Euclidean quantum M5 brane theory on S1×S5S^1 \times S^5

We consider Euclidean quantum M5 brane theory on $S^1\times S^5$. Dimensional reduction along $S^1$ gives a 5d SYM on $S^5$. We derive this 5d SYM theory from a classical Lorentzian M5 brane Lagrangian on $S^1 \times S^5$, where $S^1$ is a timelike circle of radius $T$, by performing a Scherk-Schwarz reduction along $S^1$ followed by Wick rotation of $T$.Comment: 31 page

Abelian M5-brane on S6S^6

We study the abelian M5 brane on $S^6$. From the spectrum we extract a series expansion for the heat kernel. In particular we determine the normalization for the coefficient $a$ in the M5 brane conformal anomaly. When we compare our result with what one gets by computing the Hadamard-Minakshisundaram-DeWitt-Seeley coefficients from local curvature invariants on $S^6$, we first find a mismatch of one unit. This mismatch is due to an overcounting of one zero mode. After subtracting this contribution, we finally find agreement. We perform dimensional reduction along a singular circle fiber to five dimensions where we find the conformal anomaly vanishes.Comment: 40 page

A short representation of the six-dimensional (2, 0) algebra

We construct a BPS-saturated representation of the six-dimensional (2, 0) algebra with a certain non-zero value of the `central' charge. This representation is naturally carried by strings with internal degrees of freedom rather than by point particles. Upon compactification on a circle, it reduces to a massive vector multiplet in five dimensions. We also construct quantum fields out of the creation and annihilation operators of the states of this representation, and show how they give rise to a conserved two-form current that can be coupled to a tensor multiplet. We hope that these results may be relevant for understanding the degrees of freedom associated with strings in interacting (2, 0) theories.Comment: 11 page

Determinants of Firm R&D: Evidence from Swedish Firm Level Data

This paper analyses determinants of firm R&D and if predictions from the model of creative destruction is supported by data using matched employer-employee longitudinal data on the Swedish manufacturing industry. In particular, we analyse the impact of competition on R&D. Using various measures of competition, results indicate that competition is likely to contract firm R&D expenditures. We do not find strong support for the expected large-firm advantage in R&D through scale effects. In addition, firm R&D appears positively correlated with its own export and to the R&D-intensity of other firms within the same concern, indicating the existence of knowledge spillovers.R&D; Competition; Firm size; Spillovers

Is There Really an Inverted U-shaped Relation Between Competition and R&D?

We test whether predictions of the Aghion and Howitt (2004) model are supported by firm level data. In particular, we analyze if there is an inverted U-shaped relation between competition and R&D. Results show that the inverted U-shaped relation is supported by the Herfindahl index but not by the price cost margin. Using the Herfindahl index results suggest that breaking up monopolies increases R&D while further increases in competition most likely leads to reduced R&D. Comparing different estimators, we find that time-series based estimators typically result in less clear-cut results, probably driven by a lack of time series variation in measures of competition.R&D; Competition; Firm size; Spillovers

Is There Really an Inverted U-shaped Relation Between Competition and R&D?

We test whether predictions of the Aghion and Howitt (2004) model are supported by firm level data. In particular, we analyze if there is an inverted U-shaped relation between competition and R&D. Results show that the inverted U-shaped relation is supported by the Herfindahl index but not by the price cost margin. Using the Herfindahl index results suggest that breaking up monopolies increases R&D while further increases in competition most likely leads to reduced R&D. Comparing different estimators, we find that time-series based estimators typically result in less clear-cut results, probably driven by a lack of time series variation in measures of competition.R&D; competition; firm size; spillovers

Partially twisted superconformal M5 brane in R-symmetry gauge field backgrounds

We obtain the action for a curved superconformal abelian M5 brane with the background R-symmetry gauge field turned on. We then restrict ourselves to superconformal M5 brane on a sphere times flat Minkowski space. We choose R-symmetry SO(1,4) instead of SO(5), which enables us to partially twist on Minkowski space and replace it by some curved Lorentzian manifold. We obtain M5 brane actions on $M_{1,1} \times S^4$ and $M_{1,2} \times S^3$ where actions and all fields, including the background gauge field, are real. Dimensional reduction along time gives real 5d SYM actions with nonabelian generalizations.Comment: 31 pages, a discussion on unitarity is adde

Selfdual strings and loop space Nahm equations

We give two independent arguments why the classical membrane fields should be loops. The first argument comes from how we may construct selfdual strings in the M5 brane from a loop space version of the Nahm equations. The second argument is that there appears to be no infinite set of finite-dimensional Lie algebras (such as $su(N)$ for any $N$) that satisfies the algebraic structure of the membrane theory.Comment: 28 pages, various additional comment