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Topological gravity on the lattice · Around

2010

Topological gravity on the lattice

Catterall, Simon

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In this paper we show that a particular twist of $\mathcal{N}=4$ super Yang-Mills in three dimensions with gauge group SU(2) possesses a set of classical vacua corresponding to the space of flat connections of the {\it complexified} gauge group $SL(2,C)$.

The theory also contains a set of topological observables corresponding to Wilson loops wrapping non-trivial cycles of the base manifold.
This moduli space and set of topological observables is shared with the Chern Simons formulation of three dimensional gravity and we hence conjecture that the Yang-Mills theory gives an equivalent description of the gravitational theory.
Unlike the Chern Simons formulation the twisted Yang-Mills theory possesses a supersymmetric and gauge invariant lattice construction which then provides a possible non-perturbative definition of three dimensional gravity.

Built on

E. Witten, Topological Quantum Field Theory
1988
Earlier work this paper cites.
E. Witten, (2+1)-Dimensional Gravity as an Exactly Soluble System
1988
Earlier work this paper cites.
E. Witten, Topology Changing Amplitudes in (2+1)-Dimensional Gravity
1989
Earlier work this paper cites.
A. H. Chamseddine, TOPOLOGICAL GAUGE THEORY OF GRAVITY IN FIVE-DIMENSIONS AND ALL ODD DIMENSIONS
1989
Earlier work this paper cites.
N. Marcus, The other topological twisting of n=4 yang-mills
1995
Earlier work this paper cites.

Similar

S. Carlip, Lectures on (2+1) dimensional gravity
1995
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M. Blau and G. Thompson, Aspects of N T ≥ 2 N_{T}\geq 2 Topological Gauge Theories and D- Branes
1997
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A. G. Cohen, D. B. Kaplan, E. Katz, and M. Unsal, Supersymmetry on a Euclidean spacetime lattice. II: Target theories with eight supercharges
2003
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M. Unsal, Twisted supersymmetric gauge theories and orbifold lattices
2006
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P. H. Damgaard and S. Matsuura, Classification of Supersymmetric Lattice Gauge Theories by Orbifolding
2007
Cited alongside, same era.
A. Kapustin and E. Witten, Electric-magnetic duality and the geometric Langlands program
Cited in the paper.
S. Catterall, First results from simulations of supersymmetric lattices
Cited in the paper.

Then

S. Catterall, From Twisted Supersymmetry to Orbifold Lattices
2008
Later among the works it cites.
P. H. Damgaard and S. Matsuura, Geometry of Orbifolded Supersymmetric Lattice Gauge Theories
2008
Later among the works it cites.
J. Zanelli, Lecture notes on Chern-Simons (super-)gravities. Second edition (February 2008)
Original
2008
Later among the works it cites.
S. Catterall, D. B. Kaplan, and M. Unsal, Exact lattice supersymmetry
2009
Later among the works it cites.

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