# The 39th International Symposium on Lattice Field Theory (Lattice 2022)

Aug 8 – 13, 2022
Hörsaalzentrum Poppelsdorf
Europe/Berlin timezone

## Reformulation of anomaly inflow on the lattice and construction of lattice chiral gauge theories

Aug 10, 2022, 2:20 PM
20m
CP1-HSZ/1st-1.001 - HS5 (CP1-HSZ)

### CP1-HSZ/1st-1.001 - HS5

#### CP1-HSZ

50
Oral Presentation Theoretical Developments and Applications beyond Particle Physics

### Speaker

Juan William Pedersen (The University of Tokyo)

### Description

This research aims to analyze the integrability condition of the chiral determinant of 4D overlap fermions and construct lattice chiral gauge theories.
$\quad$ We formulate the integrability condition with 5D and 6D lattice domain wall fermions. Our formulation parallels the recent cobordism classification of the global ‘t Hooft anomaly using the $\eta$-invariant based on the Dai-Freed theorem and the Atiya-Patodi-Singer index theorem in the continuum theory.
$\quad$ The necessary and sufficient condition for constructing a lattice chiral gauge theory comes down to the statement that "$\exp ( 2\pi i \eta ) = 1$ for any gauge configurations satisfying the admissibility condition in 5D lattice space.", where $\exp ( 2\pi i \eta )$ is defined as the phase of the partition function of the 5D domain wall fermion.

### Primary authors

Juan William Pedersen (The University of Tokyo) Prof. Yoshio Kikukawa (The University of Tokyo)