ABJM theory with mass and FI deformations and quantum phase transitions

Journal article, 2015

The phase structure of ABJM theory with mass m deformation and non-vanishing Fayet-Iliopoulos (FI) parameter, zeta, is studied through the use of localisation on S-3. The partition function of the theory then reduces to a matrix integral, which, in the large N limit and at large sphere radius, is exactly computed by a saddle-point approximation. When the couplings are analytically continued to real values, the phase diagram of the model becomes immensely rich, with an infinite series of third-order phase transitions at vanishing FI-parameter [1]. As the FI term is introduced, new effects appear. For any given 0 < zeta < m/2, the number of phases is finite and for zeta m /2 the theory does not have any phase transitions at all. Finally, we argue that ABJM theory with physical couplings does not undergo phase transitions and investigate the case of U(2) x U(2) gauge group in detail by an explicit calculation of the partition function.