Random Field Ising Model and Parisi-Sourlas Supersymmetry I. Supersymmetric CFT
| Autor: | Kaviraj, Apratim, Rychkov, Slava, Trevisani, Emilio |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/JHEP04(2020)090 |
| Popis: | 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 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. This conjecture however is known to fail in some simple cases, but there is no consensus on why this happens. In this paper we give new non-perturbative arguments for dimensional reduction. We recast the problem in the language of Conformal Field Theory (CFT). We then exhibit a map of operators and correlation functions from Parisi-Sourlas supersymmetric CFT in $d$ dimensions to a $(d-2)$-dimensional ordinary CFT. The reduced theory is local, i.e. it has a local conserved stress tensor operator. As required by reduction, we show a perfect match between superconformal blocks and the usual conformal blocks in two dimensions lower. This also leads to a new relation between conformal blocks across dimensions. This paper concerns the second half of the Parisi-Sourlas conjecture, while the first half (existence of a supersymmetric fixed point) will be examined in a companion work. Comment: 36 pages, 2 figures. Minor corrections, new references, some comments and clarifications in section 4, a new appendix on "Supersymmetry in the problem of critical dynamics" are added. To appear in JHEP |
| Databáze: | arXiv |
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