Localization in the theory of the quantized hall effect: a two-dimensional realization of the theta-vacuum Pruisken, A M.M. 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ELECTRON GAS; HALL EFFECT; QUANTUM ELECTRODYNAMICS; DELTA FUNCTION; DISTRIBUTION FUNCTIONS; ELECTRIC CONDUCTIVITY; EXPECTATION VALUE; MAGNETIC FIELDS; NONLINEAR PROBLEMS; SIGMA MODEL; TWO-DIMENSIONAL CALCULATIONS; U GROUPS; VACUUM STATES; YANG-MILLS THEORY; ELECTRICAL PROPERTIES; ELECTRODYNAMICS; FIELD THEORIES; FUNCTIONS; LIE GROUPS; MATHEMATICAL MODELS; PARTICLE MODELS; PHYSICAL PROPERTIES; QUANTUM FIELD THEORY; SYMMETRY GROUPS; 645400* - High Energy Physics- Field Theory It is shown that the localization problem in the theory of the quantized Hall effect is governed by the zero-component grassmannian U(2m) non-linear sigma-model with a THETA-term, a two-dimensional analogue of the THETA-vacuum in Yang-Mills theory. In this case, THETA is to be interpreted as the bare value for the Hall conductivity, determined by an underlying non-critical theory. A detailed derivation is presented starting from the replica method and a delta function distribution for the impurities. Schlumberger-Doll Research Center, Ridgefield, CT Netherlands 1984-06-04 English Journal Article Journal Name: Nucl. Phys. B; (Netherlands); Journal Volume: 235:2 Medium: X; Size: Pages: 277-298 https://doi.org/ [] 235:2 Journal ID: CODEN: NUPBB AIX-15-050832; EDB-84-179825 2010-05-17 6402091