We apply the Schrödinger functional method to the Abelian gauge theory in three dimensions with N f = 2 four-component fermions. We find that the calculated beta function does not cross zero in the range of coupling we study. This implies that the theory exhibits confinement and mass generation, rather than a conformal infared regime.

When analyzed by standard statistical methods, the time series of the daily return of financial indices appear to behave as Markov random series with no apparent temporal order or memory. This empirical result seems to be counter intuitive since investor are influenced by both short and long term past market behaviors. Consequently much effort has been devoted to unveil hidden temporal order in the market dynamics. Here we show that temporal order is hidden in the series of the variance of the stocks volatility. First we show that the correlation between the variances of the daily returns and means of segments of these time series is very large and thus cannot be the output of random series, unless it has some temporal order in it. Next we show that while the temporal order does not show in the series of the daily return, rather in the variation of the corresponding volatility series. More specifically, we found that the behavior of the shuffled time series is equivalent to that of a random time series, while that of the original time series have large deviations from the expected random behavior, which is the result of temporal structure. We found the same generic behavior in 10 different stock markets from 7 different countries. We also present analysis of specially constructed sequences in order to better understand the origin of the observed temporal order in the market sequences. Each sequence was constructed from segments with equal number of elements taken from algebraic distributions of three different slopes.

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We have carried out a Schrödinger-functional calculation for the Abelian gauge theory with N f = 2 four-component fermions in three dimensions. We find no fixed point in the beta function, meaning that the theory is confining rather than conformal.