Orthosymplectic Chern-Simons matrix model and chirality projection

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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: Jhep08(2017)003mentioning

confidence: 99%

Section: 1 Exact Valuesmentioning

confidence: 99%

Section: 1 Exact Valuesmentioning

confidence: 99%

Section: A Notation For Bras and Ketsmentioning

confidence: 99%

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

Moriyama¹,

Nakayama²,

Nosaka³

2017

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“…As in the N = 6 case, for k ≫ N 1/5 , the M-theory circle shrinks and the M-theory is well approximated by type IIA string on AdS 4 × CP 3 /Z 2 with the B-field holonomy B 2 ∼ M/k. There are some checks of this correspondence at classical level [60,61] and one-loop level [44,[62][63][64][65][66][67].…”

Section: Jhep11(2017)190mentioning

confidence: 99%

ABJ quadrality

Honda

Pang

Zhu

2017

Abstract:We study physical consequences of adding orientifolds to the ABJ triality, which is among 3d N = 6 superconformal Chern-Simons theory known as ABJ theory, type IIA string in AdS 4 × CP 3 and N = 6 supersymmetric (SUSY) Vasiliev higher spin theory in AdS 4 . After adding the orientifolds, it is known that the gauge group of the ABJ theory becomes O(N 1 ) × USp(2N 2 ) while the background of the string theory is replaced by AdS 4 × CP 3 /Z 2 , and the supersymmetries in the both theories reduce to N = 5. We propose that adding the orientifolds to the N = 6 Vasiliev theory leads to N = 5 SUSY Vasiliev theory. It turns out that the N = 5 case is more involved because there are two formulations of the N = 5 Vasiliev theory with either O or USp internal symmetry. We show that the two N = 5 Vasiliev theories can be understood as certain projections of the N = 6 Vasiliev theory, which we identify with the orientifold projections in the Vasiliev theory. We conjecture that the O(N 1 ) × USp(2N 2 ) ABJ theory has the two vector model like limits: N 2 ≫ N 1 and N 1 ≫ N 2 which correspond to the semi-classical N = 5 Vasiliev theories with O(N 1 ) and USp(2N 2 ) internal symmetries respectively. These correspondences together with the standard AdS/CFT correspondence comprise the ABJ quadrality among the N = 5 ABJ theory, string/M-theory and two N = 5 Vasliev theories. We provide a precise holographic dictionary for the correspondences by comparing correlation functions of stress tensor and flavor currents. Our conjecture is supported by various evidence such as agreements of the spectra, one-loop free energies and SUSY enhancement on the both sides. We also predict the leading free energy of the N = 5 Vasiliev theory from the CFT side. As a byproduct, we give a derivation of the relation between the parity violating phase in the N = 6 Vasiliev theory and the parameters in the N = 6 ABJ theory, which was conjectured in [1].

Complete factorization in minimal N = 4 $$ \mathcal{N}=4 $$ Chern-Simons-matter theory

Nosaka

Yokoyama

2018

Abstract:We investigate an N = 4 U(N ) k × U(N + M ) −k Chern-Simons theory coupled to one bifundamental hypermultiplet by employing its partition function, which is given by 2N + M dimensional integration via localization. Surprisingly, by performing the integration explicitly we find that the partition function completely factorizes into that of the pure Chern-Simons theory for two gauge groups and an analogous contribution for the bifundamental hypermultiplet. Using the factorized form of the partition function we argue the level/rank duality, which is also expected from the Hanany-Witten transition in the type IIB brane realization. We also present the all order 't Hooft expansion of the partition function and comment on the connection to the higher-spin theory.