Large N and double scaling limits in two dimensions

Recently, the author has constructed a series of four dimensional non-critical string theories with eight supercharges, dual to theories of light electric and magnetic charges, for which exact formulas for the central charge of the space-time supersymmetry algebra as a function of the world-sheet couplings were obtained. The basic idea was to generalize the old matrix model approach, replacing the simple matrix integrals by the four dimensional matrix path integrals of N=2 supersymmetric Yang-Mills theory, and the Kazakov critical points by the Argyres-Douglas critical points. In the present paper, we study qualitatively similar toy path integrals corresponding to the two dimensional N=2 supersymmetric non-linear sigma model with target space CP^n and twisted mass terms. This theory has some very strong similarities with N=2 super Yang-Mills, including the presence of critical points in the vicinity of which the large n expansion is IR divergent. The model being exactly solvable at large n, we can study non-BPS observables and give full proofs that double scaling limits exist and correspond to universal continuum limits. A complete characterization of the double scaled theories is given. We find evidence for dimensional transmutation of the string coupling in some non-critical string theories. We also identify en passant some non-BPS particles that become massless at the singularities in addition to the usual BPS states.Comment: 38 pages, including an introductory section that makes the paper self-contained, two figures and one appendix; v2: typos correcte

Glueball operators and the microscopic approach to N=1 gauge theories

We explain how to generalize Nekrasov's microscopic approach to N=2 gauge theories to the N=1 case, focusing on the typical example of the U(N) theory with one adjoint chiral multiplet X and an arbitrary polynomial tree-level superpotential Tr W(X). We provide a detailed analysis of the generalized glueball operators and a non-perturbative discussion of the Dijkgraaf-Vafa matrix model and of the generalized Konishi anomaly equations. We compute in particular the non-trivial quantum corrections to the Virasoro operators and algebra that generate these equations. We have performed explicit calculations up to two instantons, that involve the next-to-leading order corrections in Nekrasov's Omega-background.Comment: 38 pages, 1 figure and 1 appendix included; v2: typos and the list of references corrected, version to appear in JHE

The Proof of the Dijkgraaf-Vafa Conjecture and application to the mass gap and confinement problems

Using generalized Konishi anomaly equations, it is known that one can express, in a large class of supersymmetric gauge theories, all the chiral operators expectation values in terms of a finite number of a priori arbitrary constants. We show that these constants are fully determined by the requirement of gauge invariance and an additional anomaly equation. The constraints so obtained turn out to be equivalent to the extremization of the Dijkgraaf-Vafa quantum glueball superpotential, with all terms (including the Veneziano-Yankielowicz part) unambiguously fixed. As an application, we fill non-trivial gaps in existing derivations of the mass gap and confinement properties in super Yang-Mills theories.Comment: 31 pages, 1 figure; v2: typos corrected; references, a note on Kovner-Shifman vacua (section 4.3) and a few clarifying comments in Section 3 added; v3: cosmetic changes, JHEP versio

Firm'investment forecast: An indicator of changes in expectations in industrial investment survey

The quarterly industrial investment survey constitutes one of the main sources of information for the short-term economic analysis of industrial firms investment. However, its main questions are annual. Therefore, the use of this surveys results for the forecasting of investment on a quarterly basis requires some specific statistical treatment. This paper presents a quarterly indicator based on the changes in industrial entrepreneurs expectations as regards annual investment. This indicator derives from the estimation of the successive adaptations of entrepreneurs investment plans as times goes by, depending on the evolutions of short-term macroeconomic activity ; it proves to be strongly correlated with the fluctuations of the entrepreneurs investment growth rate (as is measured in the French Quarterly Accounts). Moreover, the indicator is available about three months ahead with respect to the first results release of the quarterly national accounts. The probability distributions of changes in expectations are not gaussian (due to heavy tails and strong concentrations near zero). Consequently, robust estimation methods for extreme observations were performed. Due to the presence of heteroskedasticity, we choosed to apply the Quasi-Generalized M-estimator» method.Firms investment, short-term forecasting, business tendency surveys, extreme values, adaptive M-regression, Quasi-Generalized M-estimator

Microscopic quantum superpotential in N=1 gauge theories

We consider the N=1 super Yang-Mills theory with gauge group U(N), adjoint chiral multiplet X and tree-level superpotential Tr W(X). We compute the quantum effective superpotential W_mic as a function of arbitrary off-shell boundary conditions at infinity for the scalar field X. This effective superpotential has a remarkable property: its critical points are in one-to-one correspondence with the full set of quantum vacua of the theory, providing in particular a unified picture of solutions with different ranks for the low energy gauge group. In this sense, W_mic is a good microscopic effective quantum superpotential for the theory. This property is not shared by other quantum effective superpotentials commonly used in the literature, like in the strong coupling approach or the glueball superpotentials. The result of this paper is a first step in extending Nekrasov's microscopic derivation of the Seiberg-Witten solution of N=2 super Yang-Mills theories to the realm of N=1 gauge theories.Comment: 23 pages, 1 figure; typos corrected, version to appear in JHE

Update On The Code Intercomparison and Benchmark For Muon Fluence and Absorbed Dose Induced By An 18-GeV Electron Beam After Massive Iron Shielding

In 1974, Nelson, Kase and Svensson published an experimental investigation on muon shielding around SLAC high-energy electron accelerators. They measured muon fluence and absorbed dose induced by 14 and 18 GeV electron beams hitting a copper/water beamdump and attenuated in a thick steel shielding. In their paper, they compared the results with the theoretical models available at that time. In order to compare their experimental results with present model calculations, we use the modern transport Monte Carlo codes MARS15, FLUKA2011 and GEANT4 to model the experimental setup and run simulations. The results are then compared between the codes, and with the SLAC data.Comment: 14 pp. Presented paper at the 13th Meeting of the task-force on Shielding aspects of Accelerators, Targets and Irradiation Facilities (SATIF-13), HZDR, October 10-12, 2016, Dresden, Germany. arXiv admin note: substantial text overlap with arXiv:1502.0168

Hadronic interactions of primary cosmic rays with the FLUKA code

The measured fluxes of secondary particles produced by the interactions of cosmic rays with the astronomical environment represent a powerful tool to infer some properties of primary cosmic rays. In this work we investigate the production of secondary particles in inelastic hadronic interactions between several cosmic rays species of projectiles and different target nuclei of the interstellar medium. The yields of secondary particles have been calculated with the FLUKA simulation package, that provides with very good accuracy the energy distributions of secondary products in a large energy range. An application to the propagation and production of secondaries in the Galaxy is presented.Comment: 8 pages, 4 figures; Contribution to the 34th International Cosmic Ray Conference, July 30 to August 6, The Hague, Netherlands; fixing a typo in the y-axis label of Fig.

Balance of opinion What about missing the weights?

Due to their early release, Business Tendency Surveys (BTS) are widely used in short term forecasting. Their questions are mainly qualitative; answers are most often used to calculate balances of opinions, which are defined as the difference between the proportions of positive answers with respect to the negative ones. These indicators are then used by forecasters as explanatory variables in econometric models. The balances of opinions are generally weighted with the firm size. However, there is no theoretical evidence of the efficiency of this kind of weighting. We propose here a model which aims at determining optimum weights; these weights should allow us to optimize the forecast of the macroeconomic variable. According to our analysis, the weights have to grow less than proportionally with the firm size. This conclusion is empirically tested through several examples derived from the French Industry BTS.Business Tendency Surveys, quantification, balance of opinion, short-term forecasting