ABJM theory with mass and FI deformations and quantum phase transitions

Anderson, Louise; Russo, Jorge G.

doi:10.1007/jhep05(2015)064

Cited by 25 publications

(48 citation statements)

References 50 publications

(191 reference statements)

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“…This averaging results in the constant eigenvalue distribution obtained in [8]. Similar behavior was obtained for the solutions containing resonances in the mass-deformed ABJM theory [32,33] and 4D N = 2 * theory [22].…”

Section: The Strong Coupling Limitsupporting

confidence: 74%

“…Finally, as mentioned in the introduction, studies of the decompactification limit in different 3D and 4D theories revealed interesting phase structure of these theories. For instance, phase transitions were found in 3D Chern-Simons coupled to the massive fundamental hypermultiplet [30], in 4D N = 2 super-QCD with massive quarks in the Veneziano limit [24], in mass-deformed ABJM theory [32,33] and finally in 4D N = 2 * SYM theory [22]. In each case theory was considered in the decompactification limit and it was shown that in the finite volume phase transitions disappear.…”

Section: Jhep07(2015)004mentioning

confidence: 99%

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Phase transitions in 5D super Yang-Mills theory

Nedelin

2015

J. High Energ. Phys.

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In this paper we study a phase structure of 5D N = 1 super Yang-Mills theory with massive matter multiplets and SU(N ) gauge group. In particular, we are interested in two cases: theory with N f massive hypermultiplets in the fundamental representation and theory with one adjoint massive hypermultiplet. If these theories are considered on S 5 their partition functions can be localized to matrix integrals, which can be approximated by their values at saddle points in the large-N limit. We solve saddle point equations corresponding to the decompactification limit of both theories. We find that in the case of the fundamental hypermultiplets theory experiences third-order phase transition when coupling is varied. We also show that in the case of one adjoint hypermultiplet theory experiences infinite chain of third-order phase transitions, while interpolating between weak and strong coupling regimes.

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Section: The Strong Coupling Limitsupporting

confidence: 74%

Section: Jhep07(2015)004mentioning

confidence: 99%

Phase transitions in 5D super Yang-Mills theory

Nedelin

2015

J. High Energ. Phys.

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“…Here we use a slightly more general procedure than [13], which will generalize to the case with insertion of Fayet-Iliopoulos deformation. Based on previous results [13,17] we assume a one-cut solution for ρ, supported in some closed interval [−A, B]. In the present case with opposite masses and equal number of hypermultiplets associated to each mass, the support will turn out to be symmetric, B = A.…”

Section: Eigenvalue Distributionmentioning

confidence: 99%

Phase transitions and Wilson loops in antisymmetric representations in Chern–Simons-matter theory

Santilli¹,

Tierz²

2019

J. Phys. A: Math. Theor.

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We study the phase transitions of three-dimensional N = 2 U (N ) Chern-Simons theory on S 3 with a varied number of massive fundamental hypermultiplets and with a Fayet-Iliopoulos parameter. We characterize the various phase diagrams in the decompactification limit, according to the number of different mass scales in the theory. For this, we extend the known solution of the saddle-point equations to the setting where the one cut solution is characterized by asymmetric intervals. We then study the large N limit of Wilson loops in antisymmetric representations, with the additional scaling corresponding to the variation of the size of the representation. We give explicit expressions, both with and without FI terms, and study 1/R corrections for the different phases. These corrections break the perimeter law behavior, as they introduce a scaling with the size of the representation. We show how the phase transitions of the Wilson loops can either be of first or second order and determine the underlying mechanism in terms of the eventual asymmetry of the support of the solution of the saddle-point equation, at the critical points. arXiv:1808.02855v2 [hep-th] 28 Aug 2018 7 Outlook 46 A Free energy second derivatives 47 A.0.1 ζ < m 1 with two mass scales 47 A.0.2 ζ < m 1 with one mass scale 47 A.0.3 ζ > m 1 with two mass scales 48 B Regions with no saddle point 48 B.0.1 Re (z) > 1 or Re (z) < −1 48 B.0.2 Re (z) around ±1

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“…See also [49][50][51]. Though the setup is different from ours, where the mABJM theory is defined on R 2,1 , it is intriguing to investigate the gravity dual for our case in the large mass region and compare the results with those of mABJM theory on S 3 .…”

Section: Jhep04(2017)104mentioning

confidence: 92%

Mass-deformed ABJM theory and LLM geometries: exact holography

Jang

Kim

Kwon

et al. 2017

J. High Energ. Phys.

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We present a detailed account and extension of our claim in arXiv:1610.01490. We test the gauge/gravity duality between the N = 6 mass-deformed ABJM theory with U k (N )×U −k (N ) gauge symmetry and the 11-dimensional supergravity on LLM geometries with SO(4)/Z k ×SO(4)/Z k isometry, in the large N limit. Our analysis is based on the evaluation of vacuum expectation values of chiral primary operators from the supersymmetric vacua of mass-deformed ABJM theory and from the implementation of Kaluza-Klein holography to the LLM geometries. We focus on the chiral primary operator with conformal dimension ∆ = 1. We show that O (∆=1) = N 3 2 f (∆=1) for all supersymmetric vacuum solutions and LLM geometries with k = 1, where the factor f (∆) is independent of N . We also confirm that the vacuum expectation value of the energy momentum tensor is vanishing as expected by the supersymmetry. We extend our results to the case of k = 1 for LLM geometries represented by rectangular-shaped Young-diagrams. In analogy with the Coulomb branch of the N = 4 super Yang-Mills theory, we argue that the discrete Higgs vacua of the mABJM theory as well as the corresponding LLM geometries are parametrized by the vevs of the chiral primary operators.

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ABJM theory with mass and FI deformations and quantum phase transitions

Cited by 25 publications

References 50 publications

Phase transitions in 5D super Yang-Mills theory

Phase transitions in 5D super Yang-Mills theory

Phase transitions and Wilson loops in antisymmetric representations in Chern–Simons-matter theory

Mass-deformed ABJM theory and LLM geometries: exact holography

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