- Noppadol Mekareeya

Title : Chern-Simons-Trinion theories: progress on a barely mentioned family of 3d N=4 SCFTs

Abstract : This talk focuses on 3d theories containing N=3 Chern-Simons vector multiplets coupled to the SU(N)^3 flavour symmetry of 3d T_N theories with Chern-Simons level k_1, k_2 and k_3. It was pointed out by Assel, Tachikawa and Tomasiello in [arXiv:2209.13984] that supersymmetry gets enhanced to N=4 when 1/k_1+1/k_2+1/k_3=0. I will demonstrate by means of the superconformal index that, even if the Chern-Simons levels do not obey this condition, there is still an infinite family of theories that flows to infrared SCFTs with N=4 supersymmetry. Moreover, I will discuss the 't Hooft anomalies of the one-form symmetries of these theories. As a by-product, it is observed that there is generally a decoupled topological sector in the infrared. The moduli space of these theories will be discussed using the Higgs and Coulomb branch limits of the index.
 

- Dongmin Gang

Title : Non-unitary RCFTs and 3D N=4 rank-0 SCFTs
Abstract : I will talk about an intriguing relation between 2D non-unitary RCFTs and 3D N=4 rank-0 SCFTs.

- Sungjay Lee

Title : Z_N dualities and Parafermions

- Wenbin Yan

Title : Mirror symmetry for circle compactified 4d N=2 SCFTs
Abstract :  In this talk we will discuss a mirror symmetry for 4d N=2 superconformal field theories (SCFTs) compactified on a circle with finite size. The mirror symmetry involves vertex operator algebra (VOA) describing the Schur sector (containing Higgs branch) of 4d theory, and the Coulomb branch of the effective 3d theory. VOA data such as simple modules, Zhu's algebra, and modular properties are matched with geometric properties like C^*-fixed varieties in Hitchin fibers, cohomologies, and some DAHA representations.

- Hee Joong Chung

Title : 3d-3d correspondence and 2d N = (0,2) boundary conditions

Abstract : In this talk, we interpret quiver forms that appear in the generating function of Donaldson-Thomas invariant or characters of CFT in terms of half-index of 3d N=2 theories with certain 2d N = (0,2) boundary conditions. We apply this relation to the 3d-3d correspondence and obtain a Lagrangian description of 3d N=2 theories T[M_3] for 3-manifolds M_3 in several contexts.

- Kazunobu Maruyoshi

Title : Surface defect index and integrable model

Abstract : In this talk, we discuss a remarkable relationship between superconformal index of four-dimensional superconformal field theory with surface defect and integrable models. As a gauge theory side, we consider N=2 or N=1 superconformal field theory on S^1 times S^3 and S^1 times lens space. The surface defect superconformal index is identified with the transfer matrices of integrable L-operators of elliptic type. We discuss the generalization of this relation to the lens space index case. This talk is based on a collaboration with Toshihiro Ota and Masahito Yamazaki.

- Tudor Dimofte

Title : Quantum groups in 3d N=4 gauge theories

Abstract : I will discuss how quantum supergroups show up in B-type topological twists of 3d N=4 gauge theories, in much the same way that quantum group show up in classic Chern-Simons theory. In particular, the representation theory of these quantum supergroups controls the extended TQFT structure of the B twist. The supergroups can be derived/constructed in several different ways, related on one hand to Kazhdan-Lustig correspondences for boundary VOA’s (based in turn on free-field realizations), and related on the other hand to Koszul duality for line operators (as in work of Costello-Paquette). The talk is based on work in progress with Thomas Creutzig and Wenjun Niu; it generalizes examples that have appeared in work of Geer-Young, Garner-Niu, and Creutzig-Garner-Geer-and myself.

- Matthew Buican

Title : Some Applications of Free Supersymmetric Fields

- Emily Nardoni : TBA

- Hirotaka Hayashi

Title : Higgsings of D-type conformal matter theories from web diagrams
Abstract : We revisit Higgsings of D-type conformal matter theories on a circle from web diagrams with trivalent gluing. We argue that the Higgsings yield web diagrams of 5d theories which arise from a circle compactification of the 6d SO(12) gauge theory with half-hypermultiplets in two different spinor representations and also from a twisted compactification of a 6d SO(12) gauge theory with spinor matter. We compute the monopole string tension and the Nekrasov partition functions from the web diagrams, finding agreement with the field theory results. 

- Andrea Ferrari

Title : Boundary vertex algebras of 3d N=4 theories and vacuum geometry

Abstract : I will give a schematic introduction to the expected relationship between vertex algebras appearing at the boundary of A/B-twisted 3d N=4 theories and the vacuum geometry of these theories. In particular, I will claim that in the presence of enough matter the Higgs branch of an A-twisted theory is expected to be related to the associated variety of its boundary VOA, and substantiate this claim by presenting in the abelian case free-field realisations modelled on this geometry. I will then go on to explain how outer automorphisms are expected to be related to Coulomb isometries. If time will permit, I will comment on finiteness conditions and present boundary VOAs of recently discovered 3d N=4 SCFTs.

- Sung Soo Kim

Title : 5d non-Lagrangian theories and O7-planes
Abstract : I will discuss novel aspects of 5d non-Lagrangian theories and orientifold O7-planes. Non-Lagrangian theories cannot be described by conventional Lagrangian descriptions under mass deformations. Due to the lack of a Lagrangian description, computing the superconformal index for such theories has been a challenge. In this talk, I will present two new methods for computing the superconformal index. One is to use the Higgs branch flows guided by Type IIB 5-brane webs. The other method is to utilize a new perspective on an O7^+-plane as a particular frozen phase of an O7^--plane with eight D7-branes, enabling us to compute the superconformal index for those non-Lagrangian theories that involve an O7^+-plane in their 5-brane descriptions.