Abstract
The phase structure of ABJM theory with mass m deformation and non-vanishing Fayet-Iliopoulos (FI) parameter, ζ, is studied through the use of localisation on \( \mathbb{S} \) 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 < ζ < m/2, the number of phases is finite and for ζ ≥ 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) × U(2) gauge group in detail by an explicit calculation of the partition function.
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Anderson, L., Russo, J.G. ABJM theory with mass and FI deformations and quantum phase transitions. J. High Energ. Phys. 2015, 64 (2015). https://doi.org/10.1007/JHEP05(2015)064
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DOI: https://doi.org/10.1007/JHEP05(2015)064