Direct derivation of “mirror” ABJ partition function

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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].

Section: Jhep11(2017)190mentioning

confidence: 56%

ABJ quadrality

Honda

Pang

Zhu

2017

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“…After establishing the closed string formalism, we show that the Hanany-Witten duality (4.8) at M = k/2 is manifest in this formalism. The closed string formalism for the ABJM theory was first conjectured in [63] and later proved in [64]. The derivation was improved largely later and generalized to the partition function of the orientifold ABJM theory with the orthosymplectic gauge group in [57,58] and the vacuum expectation values of the half-BPS Wilson loop in the ABJM theory in [65].…”

Section: A Notation For Bras and Ketsmentioning

confidence: 99%

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

Moriyama¹,

Nakayama²,

Nosaka³

2017

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.

“…However, the ABJ partition function in the HS limit (1.1) has not been much investigated in the literature. In the current paper, building on our earlier work [92,93], we develop a systematic procedure to compute a large M expansion of the partition function and start exploring the highly stringy regime of the HS/ABJ duality at finite N . The HS limit can alternatively be extracted from the conifold expansion developed in [94], but our approach has the advantage of directly giving the 1/M expansion.…”

Section: Jhep08(2016)174mentioning

confidence: 99%

“…Later, the expression (3.7) was derived in [93] directly from the matrix integral (3.1) using the Cauchy-Vandermonde formula.…”

Section: Jhep08(2016)174mentioning

confidence: 99%

ABJ theory in the higher spin limit

Hirano

Honda

Shigemori

2016

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Abstract:We study the conjecture made by Chang, Minwalla, Sharma, and Yin on the duality between the N = 6 Vasiliev higher spin theory on AdS 4 and the N = 6 Chern-Simons-matter theory, so-called ABJ theory, with gauge group U(N ) × U(N + M ). Building on our earlier results on the ABJ partition function, we develop the systematic 1/M expansion, corresponding to the weak coupling expansion in the higher spin theory, and compare the leading 1/M correction, with our proposed prescription, to the one-loop free energy of the N = 6 Vasiliev theory. We find an agreement between the two sides up to an ambiguity that appears in the bulk one-loop calculation.