Title and Abstract
Yinan Wang
3d N=2 from M-theory on CY4 and IIB brane box-Part I
I will present our new framework of constructing 3d N=2 SUSY field theories/SCFTs I will present our new framework of constructing 3d N=2 SUSY field theories/SCFTs from M-theory on non-compact Calabi-Yau fourfolds and their singular limits. I will discuss the geometric ingredients that give rise to 3d gauge fields, matter, flavor symmetries, 1-form symmetries, non-abelian gauge theory and the SCFT limit, as well as the effects of G4-flux and superpotential. The main example will be a toric CY4 – the local P1P1P1.
Reference: 2312.17082 w/ M. Najjar, J. Tian
Jiahua Tian
3d N=2 from M-theory on CY4 and IIB brane box-Part II
Following the talk by Professor Yi-Nan Wang, in part II I will first present more examples geometrically engineered by M-theory on C^4 orbifolds. Via generalized McKay correspondence we are able to determine several physical quantities of the 3D N=2 theory that are closely related to the group theoretical data of finite subgroups of SU(4). I will then introduce a new way to construct 3D N=2 theories via a brane box method. A brane box can be visualized as a diagram of intersecting planes in R^3 and is shown to be dual to a toric CY4. The planes in a brane box diagram are naturally interpreted as effective 4-branes in 8D maximal supersymmetric theory via IIB/M-theory duality. Various physical properties of the 3D N=2 theory are shown to be related to the diagrammatical properties of the brane box diagram. I will also discuss the stringy states and the codimension-2 branes in the brane box system, along with their physical applications.
Jiakang Bao
On the 2-3-4 of Crystal Melting
I will discuss the counting of BPS states of quiver quantum mechanics in the setting of Type IIA string theory on toric Calabi-Yau (CY) threefolds and fourfolds. For CY threefolds, it is well-known that the BPS spectra are encoded by the (3d) crystal melting models. It turns out that the fixed points are still labelled by the similar combinatorial structure for the fourfolds, but the (4d) crystals do not contain the full information. For both threefolds and fourfolds, this can be seen from the JK residue formula, where it also recovers the weights (which are just signs for threefolds but are more non-trivial for fourfolds) in the BPS partition function. In the threefold cases, the (2-parametric) quiver Yangians realize the BPS algebras with the crystals as their representations. I will also mention the difficulties of such generalizations to the fourfold cases.
Jie Gu
Resurgent structures of free energies and Wilson loops in topological string
Perturbative series in topological string theory, such as perturbative free energies and perturbative Wilson loops, can be computed to higher orders. They also have non-perturbative corrections, and the resurgence theory predicts that they can be encoded in trans-series, and furthermore they control the perturbative series via Stokes transformations. Based on the previous results of Couso-Santamaria et.al., we solve the non-perturbative trans-series for both free energies and Wilson loops exactly through a trans-series extension of the BCOV holomorphic anomaly equations. We also give strong evidence that the Stokes constants associated to the Stokes transformations are identified with BPS/DT invariants.
Yehao Zhou
Vertex algebras and Nakajima quiver varieties
Given a framed quiver Q, one can associate a vertex algebra V(Q) by a BRST reduction procedure. V(Q) is closely related to 1) vertex algebra associated to the 4d N=2 quiver gauge theory of Q; 2) boundary vertex algebra of the H-twisted 3d N=4 quiver gauge theory of Q. In the recent work of Arakawa-Kuwabara-Moller, a sheaf of \hbar-adic vertex algebras on the Hilbert scheme of C^2 is defined. A generalization of their construction leads to a sheaf of \hbar-adic vertex algebras on the Nakajima quiver variety M(Q) for every Q. There is a natural vertex algebra map from V(Q) to the global section of the aforementioned sheaf, and I will exploit this map to study the properties of V(Q). In particular I will introduce a reduction operation on the quiver variety which induces a map from V(Q) to V(Q’) where Q’ is a quiver with one less node. In good situations, iterative quiver reductions result in free-field realization of V(Q). In type A examples, such free-field realization helps to identify affine W-algebra as vertex subalgebra of V(Q). This talk is based on the joint works (2312.13363 and another in preparation) with Ioana Coman, Myungbo Shim, and Masahito Yamazaki.