2024/10/01 by Apratim Kaviraj, Kaviraj, Apratim, Philine van Vliet +1 · 1 citation
Mathematics · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2410.00958
openalex publication_date 2024/10/01 · openalex created_date 2024/10/20 · openalex updated_date 2026/08/01
We explore a supersymmetric (SUSY) theory that arises in the Landau level problem with disorder. Charged particles in a strong magnetic field and a local potential are described by small excitations around the ground state, the lowest Landau level (LLL). Around forty years ago Brézin, Gross and Itzykson showed that for a disorder potential certain observables in the LLL limit are described by a chiral SUSY theory. As a consequence, the problem undergoes a dimensional reduction by two dimensions, simplifying the computations. We generalize their findings by identifying the chiral SUSY as a special limit of a `magnetic Parisi-Sourlas (PS)' theory. The latter is a modification of the theories associated to fixed points of random field models. We show that the SUSY features extend to a much larger class of observables and to higher Landau levels. Finally we identify a set of new super-Ward identities and show how observables in the disordered theory must satisfy them.