Six-dimensional F-theory compactifications provide a geometric framework for constructing UV complete quantum theory of gravity, in which gauge symmetries and charged matter arise from singularities of elliptically fibered Calabi–Yau threefolds. An important consistency condition on these theories is the cancellation of gravitational anomalies.
I will first review this physical picture and explain how matters localize at singularities, then explain how six-dimensional matter representations can be constructed from the CoHA/BPS cohomology of resolved cDV singularities, equipped with a natural action of the gauge algebra. Finally, I will give a geometric derivation of the 6D gravitational anomaly cancellation condition, reducing it through five-dimensional Coulomb/Higgs branch physics to a local statement about singularities of elliptic Calabi–Yau threefolds.
About the speaker:
Kai Xu is an Assistant Professor at the Yau Mathematical Sciences Center (YMSC), Tsinghua University. He received his Ph.D. in Mathematics from Harvard University and subsequently held a postdoctoral fellowship in the Department of Physics at Harvard. His research lies at the interface of algebraic geometry, string theory, and quantum gravity.
Prof. Yinan Wang