Infrared properties of boundaries in 1-d quantum systems

Details Infrared properties of boundaries in 1-d quantum systems Infrared properties of boundaries in 1-d quantum systems

2005-12-01

arxiv.org/abs/hep-th/0512023v1

J.Stat.Phys.0603:P014,2006

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, Latex

Scientific paper

10.1088/1742-5468/2006/03/P03014

We present some partial results on the general infrared behavior of bulk-critical 1-d quantum systems with boundary. We investigate whether the boundary entropy, s(T), is always bounded below as the temperature T decreases towards 0, and whether the boundary always becomes critical in the IR limit. We show that failure of these properties is equivalent to certain seemingly pathological behaviors far from the boundary. One of our approaches uses real time methods, in which locality at the boundary is expressed by analyticity in the frequency. As a preliminary, we use real time methods to prove again that the boundary beta-function is the gradient of the boundary entropy, which implies that s(T) decreases with T. The metric on the space of boundary couplings is interpreted as the renormalized susceptibility matrix of the boundary, made finite by a natural subtraction.

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