Supersymmetric Wilson loops in N = 4 $$ \mathcal{N}=4 $$ super Chern-Simons-matter theory

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%

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

Moriyama¹,

Nakayama²,

Nosaka³

2017

“…As proved in [2,3], the classical fermionic 1/2 BPS loops are both cohomologically equivalent to the 1/4 BPS bosonic operator given in eq. (2.4).…”

Section: Cohomological Equivalencementioning

confidence: 76%

“…We begin by reviewing BPS Wilson loop (WL) operators for N = 4 CS-matter theories introduced in [2,3].…”

Section: Bps Wilson Loops In N = 4 Cs-matter Theoriesmentioning

confidence: 99%

“…Note that matter couplings involve scalars q (1) from the hypermultiplet connecting nodes 1 and 2 (solid line in figure 1), and scalars q (0) , q (2) from the adjacent twisted hypermultiplets (dashed lines in figure 1). …”

Section: The Bosonic 1/4 Bps Wlmentioning

confidence: 99%

“…These operators were defined in [2][3][4][5][6] and we review their construction in section 2 along with a quick glimpse at the structure of the N = 4 CS models [7,8].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The quantum 1/2 BPS Wilson loop in N = 4 $$ \mathcal{N}=4 $$ Chern-Simons-matter theories

Bianchi

Leoni

Mauri

et al. 2016

In three dimensional N = 4 Chern-Simons-matter theories two independent fermionic Wilson loop operators can be defined, which preserve half of the supersymmetry charges and are cohomologically equivalent at classical level. We compute their three-loop expectation value in a convenient color sector and prove that the degeneracy is uplifted by quantum corrections. We expand the matrix model prediction in the same regime and by comparison we conclude that the quantum 1/2 BPS Wilson loop is the average of the two operators. We provide an all-loop argument to support this claim at any order. As a by-product, we identify the localization result at three loops as a correction to the framing factor induced by matter interactions. Finally, we comment on the quantum properties of the non-1/2 BPS Wilson loop operator defined as the difference of the two fermionic ones.

Two-point functions in ABJM matrix model

Kubo

Moriyama

2018

We introduce non-trivial two-point functions of the super Schur polynomials in the ABJM matrix model and study their exact values with the Fermi gas formalism. We find that, although defined non-trivially, these two-point functions enjoy two simple relations with the one-point functions. One of them is associated with the Littlewood-Richardson rule, while the other is more novel. With plenty of data, we also revisit the one-point functions and study how the diagonal BPS indices are split asymmetrically by the degree difference.