Higher Berry Phase of Free Dirac Fermions

Abstract: The infrared fixed point of a trivially gapped quantum field theory is described by an invertible field theory, which captures its response to various external background fields. The set of background fields can include spacetime-dependent coupling constants, in which case we call the corresponding invertible theory a parameterized invertible field theory. The partition function of a parameterized invertible field theory is called a higher Berry phase, as it captures the response of the theory to the adiabatic variation of the coupling constants across spacetime. I'll discuss a class of such parameterized invertible field theories arising from free Dirac fermions with spacetime-dependent mass parameters. The universal form of the higher Berry curvature will be derived using the APS index theorem, and an example of a nontrivial parameterized invertible theory with a vanishing Berry curvature will be explained.

MathematicsPhysics

Audience: researchers in the topic

Symmetry Seminar

Series comments: Weekly seminar on generalized symmetries in QFT, string theory and related topics.