𝒩 = 5, 6 superconformal Chern-Simons theories and M2-branes on orbifolds

In the so-called (2, 2) theory, which is the U(N ) 4 circular quiver superconformal Chern-Simons theory with levels (k, 0, −k, 0), it was known that the instanton effects are described by the free energy of topological strings whose Gopakumar-Vafa invariants coincide with those of the local D 5 del Pezzo geometry. By considering two types of one-parameter rank deformations U(N )×U(N + M )×U(N + 2M )×U(N + M ) and U(N + M )×U(N )×U(N + M )×U(N ), we classify the known diagonal BPS indices by degrees. Together with other two types of one-parameter deformations, we further propose the topological string expression when both of the above two deformations are turned on.

Section: Introductionmentioning

confidence: 93%

Section: Instanton Effectsmentioning

confidence: 99%

Instanton effects in rank deformed superconformal Chern-Simons theories from topological strings

Moriyama¹,

Nakayama²,

Nosaka³

2017

“…Subsequent work [4][5][6] revealed that such CSm theories, which can be generalized to SU(N )×SU(M ) [7,8], are equivalent to theories constructed using three-algebras whose structure constants enjoy lesser symmetry compared with that of the BLG theory.…”

Section: Jhep11(2013)050mentioning

confidence: 99%

On three-algebra and bi-fundamental matter amplitudes and integrability of supergravity

Huang

Johansson

Lee

2013

Self Cite

We explore tree-level amplitude relations for SU(N )×SU(M ) bi-fundamental matter theories. Embedding the group-theory structure in a Lie three-algebra, we derive Kleiss-Kuijf-like relations for bi-fundamental matter theories in general dimension. We investigate the three-algebra color-kinematics duality for these theories. Unlike the YangMills two-algebra case, the three-algebra Bern-Carrasco-Johansson relations depend on the spacetime dimension and on the detailed symmetry properties of the structure constants. We find the presence of such relations in three and two dimensions, and absence in D > 3. Surprisingly, beyond six point, such relations are absent in the Aharony-Bergman-JafferisMaldacena theory for general gauge group, while the Bagger-Lambert-Gustavsson theory, and its supersymmetry truncations, obey the color-kinematics duality like clockwork. At four and six points the relevant partial amplitudes of the two theories are bijectively related, explaining previous results in the literature. In D = 2 the color-kinematics duality gives results consistent with integrability of two-dimensional N = 16 supergravity: the four-point amplitude satisfies a Yang-Baxter equation; the six-and eight-point amplitudes vanish for certain kinematics away from factorization channels, as expected from integrability.

“…One interesting feature of the ABJM theory is that it allows supersymmetry preserving mass deformation [17,18]. That is, the resulting mass-deformed theory called the mABJM theory has still N = 6 supersymmetry though the conformal symmetry of the original theory is broken under the deformation.…”

Section: Vacua Of the Mabjm Theory And The Llm Geometriesmentioning

confidence: 99%

“…Our analysis is based on the 3-dimensional mass-deformed Aharony-Bergman-Jafferis-Maldacena theory (mABJM) of massive M2-branes, which has N = 6 supersymmetry and U k (N )×U −k (N ) gauge symmetry, where k is the Chern-Simons level [17,18]. The mass-deformed theory is obtained from the original ABJM theory [19] by adding a relevant deformation which preserves the full supersymmetry as well as the JHEP04 (2017)104 gauge symmetry while the conformal symmetry is completely broken and the SU(4) global symmetry is reduced to SU(2)×SU(2)×U (1).…”

Section: Jhep04(2017)104 1 Introductionmentioning

confidence: 99%

Mass-deformed ABJM theory and LLM geometries: exact holography

Jang

Kim

Kwon

et al. 2017

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.