ABJM Wilson loops in arbitrary representations

Hatsuda, Yasuyuki; Honda, Masazumi; Moriyama, Sanefumi; Okuyama, Kazumi

doi:10.1007/jhep10(2013)168

Cited by 65 publications

(139 citation statements)

References 85 publications

(203 reference statements)

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“…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]. However, the ABJ partition function in the HS limit (1.1) has not been much investigated in the literature.…”

Section: Jhep08(2016)174mentioning

confidence: 99%

ABJ theory in the higher spin limit

Hirano

Honda

Shigemori

2016

J. High Energ. Phys.

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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.

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Section: Jhep08(2016)174mentioning

confidence: 99%

ABJ theory in the higher spin limit

Hirano

Honda

Shigemori

2016

J. High Energ. Phys.

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“…Pictorially these are the numbers of boxes counted from the diagonal line shifted by M. (See figure 1.) As a corollary [7], for the special case of the ABJM matrix model M = 0, we find the relation…”

Section: Generalized Giambelli Compatibilitymentioning

confidence: 59%

“…Let us first summarizes our result of [7,8]. We define the ABJ(M) matrix model in canonical ensemble as…”

Section: Half-bps Wilson Loop In Arbitrary Representationsmentioning

confidence: 99%

“…Then, we find a theorem [7,8,11] stating that the normalized grand canonical vacuum expectation value can be expressed by a determinant…”

Section: Generalized Giambelli Compatibilitymentioning

confidence: 99%

“…The analysis for the ABJM partition function was also extended to the case of the half-BPS Wilson loop expectation values in [7] and the case of the ABJ partition function in [8].…”

Section: Cancellation Mechanismmentioning

confidence: 99%

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M-theory and matrix models

Moriyama¹

2015

Proceedings of KMI International Symposium 2013 on “Quest for the Origin of Particles and the Universe — PoS(KMI2013)

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We summarize our results on the ABJ(M) matrix model, which is the vacuum expectation value of a supersymmetric Wilson loop operator in the M2-brane worldvolume theory. We first give a Giambelli formula for the ABJ(M) matrix model. This formula implies that the fractional brane can be interpreted as a composite state of string excitations. We also present an exact instanton expansion of the ABJM partition function. This instanton expansion is especially interesting, because the coefficients of the string worldsheet instanton are divergent at certain Chern-Simons levels, though the divergences are completely cancelled by the divergences coming from the coefficients of the other membrane instanton. This is reminiscent of the lessons we learned in the non-perturbative study of string theory: String theory is a consistent theory only after including the non-perturbative branes. KMI International Symposium

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$$ \mathcal{N} $$ = 2* Schur indices

Hatsuda

Okazaki

2023

J. High Energ. Phys.

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We find closed-form expressions for the Schur indices of 4d $$ \mathcal{N} $$ N = 2* super Yang-Mills theory with unitary gauge groups for arbitrary ranks via the Fermi-gas formulation. They can be written as a sum over the Young diagrams associated with spectral zeta functions of an ideal Fermi-gas system. These functions are expressed in terms of the twisted Weierstrass functions, generating functions for quasi-Jacobi forms. The indices lie in the polynomial ring generated by the Kronecker theta function and the Weierstrass functions which contains the polynomial ring of the quasi-Jacobi forms. The grand canonical ensemble allows for another simple exact form of the indices as infinite series. In addition, we find that the unflavored Schur indices and their limits can be expressed in terms of several generating functions for combinatorial objects, including sum of triangular numbers, generalized sums of divisors and overpartitions.

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ABJM Wilson loops in arbitrary representations

Cited by 65 publications

References 85 publications

ABJ theory in the higher spin limit

ABJ theory in the higher spin limit

M-theory and matrix models

$$ \mathcal{N} $$ = 2* Schur indices

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