New Publication by Spiro Karigiannis

Title: Introduction to G2 geometry

 Spiro Karigiannis

Abstract: These notes give an informal and leisurely introduction to G2 geometry for beginners. A special emphasis is placed on understanding the special linear algebraic structure in 7 dimensions that is the pointwise model for G2 geometry, using the octonions. The basics of G2-structures are introduced, from a Riemannian geometric point of view, including a discussion of the torsion and its relation to curvature for a general G2-structure, as well as the connection to Riemannian holonomy. The history and properties of torsion-free G2 manifolds are considered, and we stress the similarities and differences with Ka ̈hler and Calabi-Yau manifolds. The notes end with a brief survey of three important theorems about compact torsion-free G2 manifolds.


New Publication by Enno Keßler, Artan Sheshmani and Shing-Tung Yau

Title: Super $J$-holomorphic Curves: Construction of the Moduli Space
Enno Keßler, Artan Sheshmani and Shing-Tung Yau

Abstract: Let $M$ be a super Riemann surface with holomorphic distribution $\mathcal{D}$ and $N$ a symplectic manifold with compatible almost complex structure $J$. We call a map $\Phi\colon M\to N$ a super $J$-holomorphic curve if its differential maps the almost complex structure on $\mathcal{D}$ to $J$. Such a super $J$-holomorphic curve is a critical point for the superconformal action and satisfies a super differential equation of first order. Using component fields of this super differential equation and a transversality argument we construct the moduli space of super $J$-holomorphic curves as a smooth subsupermanifold of the space of maps $M\to N$.

Arxiv: 1911.05607

Recent Publications by Juven Wang

Phys. Rev. D 100, 085012 – Published 21 October 2019

Title: Quantum 4d Yang-Mills theory and time-reversal symmetric 5d higher-gauge topological field theory

Zheyan Wan,  Juven Wang , and Yunqin Zheng

Abstract: We explore various 4d Yang-Mills gauge theories (YM) living as boundary conditions of 5d gapped short-/long-range entangled (SRE/LRE) topological states. Specifically, we explore 4d time-reversal symmetric pure YM of an SU(2) gauge group with a second-Chern-class topological term at θ=π [SU(2)θ=π YM], by turning on the background fields for both the time reversal (i.e., on unorientable manifolds) and the one-form center global symmetry. We find four siblings of SU(2)θ=π YM with distinct couplings to background fields, labeled by (K1,K2)K1=0, 1 specifies Kramers singlet/doublet Wilson line and new mixed higher ’t Hooft anomalies; K2=0, 1 specifies the boson/fermionic Wilson line and a new Wess-Zumino-Witten–like counterterm. Higher anomalies indicate that to realize all higher n-global symmetries locally on n simplices, the 4d theory becomes a boundary of a 5d higher-symmetry-protected topological state (SPTs, as an invertible topological quantum field theory (iTQFT) or a cobordism invariant in math, or as a 5d higher-symmetric interacting topological superconductor in condensed matter)… Continue reading Recent Publications by Juven Wang