ABJM Theory with mass and FI deformations and Quantum Phase Transitions

Abstract

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 ${\mathbb{S}}^3$. 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. As the FI term is introduced, new effects appear. For any given $0<\zeta <m/2$, the number of phases is finite and for $\zeta \ge m/2$ 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 $U(2)\times U(2)$ gauge group in detail by an explicit calculation of the partition function.

42 pages, 7 figures. Minor revisions of eq. (19) and section 6.2.2 to agree with JHEP-version

References in corpus (6)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Fractional M2-branes
• N=2* Super-Yang-Mills Theory at Strong Coupling
• Quantum Phase Transitions in Mass-Deformed ABJM Matrix Model
• N=2 gauge theories and quantum phases
• Phases of planar 5-dimensional supersymmetric Chern-Simons theory

Cited by in corpus (20)

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• Large N behavior of mass deformed ABJM theory
• Mass Deformed ABJM Theory on Three Sphere in Large N limit
• Exact Holography of the Mass-deformed M2-brane Theory
• Phases of five-dimensional supersymmetric gauge theories
• Matrix models for 5d super Yang-Mills
• Mass-deformed ABJM Theory and LLM Geometries: Exact Holography
• SU(N) q-Toda equations from mass deformed ABJM theory
• Phase transitions and Wilson loops in antisymmetric representations in Chern-Simons-matter theory
• Exact partition function in $U(2)\times U(2)$ ABJM theory deformed by mass and Fayet-Iliopoulos terms
• Identification of Bulk coupling constant in Higher Spin/ABJ correspondence
• Mordell integrals and Giveon-Kutasov duality
• More Large $N$ limits of 3d gauge theories
• Non-topological Vortex Configurations in the ABJM Model
• Aspects of Massive Gauge Theories on Three Sphere in Infinite Mass Limit
• Duality Cascades and Affine Weyl Groups
• BPS Wilson loops in mass-deformed ABJM theory: Fermi gas expansions and new defect CFT data
• Mass deformed ABJM and $\mathcal{P}\mathcal{T}$ symmetry
• Mass-deformed ABJ and ABJM theory, Meixner-Pollaczek polynomials, and $su(1,1)$ oscillators
• Dualities and loops on squashed $S^3$