### Three Alternative Sigma Models of Disorder and Their Relative Merits

**Sacksteder, V ***(Asia Pacific Center)*

Thursday 11 December 2008, 14:40-15:20

Seminar Room 2, Newton Institute Gatehouse

#### Abstract

Wegner's model of weakly coupled metallic grains is believed to
capture the physics of Anderson localization, but has resisted full
mathematical control in two or more dimensions. In zero dimensions it
can be exactly transformed to two different matrix models, the first
involving graded (supersymmetric) matrices. The second was introduced
more recently by Fyodorov and avoids the use of graded matrices. The
SUSY model was generalized long ago to D dimensions and results in the
famous supersymmetric sigma model. However the generalization process
lacks mathematical rigor, relying heavily on effective field theory
ideas and an implicit continuum limit. In this talk I will briefly
review the SUSY generalization process and its difficulties and then
describe what can be learned from generalizing Fyodorov's model to D
dimensions. Lastly and most importantly I will present my work on a
third model originated by Spencer and Disertori which is identical to
Fyodorov's model in zero dimensions but which opens new mathematical
possibilities in D dimensions.

#### Presentation