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2018

Topological fermion condensates from anomalies

Catterall, Simon, Laiho, Jack, Unmuth-Yockey, Judah

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We show that a class of fermion theory formulated on a compact, curved manifold will generate a condensate whose magnitude is determined only by the volume and Euler characteristic of the space.

The construction requires that the fermions be treated as K\"{a}hler-Dirac fields and the condensate arises from an anomaly associated with a $U(1)$ global symmetry which is subsequently broken to a discrete subgroup.
Remarkably the anomaly survives under discretization of the space which allows us to compute the condensate on an arbitrary triangulation.
The results, being topological in character, should hold in a wide range of gravitationally coupled fermion theories both classical and quantum

Topological fermion condensates from anomalies · Around

Built on

E. Kahler Rend. Math 3-4, 21
1962
Earlier work this paper cites.
G. ’t Hooft, Symmetry Breaking Through Bell-Jackiw Anomalies , Phys. Rev. Lett. 37
1976
Earlier work this paper cites.
L. Susskind, Lattice Fermions , Phys. Rev. D16
1977
Earlier work this paper cites.
T. Banks, Y. Dothan and D. Horn, GEOMETRIC FERMIONS , Phys. Lett. 117B
1982
Earlier work this paper cites.

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S. Catterall, Simulations of dynamically triangulated quantum gravity - an algorithm for arbitrary dimension , Computer Physics Communications 87
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S. Catterall, J. Laiho and J. Unmuth-Yockey, in preparation ,
Original
Cited in the paper.

Then

S. Catterall, D. B. Kaplan and M. Unsal, Exact lattice supersymmetry , Phys. Rept. 484
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J. Ambjorn, J. Jurkiewicz and R. Loll, Causal Dynamical Triangulations and the Quest for Quantum Gravity , in Proceedings, Foundations of Space and Time: Reflections on Quantum Gravity: Cape Town, South Africa , pp. 321–337, 2010 · 2010
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J. Laiho, S. Bassler, D. Coumbe, D. Du and J. T. Neelakanta, Lattice Quantum Gravity and Asymptotic Safety , Phys. Rev. D96
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