be kept small enough so that backreaction is under control.Comment: 41 pages, 3 appendices, 1 figure, PDFLaTex; various clarifications added along with a new appendix on b-axions and wrapped D5 branes;version matches the one published in JHE

On the algebraic structure of conditional events: 13th European conference, ECSQARU 2015, Compiègne, France, July 15-17, 2015.

This paper initiates an investigation of conditional measures as simple measures on conditional events. As a first step towards this end we investigate the construction of conditional algebras which allow us to distinguish between the logical properties of conditional events and those of the conditional measures which we can be attached to them. This distinction, we argue, helps us clarifying both concepts

The Constraints of Conformal Symmetry on RG Flows

If the coupling constants in QFT are promoted to functions of space-time, the dependence of the path integral on these couplings is highly constrained by conformal symmetry. We begin the present note by showing that this idea leads to a new proof of Zamolodchikov's theorem. We then review how this simple observation also leads to a derivation of the a-theorem. We exemplify the general procedure in some interacting theories in four space-time dimensions. We concentrate on Banks-Zaks and weakly relevant flows, which can be controlled by ordinary and conformal perturbation theories, respectively. We compute explicitly the dependence of the path integral on the coupling constants and extract the change in the a-anomaly (this agrees with more conventional computations of the same quantity). We also discuss some general properties of the sum rule found in arXiv:1107.3987 and study it in several examples.Comment: 25 pages, 5 figure

Shear Modes, Criticality and Extremal Black Holes

We consider a (2+1)-dimensional field theory, assumed to be holographically dual to the extremal Reissner-Nordstrom AdS(4) black hole background, and calculate the retarded correlators of charge (vector) current and energy-momentum (tensor) operators at finite momentum and frequency. We show that, similar to what was observed previously for the correlators of scalar and spinor operators, these correlators exhibit emergent scaling behavior at low frequency. We numerically compute the electromagnetic and gravitational quasinormal frequencies (in the shear channel) of the extremal Reissner-Nordstrom AdS(4) black hole corresponding to the spectrum of poles in the retarded correlators. The picture that emerges is quite simple: there is a branch cut along the negative imaginary frequency axis, and a series of isolated poles corresponding to damped excitations. All of these poles are always in the lower half complex frequency plane, indicating stability. We show that this analytic structure can be understood as the proper limit of finite temperature results as T is taken to zero holding the chemical potential fixed.Comment: 28 pages, 7 figures, added reference

The particle number in Galilean holography

Recently, gravity duals for certain Galilean-invariant conformal field theories have been constructed. In this paper, we point out that the spectrum of the particle number operator in the examples found so far is not a necessary consequence of the existence of a gravity dual. We record some progress towards more realistic spectra. In particular, we construct bulk systems with asymptotic Schrodinger symmetry and only one extra dimension. In examples, we find solutions which describe these Schrodinger-symmetric systems at finite density. A lift to M-theory is used to resolve a curvature singularity. As a happy byproduct of this analysis, we realize a state which could be called a holographic Mott insulator.Comment: 29 pages, 1 rudimentary figure; v2: typo in eqn (3.4), added comments and ref

On renormalization group flows and the a-theorem in 6d

We study the extension of the approach to the a-theorem of Komargodski and Schwimmer to quantum field theories in d=6 spacetime dimensions. The dilaton effective action is obtained up to 6th order in derivatives. The anomaly flow a_UV - a_IR is the coefficient of the 6-derivative Euler anomaly term in this action. It then appears at order p^6 in the low energy limit of n-point scattering amplitudes of the dilaton for n > 3. The detailed structure with the correct anomaly coefficient is confirmed by direct calculation in two examples: (i) the case of explicitly broken conformal symmetry is illustrated by the free massive scalar field, and (ii) the case of spontaneously broken conformal symmetry is demonstrated by the (2,0) theory on the Coulomb branch. In the latter example, the dilaton is a dynamical field so 4-derivative terms in the action also affect n-point amplitudes at order p^6. The calculation in the (2,0) theory is done by analyzing an M5-brane probe in AdS_7 x S^4. Given the confirmation in two distinct models, we attempt to use dispersion relations to prove that the anomaly flow is positive in general. Unfortunately the 4-point matrix element of the Euler anomaly is proportional to stu and vanishes for forward scattering. Thus the optical theorem cannot be applied to show positivity. Instead the anomaly flow is given by a dispersion sum rule in which the integrand does not have definite sign. It may be possible to base a proof of the a-theorem on the analyticity and unitarity properties of the 6-point function, but our preliminary study reveals some difficulties.Comment: 41 pages, 5 figure