47 citations · 256 across the 17 of their papers we have counts for
17 papers
Dimer geometry, amoebae and a vortex dimer model
Charles Nash, Denjoe O'Connor
We present a geometrical approach for studying dimers. We introduce a connection for dimer problems on bipartite and non-bipartite graphs. In the bipartite case the connection is f…
The Zero Temperature Phase Diagram of the Kitaev Model
Charles Nash, Denjoe O'Connor
We show that the zero temperature phase diagram of the vortex free sector of the Kitaev model is in one to one correspondence with that of the classical dimer model on the same lat…
Chern-Simons action for zero-mode supporting gauge fields in three dimensions
C. Adam, B. Muratori, C. Nash
Recent results on zero modes of the Abelian Dirac operator in three dimensions support to some degree the conjecture that the Chern-Simons action admits only certain quantized valu…
Chiral Fermions and Spinc structures on Matrix approximations to manifolds
Brian P. Dolan, C. Nash
The Atiyah-Singer index theorem is investigated on various compact manifolds which admit finite matrix approximations (``fuzzy spaces'') with a view to applications in a modified K…
Particle creation via relaxing hypermagnetic knots
C. Adam, B. Muratori, C. Nash
We demonstrate that particle production for fermions coupled chirally to an Abelian gauge field like the hypercharge field is provided by the microscopic mechanism of level crossin…
Zero modes in finite range magnetic fields
C. Adam, B. Muratori, C. Nash
We find a class of Fermion zero modes of Abelian Dirac operators in three dimensional Euclidean space where the gauge potentials and the related magnetic fields are nonzero only in…
On non- solutions to the Seiberg-Witten equations
C. Adam, B. Muratori, C. Nash
We show that a previous paper of Freund describing a solution to the Seiberg-Witten equations has a sign error rendering it a solution to a related but different set of equations.…
Multiple zero modes of the Dirac operator in three dimensions
C. Adam, B. Muratori, C. Nash
One of the key properties of Dirac operators is the possibility of a degeneracy of zero modes. For the Abelian Dirac operator in three dimensions the construction of multiple zero…
Hopf instantons and the Liouville equation in target space
C. Adam, B. Muratori, C. Nash
We generalise recent results on Hopf instantons in a Chern--Simons and Fermion theory in a fixed background magnetic field. We find that these instanton solutions have to obey the…
Degeneracy of zero modes of the Dirac operator in three dimensions
C. Adam, B. Muratori, C. Nash
One of the key properties of Dirac operators is the possibility of a degeneracy of zero modes. For the Abelian Dirac operator in three dimensions the question whether such multiple…
Hopf instantons in Chern-Simons theory
C. Adam, B. Muratori, C. Nash
We study an Abelian Chern-Simons and Fermion system in three dimensions. In the presence of a fixed prescribed background magnetic field we find an infinite number of fully three-d…
Zero modes of the Dirac operator in three dimensions
C. Adam, B. Muratori, C. Nash
We investigate zero modes of the Dirac operator coupled to an Abelian gauge field in three dimensions. We find that the existence of a certain class of zero modes is related to a s…
Modular invariance, lattice field theories and finite size corrections
Charles Nash, Denjoe O' Connor
We give a lattice theory treatment of certain one and two dimensional quantum field theories. In one dimension we construct a combinatorial version of a non-trivial field theory on…
Modular Invariance of Finite Size Corrections and a Vortex Critical Phase
Charles Nash, Denjoe O'Connor
We analyze a continuous spin Gaussian model on a toroidal triangular lattice with periods and where the spins carry a representation of the fundamental group of the tor…
BRST Quantisation and the Product Formula for the Ray-Singer Torsion
Charles Nash, Denjoe O' Connor
We give a quantum field theoretic derivation of the formula obeyed by the Ray-Singer torsion on product manifolds. Such a derivation has proved elusive up to now. We use a BRST for…
Determinants of Laplacians, the Ray-Singer Torsion on Lens Spaces and the Riemann zeta function
Charles Nash, Denjoe O' Connor
We obtain explicit expressions for the determinants of the Laplacians on zero and one forms for an infinite class of three dimensional lens spaces . These expressions can b…
Ray-Singer Torsion, Topological field theories and the Riemann zeta function at s=3
Charles Nash, Denjoe O' Connor
Starting with topological field theories we investigate the Ray-Singer analytic torsion in three dimensions. For the lens Spaces L(p;q) an explicit analytic continuation of the app…