Random field models and Parisi-Sourlas supersymmetry
Lundi 24/01/2022, 14:00-15:00
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Quenched disorder is very important but notoriously hard. In 1979, Parisi and Sourlas proposed an interesting and powerful conjecture about the infrared fixed points with random field (RF) type of disorder: such fixed points should possess an unusual supersymmetry, by which they reduce in two less spatial dimensions to usual non-supersymmetric non-disordered fixed points. The conjecture is known to hold for the RF φ^3 model but not for RF φ^4 model in d < 5 dimensions, however there is no consensus on why this happens. We argue that:
1) dimensional reduction works for any Parisi-Sourlas SUSY fixed point;
2) the SUSY fixed point is not always reached because of new relevant SUSY-breaking interactions.
We attack the point 1) using axiomatic CFT techniques while we study the point 2) using the perturbative renormalization group in a judiciously chosen field basis, allowing systematic exploration of the space of interactions. Our computations agree with the numerical results for both cubic and quartic potential.