Dynamical (super)symmetry vacuum properties of the supersymmetric Chern-Simons-matter model

By computing the two-loop effective potential of the D=3 N=1 supersymmetric Chern-Simons model minimally coupled to a massless self-interacting matter superfield, it is shown that supersymmetry is preserved, while the internal U(1) and the scale symmetries are broken at two-loop order, dynamically generating masses both for the gauge superfield and for the real component of the matter superfield.

Solvability in the large for a class of complex vector fields on the cylinder

This work deals with global solvability of a class of complex vector fields of the form L = partial derivative/partial derivative t + (a(x, t)+ ib(x, t))partial derivative/partial derivative x, where a and b are real-valued C-infinity functions, defined on the cylinder Omega = R x S-1. Relatively compact (Sussmann) orbits are allowed. The connection with Malgrange's notion of L-convexity for supports is investigated. (C) 2011 Elsevier Masson SAS. All rights reserved.

Solvability near the characteristic set for a special class of complex vector fields

This work deals with the solvability near the characteristic set Sigma = {0} x S-1 of operators of the form L = partial derivative/partial derivative t+(x(n) a(x)+ ix(m) b(x))partial derivative/partial derivative x, b not equivalent to 0 and a(0) not equal 0, defined on Omega(epsilon) = (-epsilon, epsilon) x S-1, epsilon > 0, where a and b are real-valued smooth functions in (-epsilon, epsilon) and m >= 2n. It is shown that given f belonging to a subspace of finite codimension of C-infinity (Omega(epsilon)) there is a solution u is an element of L-infinity of the equation Lu = f in a neighborhood of Sigma; moreover, the L-infinity regularity is sharp.