Calendar

On November 28 – Dec 1, 2022, the CMSA will host a Workshop on Representation Theory, Calabi-Yau Manifolds, and Mirror Symmetry.

For more information, please see: https://cmsa.fas.harvard.edu/event/representation-theory-calabi-yau-manifolds-and-mirror-symmetry/

 In this talk I will discuss the application of the Cobordism Conjecture to type IIB supergravity with non-trivial duality bundle. Calculating the relevant bordism groups we find that they are highly non-trivial and would predict the presence of various global symmetries in the underlying theory. Since quantum gravity theories do not allow for global symmetries, we discuss which defects need to be included to break them completely. Interestingly, we find many backgrounds that are well-known in the F-theory literature, such as [p,q]-7-branes, non-Higgsable clusters, as well as S-folds and their generalizations to higher codimensions. Further including worldsheet reflections, predicts the existence of a new non-supersymmetric 7-brane with interesting properties and applications, which I will discuss in more detail.

The Motivated by the higher Chern bands of twisted graphene multilayers, we consider flat bands with

arbitrary Chern number C with ideal quantum geometry. While C>1 bands differ from Landau levels, we

show that these bands host exact fractional Chern insulator (FCI) ground states for short range

interactions. We show how to decompose ideal higher Chern bands into separate ideal bands with Chern

number 1 that are intertwined through translation and rotation symmetry. The decomposed bands admit

an SU(C) action that combines real space and momentum space translations. Remarkably, they also

allow for analytic construction of exact many-body ground states, such as generalized quantum Hall

ferromagnets and FCIs, including flavor-singlet Halperin states and Laughlin ferromagnets in the limit

of short-range interactions. In this limit, the SU(C) action is promoted to a symmetry on the ground state

subspace. While flavor singlet states are translation symmetric, the flavor ferromagnets correspond to

translation broken states and admit charged skyrmion excitations corresponding to a spatially varying

density wave pattern. We confirm our analytic predictions with numerical simulations of ideal bands of

twisted chiral multilayers of graphene, and discuss consequences for experimentally accessible systems

such as monolayer graphene twisted relative to a Bernal bilayer.

For more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/quantum-matter-seminar/

I will discuss various aspects of the geometry of Quot schemes of torsion quotients on a smooth projective curve. I will describe in particular results on the cohomology of tautological vector bundles over the Quot scheme, which mirror a parallel picture in the geometry of the Hilbert scheme of points over a surface. The subject has an interesting combinatorial and computational flavor. The talk is partly based on joint work with D. Oprea and S. Sam.

We explore generalized global symmetries in theories of physics beyond the Standard Model. Theories of Z′ bosons generically contain ‘non-invertible’ chiral symmetries, whose presence indicates a natural paradigm to break this symmetry by an exponentially small amount in an ultraviolet completion. For example, in models of gauged lepton family difference such as the phenomenologically well-motivated U(1)Lμ−Lτ, there is a non-invertible lepton number symmetry which protects neutrino masses. We embed these theories in gauged non-Abelian horizontal lepton symmetries, e.g. U(1)Lμ−Lτ⊂SU(3)H, where the generalized symmetries are broken nonperturbatively by the existence of lepton family magnetic monopoles. In such theories, either Majorana or Dirac neutrino masses may be generated through quantum gauge theory effects from the charged lepton Yukawas e.g. yν∼yτexp(−Sinst). These theories require no bevy of new fields nor ad hoc additional global symmetries, but are instead simple, natural, and predictive: the discovery of a lepton family Z′ at low energies will reveal the scale at which Lμ−Lτ emerges from a larger gauge symmetry.

For more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/quantum-matter-seminar/