Hiroaki Kanno (Nagoya), Super Macdonald polynomials and instanton counting on the blow-up

The super Macdonald polynomials generalize the Macdonald polynomials to the super space with the Grassmann coordinates \(\theta_i\). They form a basis of a level zero representation of the quantum toroidal algebra of type \(\mathfrak{gl}_{1|1}\). The Pieri rule of the super Macdonald polynomials is obtained from the action of the raising operators of the algebra. We show the relation of the Pieri coefficients to the Nekrasov factor for the instanton counting on the blow-up of \(\mathbb{C}^2\).
The talk is based on a collaboration with R.Ohkawa and J.Shiraishi.

Shi Cheng (SIMIS), Surgery and branched cover for 3d theories

Since the discovery of 3d/3d correspondence, three-manifolds are noticed to be a powerful tool to construct 3d N=2 gauge theories, in parallel to Calabi-Yau manifolds. However, both are not completely established yet. In this talk, we focus on the three-manifold approach, which itself also has two parallel methods. One is the surgery of three-manifolds, found by Gadde, Gukov, and Putrov in paper “Fivebranes and 4-manifolds”. Another one is the double branched cover, found by Cecotti, Córdova, and Vafa in “Braids, walls, and mirrors”. In this talk, by using mathematical ideas, we try to complete and unify these two methods.

Katsushi Ito (ISCT), Integrals of Motion and ODE/IM correspondence

The ODE/IM correspondence is the relation between the spectral analysis of ordinary differential equations and the functional relation approach to two-dimensional quantum integrable models. In this talk, I will consider the relation between the linear-differential system associated with an affine Toda field theory based on an affine Lie algebra \(\hat{g}\) and two-dimensional conformal field theory with W-algebra symmetry for its Langlands dual \(\hat{g}^{\vee}\). We calculate the WKB periods for the ODE, which are shown to correspond to the classical conserved currents of the Drinfeld-Sokolov integrable hierarchies. They are shown to agree with the quantum integrable motions of the conformal field theories with W-algebra symmetry. This correspondence provides an exact parameter relation bewteen ODE and IM and a better way of computing of higher integrals of motion in CFT.

Mykola Dedushenko (SIMIS), TBA

Shota Komatsu (CERN), TBA

Junbao Wu (Tianjin), Holographic Wilson Loop One-point Functions in ABJM Theory

We compute the correlation function between a circular half-BPS Wilson loop (or straight Wilson line) and a local operator in ABJM theory utilizing its M-theory description. The local operator can be a 1/3-BPS single-trace chiral primary operator or the stress-energy tensor. Using the AdS/CFT correspondence, these correlators are dual to fluctuations of a probe M2-brane in \( AdS_4 \times S^7/Z_k \). We derive analytic results for both cases and compare them with existing results based on supersymmetric localization in the literature. In the large-N limit with k finite, our holograkphic results exhibit perfect agreement with localization. This talk is based on work done with Xiao-Yi Zhang and Yunfeng Jiang.