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 New applications of the renormalization group method in nuclear, particle and
 condensed matter physics

 (INT workshop February 22-26, 2010)

  Reported by: Mike Birse (U. Manchester), Yannick Meurice (U Iowa), and Shan-Wen Tsai (UC Riverside)
  Date posted April 12, 2010

The ideas of the renormalization group (RG) and scale invariance have played central roles in physics and are associated with the emergence of key concepts such as universality, self-similarity, scaling and asymptotic freedom. The RG provides a universal language spoken by scientists working in very different areas. Despite this universality, practical applications have often been developed independently in these areas, often without much communication among them. The goal of the worskhop was to bring together RG practitioners who are working in nuclear, particle, atomic and condensed matter physics. While there may have been RG conferences with different fields represented, we believe that our workshop was the first to emphasize the communication of new and exciting results across traditional boundaries and to stimulate the exchange of theoretical techniques. We are glad to report that the goals were met beyond our original expectations.

The workshop ran over five days and attracted 35 participants. Several speakers were asked to provide pedagogical introductions to specific areas so that people from other fields had the necessary background for the more technical talks. Where possible, we organised talks around ideas that crossed boundaries. For example, the Efimov effect arises in both nuclear and cold-atom physics; it is also being studied using functional RG methods; and it corresponds to a 1/r2 potential that can provide an example of loss of conformal symmetry.

Central themes of the workshop were: the roles of scale invariance and conformal symmetry; functional or "exact" RG methods; global aspects of RG flows; effective theories of fermions based on expansions around fixed points of the RG; the elucidation of phase diagrams. These ideas were applied to systems that ranged from quantum gravity to classical fluid flow, and also included QCD and similar gauge theories, nuclei, few-body atomic systems and atomic condensates, high-Tc cuprate superconductors, lattices of dipolar molcules, and graphene.

As a result, the workshop was very beneficial. It provided an opportunity for RG practitioners from very different backgrounds to communicate. Longer discussions would have taken place had the schedule allowed it. We view the workshop as an important step in the creation of a worldwide RG community.

Figure RG flows for the complex strength of a contact interaction in the presence of: (A) a weakly attractive 1/r2 potential, showing stable and unstable fixed points; (B) a strongly attractive potential, showing limit-cycle flows which correspond to the Efimov effect. (From Sergej Moroz.)