Summing up all genus free energy of ABJM matrix model

Supergravity with eight supercharges in a four-dimensional Euclidean space is constructed at the full non-linear level by performing an off-shell time-like reduction of five-dimensional supergravity. The resulting four-dimensional theory is realized off-shell with the Weyl, vector and tensor supermultiplets and a corresponding multiplet calculus. Hypermultiplets are included as well, but they are themselves only realized with on-shell supersymmetry. We also briefly discuss the non-linear supermultiplet. The off-shell reduction leads to a full understanding of the Euclidean theory. A complete multiplet calculus is presented along the lines of the Minkowskian theory. Unlike in Minkowski space, chiral and anti-chiral multiplets are real and supersymmetric actions are generally unbounded from below. Precisely as in the Minkowski case, where one has different formulations of Poincaré supergravity upon introducing different compensating supermultiplets, one can also obtain different versions of Euclidean supergravity.

Section: Jhep12(2017)011mentioning

confidence: 99%

Euclidean supergravity

Wit

Reys

2017

“…Inspired by the seminal work of Drukker, Marino, and Putrov [71,72] and, in good part, with the use of the elegant Fermi gas approach developed by Marino and Putrov [73], a great deal about the ABJ(M) partition function has been uncovered, in particular, at large N , both in perturbative [73,74] and nonperturbative expansions [75][76][77][78][79][80][81][82]. There has also been significant progress in the study of Wilson loops in the ABJ(M) theory [83][84][85][86] as well as the partition functions of more general Chern-Simons-matter theories [87][88][89][90][91].…”

Section: Jhep08(2016)174mentioning

confidence: 99%

ABJ theory in the higher spin limit

Hirano

Honda

Shigemori

2016

Self Cite

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.

“…Namely, after using the localization technique [5], the partition function of the ABJM theory on S 3 , which is originally defined by the infinite-dimensional path integral, is reduced to a finite-dimensional matrix integration. Then, the 't Hooft expansion 1 of the matrix model is applicable [8][9][10]. Due to the peculiar power 3/2, it is natural to ask what the corrections in the large N limit are.…”

Section: Introductionmentioning

confidence: 99%

“…Due to the peculiar power 3/2, it is natural to ask what the corrections in the large N limit are. The perturbative corrections were found to be summed up to the Airy function [10], which turned out to be just a starting point of the full exploration. One of the celebrating results in this matrix model is the correspondence to the topological string theory.…”

Section: Introductionmentioning

confidence: 99%

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

Moriyama¹,

Nakayama²,

Nosaka³

2017

Self Cite

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.