Title and Abstract
Sung-Soo Kim
5d non-Lagrangian theories, index functions, and O7-planes
abstract
Futoshi Yagi
Seiberg-Witten curves from 5-brane webs with orientifold planes
We discuss the systematic construction of Seiberg-Witten curves for 5d N=1 gauge theories realized by 5-brane webs. Especially, we focus on the case where 5-brane webs include O7-planes or O5-planes. In addition to the natural reflection invariance due to the orientifold plane, additional constraints should be imposed on the Seiberg-Witten curve. We consider SO/Sp gauge theories and SU gauge theories with hypermultiplets in symmetric/antisymmetric representation. Based on these Seiberg-Witten curves, we observe an intriguing relation between theories with an O7+ -plane and those with an O7- -plane and 8 D7-branes. We also compute the Seiberg-Witten curve for non-Lagrangian theories, such as the local P2 theory with an adjoint.
Du Pei
On new invariants and phases of supersymmetric quantum field theories
In this talk, we will explore a novel approach to study supersymmetric quantum field theories using tools from stable homotopy theory. We will explain how this approach leads to new invariants that can be used to detect subtle differences between phases that escape the detection of more conventional invariants.
Xin Wang
Bootstrapping Integrable Systems from 5D Gauge Theories
The Bethe/gauge correspondence establishes a connection between the vacuum structure of supersymmetric gauge theories and quantum integrable systems. In this presentation, I will explore the correspondence between quantum integrable systems and 5D \mathcal{N}=1 supersymmetric quantum field theories. In this context, the half-BPS codimension two defect partition function of the gauge theory serves as the eigenfunction of the quantum Hamiltonians in the associated quantum integrable system. By first calculating the defect partition function, we can then use it to bootstrap the quantum Hamiltonians of the integrable systems. In our project, we employ the blowup equations for the defect partition functions to explicitly bootstrap the quantum Hamiltonians of 5D \mathcal{N}=1 theories, even when they may not have the ADHM descriptions.
Mauricio Romo
A-branes, exponential networks and quiver representations
The machinery of exponential/spectral networks can be used to define a counting of stable A-branes on conic bundle Calabi-Yau 3-folds, mirror to Donaldson-Thomas invariants. I will explain how, in certain cases, critical networks can be interpreted as fixed points of the moduli space of foliations and their interpretation as quiver representations.