Mass-deformed super Yang-Mills theories from M2-branes with flux

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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.

Section: Jhep04(2017)104 1 Introductionmentioning

confidence: 59%

Mass-deformed ABJM theory and LLM geometries: exact holography

Jang

Kim

Kwon

et al. 2017

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“…k . This identification has appeared in the context of the compactification of ABJM theory (from M2 to D2) [33,34,35]. See also Refs.…”

Section: Bps Objects In the Massless Theorymentioning

confidence: 91%

BPS vortices, Q-balls, and Q-vortices in $ \mathcal{N} $ = 6 Chern-Simons matter theory

Go¹,

Kim²,

Kim³

et al. 2013

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We investigate the vortex-type BPS equations in the ABJM theory without and with mass-deformation. We systematically classify the BPS equations in terms of the number of supersymmetry and the R-symmetries of the undeformed and mass-deformed ABJM theories. For the undeformed case, we analyze the N = 2 BPS equations for U(2)×U(2) gauge symmetry and obtain a coupled differential equation which can be reduced to either Liouvilleor Sinh-Gordon-type vortex equations according to the choice of scalar functions. For the mass-deformed case with U(N )×U(N ) gauge symmetry, we obtain some number of pairs of coupled differential equations from the N = 1, 2 BPS equations, which can be reduced to the vortex equations in Maxwell-Higgs theory or Chern-Simons matter theories as special cases. We discuss the solutions. In N = 3 vortex equations Chern-Simons-type vortex equation is not allowed. We also show that N =

“…See e.g. [47] for the details. As a result of the vacuum solution (3.22), N D3-branes are polarized into l D5-branes with JHEP12(2020)060 the fuzzy-two spheres having different radii, for instance, for the n k -dimensional irreducible representation the radius is given by…”

Section: Jhep12(2020)060mentioning

confidence: 99%

Super Yang-Mills theories with inhomogeneous mass deformations

Kim

Kwon

Tolla

2020

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We construct the 4-dimensional $$ \mathcal{N}=\frac{1}{2} $$ N = 1 2 and $$ \mathcal{N} $$ N = 1 inhomogeneously mass-deformed super Yang-Mills theories from the $$ \mathcal{N} $$ N = 1* and $$ \mathcal{N} $$ N = 2* theories, respectively, and analyse their supersymmetric vacua. The inhomogeneity is attributed to the dependence of background fluxes in the type IIB supergravity on a single spatial coordinate. This gives rise to inhomogeneous mass functions in the $$ \mathcal{N} $$ N = 4 super Yang-Mills theory which describes the dynamics of D3-branes. The Killing spinor equations for those inhomogeneous theories lead to the supersymmetric vacuum equation and a boundary condition. We investigate two types of solutions in the $$ \mathcal{N}=\frac{1}{2} $$ N = 1 2 theory, corresponding to the cases of asymptotically constant mass functions and periodic mass functions. For the former case, the boundary condition gives a relation between the parameters of two possibly distinct vacua at the asymptotic boundaries. Brane interpretations for corresponding vacuum solutions in type IIB supergravity are also discussed. For the latter case, we obtain explicit forms of the periodic vacuum solutions.