Lectures: Zhiyuan Wang--Abstract QFTs and Their Realizations(Dec 21-22-23, 2021)



TitleAbstract QFTs and Their Realizations

SpeakerZhiyuan Wang(王知远)

Affiliation: Peking Universtiy

Time: 14:00-15:30, Tuesday, December 21st, 2021

           14:00-15:30, Wednesday, December 22nd, 2021

           14:00-15:30, Thursday, December 23rd, 2021(UTC+8, Beijing Time)

Venue: Room 1502, Shing-Tung Yau Center, Yifu Architecture Building, Sipailou Campus of Southeast University, Nanjing

Inviter: Jun Wang(王俊)Yunfeng Jiang(江云峰)


The aim of these three lectures is to introduce a formalism called abstract quantum field theories and their realizations.

The first two lectures will be pedagogical, in which I will recall some preliminaries of moduli spaces of curves, formal Gaussian integrals, integration over Hermitian matrices, and their relation to Feynman graphs. These results are well-known in literatures.

In the third lecture I will introduce the construction of the abstract QFT for stable graphs and fat graphs, and their realizations. This is a joint work with J. Zhou. We define the abstract partition function and abstract free energy as formal summations of graphs, and derive recursion relations for them using operators inspired by geometry of moduli spaces of curves. By assigning Feynman rules, we obtain some specific theories or problems and their recursion relations (such as the holomorphic anomaly type equations, Virasoro constraints, etc.) in this way.


About the Speaker


Slides--Wang Zhiyuan-Abstract QFTs Realizations and Recursion Relations -20211223.pdf