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Jonathan Heckman: Lectures

June 8, 2022
TITLE: Getting High on Gluing Orbifolds

ABSTRACT:
Quantum field theories (QFTs) engineered from M-theory on singular non-compact manifolds often enjoy a rich dictionary between physical data and geometric quantities. For instance, when real codimension-4 ADE orbifold singularities extend out to the asymptotic boundary, the local operators of the QFT form representations of a (so-called) flavor group whose Lie algebra is specified by the ADE-types. We present a novel geometric procedure to calculate the global structure of this group. Additionally, taking into account line operators of the QFT, this structure may generalize to a 2-group and we give a geometric picture for this as well. For part I of this talk series, we will discuss these ideas in the context of 5d superconformal field theories engineered from M-theory on quotients of C^3.

September 12, 2021
TITLE: Quantum Reflections in 3D QFTs and their Local Spin(7) Counterparts

ABSTRACT:
Compactifications of M-theory on local Spin(7) spaces with singularities provide a flexible framework for realizing 3D quantum field theories (QFTs). We explain how physical anomalies associated with reflections translate in the local Spin(7) geometry to certain index-theoretic structures which take values mod 16 rather than over the integers. This is in contrast with the case of M-theory on a local G2 space and F-theory on an elliptically fibered Calabi-Yau fourfold, where the analogous indices for 4D quantum field theories take values over the integers. Our primary tool used to establish this correspondence involves Higgs bundles on four-manifolds and three-manifolds. Based on joint work with M. Cvetic, E. Torres and G. Zoccarato.

April 12, 2019
TITLE: F-Theory and Spin7 Manifolds

ABSTRACT:
We discuss some recent progress in understanding 4D vacua obtained from F-theory on Spin(7) manifolds. Such backgrounds provide a potentially attractive way to avoid fine-tuning to cancel zero point energies. We present a general proposal for cosmological solutions in this framework, and also develop the physical formalism of local Spin(7) geometries containing a four-manifold of ADE singularities.

Based on work with C. Lawrie, L. Lin, and G. Zoccarato, hep-th/1811.01959

and C. Lawrie, L. Lin, J. Sakstein and G. Zoccarato, hep-th/1901.10489.