北京雁栖湖应用数学研究院

李淇明 , 安东·普里比托克

Alexander Belavin

2025年04月03日 14:55 至 16:30

A3-4-301

Zoom 462 110 5973 (BIMSA)

Heterotic string Gepner models in 4-dimensions are hybrid theories of a left-moving Superstring whose additional 6-dimensions are compactified on the product of the $N=2$-SCFT minimal models, which is equivalent to a compactification on Calabi-Yau manifold, and a right-moving Bosonic string, whose additional 6 dimensions are also compactified on the product $N=2$ minimal models, and the remaining 13 dimensions of which form the torus of $ E(8) \times SO(10) $. Such heterotic models have $N=1$ space-time symmetry arising in its left-moving part and $E(6)$ gauge symmetry arising in its right-moving part. These symmetries are necessary for phenomenological reasons and to obtain Grand Unified Theories. In Gepner's work, the requirement that leads to the models having the desired spacetime symmetry and gauge symmetry was the requirement that spacetime symmetry should be compatible with modular invariance. We will show that the requirement of mutual locality of the left-moving vertices of physical states with SUSY currents and the right moving vertices with currents of $E(6)$-gauge symmetry, together with the requirement of mutual locality of full vertices of physical states leads to the same theory.

Aleksander A. Belavin is internationally renowned for his seminal contributions to theoretical physics, which have profoundly shaped the development of quantum field theory and string theory. He was one of the founders of the BPST instanton, a landmark discovery that significantly advanced the understanding of the chiral anomaly and opened new directions in non-perturbative quantum field theory. In his earlier works, he provided pioneering evidence for novel coupling regimes in gauge theories. He later introduced the S-matrices, describing exactly solvable models in two-dimensional relativistic quantum field theory (Belavin S-matrix). Among his influential achievements is the foundational BPZ paper, co-authored with A. Polyakov and A. Zamolodchikov, which established the framework of two-dimensional conformal field theory and became central to the development of string theory and statistical mechanics. His subsequent collaboration with V. Knizhnik led to the Belavin–Knizhnik theorem on dual amplitudes in string theory. These milestones represent only part of A. Belavin’s scientific achievements in theoretical and mathematical physics. In recognition of his achievements, he was awarded the Pomeranchuk Prize in 2007 for his remarkable contributions to quantum field theory, including the discovery of instanton solutions in QCD and deep insights into two-dimensional conformal string theory. In 2011, he received the Lars Onsager Prize for the creation of conformal field theory.