Induced topological gravity and anomaly inflow from Kähler-Dirac fermions in odd dimensions

We show that the effective action that results from integrating out massive K¨ahler-Dirac fermions propagating on a curved three dimensional space is a topological gravity theory of Chern-Simons type. In the presence of a domain wall, massless, two dimensional K¨ahler-Dirac fermions appear that are localized to the wall. Potential gravitational anomalies arising for these domain wall fermions are cancelled via anomaly inflow from the bulk gravitational theory. We also study the invariance of the theory under large gauge transformations. The analysis and conclusions generalize straightforwardly to higher dimensions.

[1]  A. Wipf,et al.  Symmetries of Thirring Models on 3D Lattices , 2022, Symmetry.

[2]  S. Hands.  The Planar Thirring Model with Kähler-Dirac Fermions , 2021, Symmetry.

[3]  S. Catterall,et al.  Anomalies and symmetric mass generation for Kähler-Dirac fermions , 2021, Physical Review D.

[4]  S. Catterall.  Chiral lattice fermions from staggered fields , 2020, Physical Review D.

[5]  Shlomo S. Razamat,et al.  Gapped Chiral Fermions , 2020, 2009.05037.

[6]  Juven C. Wang,et al.  Beyond Standard Models and Grand Unifications: anomalies, topological terms, and dynamical constraints via cobordisms , 2019, 1910.14668.

[7]  M. Montero,et al.  Dai-Freed anomalies in particle physics , 2018, Journal of High Energy Physics.

[8]  J. Laiho,et al.  Topological fermion condensates from anomalies , 2018, Journal of High Energy Physics.

[9]  S. Chandrasekharan,et al.  Generating a nonperturbative mass gap using Feynman diagrams in an asymptotically free theory , 2017, 1709.06048.

[10]  S. Catterall,et al.  Topology and strong four fermion interactions in four dimensions , 2017, 1708.06715.

[11]  S. Chandrasekharan,et al.  Fermion masses through four-fermion condensates , 2016, 1606.06312.

[12]  S. Chandrasekharan,et al.  Origin of fermion masses without spontaneous symmetry breaking , 2015, 1511.09071.

[13]  S. Catterall.  Fermion mass without symmetry breaking , 2015, 1510.04153.

[14]  Cenke Xu,et al.  Interacting topological insulator and emergent grand unified theory , 2014, 1412.4784.

[15]  X. Qi.  A new class of (2 + 1)-dimensional topological superconductors with topological classification , 2012, 1202.3983.

[16]  A. Kitaev,et al.  Effects of interactions on the topological classification of free fermion systems , 2009, 0904.2197.

[17]  D. Kaplan,et al.  Exact lattice supersymmetry , 2008, 0903.4881.

[18]  J. Zanelli.  Lecture notes on Chern-Simons (super-)gravities , 2005 .

[19]  D. Kaplan.  A Method for simulating chiral fermions on the lattice , 1992, hep-lat/9206013.

[20]  A. Chamseddine.  Topological gravity and supergravity in various dimensions , 1990 .

[21]  A. Chamseddine.  Topological gauge theory of gravity in five and all odd dimensions , 1989 .

[22]  Shuichi Ojima.  Derivation of Gauge and Gravitational Induced Chern-Simons Terms in Three Dimensions , 1989 .

[23]  Edward Witten,et al.  (2+1)-Dimensional Gravity as an Exactly Soluble System , 1988 .

[24]  P. Becher,et al.  The Dirac-Kähler equation and fermions on the lattice , 1982 .

[25]  E. Witten.  An SU(2) anomaly , 1982 .

[26]  J. Rabin.  Homology theory of lattice fermion doubling , 1982 .

[27]  R. Delbourgo,et al.  The gravitational correction to PCAC , 1972 .

[28]  T. Morimoto,et al.  S ep 2 01 5 Breakdown of the topological classification Z for gapped phases of noninteracting fermions by quartic interactions , 2018 .

[29]  C. Callan,et al.  ANOMALIES AND FERMION ZERO MODES ON STRINGS AND DOMAIN WALLS , 1985 .

[30]  D. Horn,et al.  GEOMETRIC FERMIONS ~ , 1982 .