On large N solution of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn></mml:math>Chern–Simons-adjoint theories

Suyama, Takao

doi:10.1016/j.nuclphysb.2012.10.017

Cited by 13 publications

(43 citation statements)

References 61 publications

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“…Thus, for m 2 < B − A, there will only be one resonance originating from the leftmost endpoint −A, and for 2B > m 2 > B − A, there will be one resonance originating from the rightmost endpoint B. [As discussed above, for m 2 > 2B, there are no resonance points inside the interval, and the solution is thus given by (26). ]…”

Section: Simple Examplesmentioning

confidence: 99%

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ABJM theory with mass and FI deformations and quantum phase transitions

Anderson

Russo

2015

J. High Energ. Phys.

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The phase structure of ABJM theory with mass m deformation and nonvanishing Fayet-Iliopoulos (FI) parameter, ζ, 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 < 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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Section: Simple Examplesmentioning

confidence: 99%

“…In the complete phase diagram shown in fig. 3, the uniform eigenvalue density (26) is the density in the shaded region below the lowest blue line. The solution (30) represents the eigenvalue density in the triangular region above this blue line, having the green (λ = m 1 2) and black (λ = m 2 ) lines as the other sides.…”

Section: Simple Examplesmentioning

confidence: 99%

ABJM theory with mass and FI deformations and quantum phase transitions

Anderson

Russo

2015

J. High Energ. Phys.

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“…The matrix model (3.3) was called the N f matrix model in [99], where it was analyzed in detail. It turns out that this model can be mapped to an O(2) matrix model [100] and studied with the techniques of [101,102] (similarly to what was done in [95]). The planar solution turns out to be very simple.…”

Section: The 'T Hooft Expansion Of Chern-simons-matter Theoriesmentioning

confidence: 99%

Localization at largeNin Chern–Simons-matter theories

Mariño¹

2017

J. Phys. A: Math. Theor.

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We review some exact results for the matrix models appearing in the localization of Chern-Simons-matter theories, focusing on the structure of non-perturbative effects and on the Mtheory expansion of ABJM theory. We also summarize some of the results obtained for other Chern-Simons-matter theories, as well as recent applications to topological strings. This is a contribution to the review volume "Localization techniques in quantum field theories" (eds. V. Pestun and M. Zabzine) which contains 17 Chapters available at [1]

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“…earlier works [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54]. Especially it is worthwhile to mention that, according to [15] the expression of the coefficient C was given a geometrical interpretation as the classical volume inside the Fermi surface.…”

Section: Jhep11(2014)164mentioning

confidence: 99%

Partition functions of superconformal Chern-Simons theories from Fermi gas approach

Moriyama

Nosaka

2014

J. High Energ. Phys.

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Abstract:We study the partition function of three-dimensional N = 4 superconformal Chern-Simons theories of the circular quiver type, which are natural generalizations of the ABJM theory, the worldvolume theory of M2-branes. In the ABJM case, it was known that the perturbative part of the partition function sums up to the Airy function as Z(N ) = e A C −1/3 Ai[C −1/3 (N − B)] with coefficients C, B and A and that for the non-perturbative part the divergences coming from the coefficients of worldsheet instantons and membrane instantons cancel among themselves. We find that many of the interesting properties in the ABJM theory are extended to the general superconformal Chern-Simons theories. Especially, we find an explicit expression of B for general N = 4 theories, a conjectural form of A for a special class of theories, and cancellation in the non-perturbative coefficients for the simplest theory next to the ABJM theory.

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On large N solution ofN=3Chern–Simons-adjoint theories

Cited by 13 publications

References 61 publications

ABJM theory with mass and FI deformations and quantum phase transitions

ABJM theory with mass and FI deformations and quantum phase transitions

Localization at largeNin Chern–Simons-matter theories

Partition functions of superconformal Chern-Simons theories from Fermi gas approach

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