Title: Anomalies and symmetric mass generation for Kähler-Dirac fermions

Abstract

We show that massless Kähler-Dirac fermions exhibit a mixed gravitational anomaly involving an exact U (1) symmetry which is unique to Kähler-Dirac fields. Under this U (1) symmetry the partition function transforms by a phase depending only on the Euler character of the background space. Compactifying flat space to a sphere we learn that the anomaly vanishes in odd dimensions but breaks the symmetry down to Z₄ in even dimensions. This Z₄ is sufficient to prohibit bilinear terms from arising in the fermionic effective action. Four fermion terms are allowed but require multiples of two flavors of Kähler-Dirac field. In four dimensional flat space each Kähler-Dirac field can be decomposed into four Dirac spinors and hence these anomaly constraints ensure that eight Dirac fermions or, for real representations, sixteen Majorana fermions are needed for a consistent interacting theory. These constraints on fermion number agree with known results for topological insulators and recent work on discrete anomalies rooted in the Dai-Freed theorem. Our work suggests that Kähler-Dirac fermions may offer an independent path to understanding these constraints. Finally we point out that this anomaly survives intact under discretization and hence is relevant in understanding recent numerical results on lattice models possessingmore » massive symmetric phases.« less

Authors:

Butt, Nouman; Catterall, Simon ;

• Search DOE PAGES for author "Catterall, Simon"
• Search DOE PAGES for ORCID "0000-0003-2735-2682"
• Search orcid.org for ORCID "0000-0003-2735-2682"

Pradhan, Arnab; Toga, Goksu Can

• Search DOE PAGES for author "Toga, Goksu Can"
• Search DOE PAGES for ORCID "0000-0002-0316-2502"
• Search orcid.org for ORCID "0000-0002-0316-2502"

Publication Date:

2021-11-09

Research Org.:

Syracuse Univ., NY (United States)

Sponsoring Org.:

USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:

1829539

Alternate Identifier(s):

OSTI ID: 1834396

Grant/Contract Number:  

SC0009998

Resource Type:

Published Article

Journal Name:

Physical Review D

Additional Journal Information:

Journal Name: Physical Review D Journal Volume: 104 Journal Issue: 9; Journal ID: ISSN 2470-0010

Publisher:

American Physical Society

Country of Publication:

United States

Language:

English

Subject:

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS