Related papers: Index Theory, Gerbes, and Hamiltonian Quantization
In gauge theories the field configurations often occur in distinct topological sectors. In a lattice regularised system with chiral fermions, these sectors can be defined by referring to the Atiyah-Singer Index Theorem. However, if such a…
When a quantum field theory is trivially gapped, its infrared fixed point is an invertible field theory. The partition function of the invertible field theory records the response to various background fields in the long-distance limit. The…
Topological fermions as excitations from multi-degenerate Fermi points have been attracting increasing interests in condensed matter physics. They are characterized by topological charges, and magnetic fields are usually applied in…
The use of bundle gerbes and bundle gerbe modules is considered as a replacement for the usual theory of Clifford modules on manifolds that fail to be spin. It is shown that both sides of the Atiyah-Singer index formula for coupled Dirac…
An index theory for projective families of elliptic pseudodifferential operators is developed when the twisting, i.e. Dixmier-Douady, class is decomposable. One of the features of this special case is that the corresponding Azumaya bundle…
We define the gauge-equivariant index of a family of elliptic operators invariant with respect to the free action of a family $\GR \to B$ of Lie groups (these families are called ``gauge-invariant families'' in what follows). If the fibers…
We define the equivariant family index of a family of elliptic operators invariant with respect to the free action of a bundle $\GR$ of Lie groups. If the fibers of $\GR \to B$ are simply-connected solvable, we then compute the Chern…
In this paper, we construct the index bundle gerbe of a family of self-adjoint Dirac-type operators, refining a construction of Segal. In a special case, we construct a geometric bundle gerbe called the caloron bundle gerbe, which comes…
We examine the noncommutative index theory associated to the dynamics of a Delone set and the corresponding transversal groupoid. Our main motivation comes from the application to topological phases of aperiodic lattices and materials, and…
A new supersymmetric proof of the Atiyah-Singer index theorem is presented. The Peierls bracket quantization scheme is used to quantize the supersymmetric classical system corresponding to the index problem for the twisted Dirac operator.…
In [Carey, A.L., J. Mickelsson, and M. K. Murray: Comm. Math. Phys. 183, 707 (1997)] Schwinger terms in hamiltonian quantization of chiral fermions coupled to vector potentials were computed, using some ideas from the theory of gerbes, with…
We formulate and prove a generalization of the Atiyah-Singer family index theorem in the context of the theory of spaces of manifolds \`a la Madsen, Tillmann, Weiss, Galatius and Randal-Williams. Our results are for Dirac-type operators…
We determine the zero eigenmode spectrum of Minimally Doubled Fermions (MDF), namely in Karsten-Wilczek (KW) and Borici-Creutz (BC) formulations on the 4-dimensional space-time lattice. We employ background gauge fields with integer valued…
We construct invertible field theories generalizing abelian prequantum spin Chern-Simons theory to manifolds of dimension 4k+3 endowed with a Wu structure of degree 2k+2. After analysing the anomalies of a certain discrete symmetry, we…
We study the Fadell-Husseini index of the configuration space F(R^d,n) with respect to different subgroups of the symmetric group S_n. For p prime and d>0, we completely determine Index_{Z/p}(F(R^d,p);F_p) and partially describe…
In this work, we study topological properties of surface bundles, with an emphasis on surface bundles with a spin structure. We develop a criterion to decide whether a given manifold bundle has a spin structure and specialize it to surface…
This paper further develops the combinatorial approach to quantization of the Hamiltonian Chern Simons theory advertised in \cite{AGS}. Using the theory of quantum Wilson lines, we show how the Verlinde algebra appears within the context of…
We give a new proof of an index theorem for fiber bundles of compact topological manifolds due to Dwyer, Weiss, and Williams, which asserts that the parametrized $A$-theory characteristic of such a fiber bundle factors canonically through…
We study 5d fermionic CS theory with a fermionic 2-form gauge potential. This theory can be obtained from 5d MSYM theory by performing the maximal topological twist. We put the theory on a five-manifold and compute the partition function.…
Into a geometric setting, we import the physical interpretation of index theorems via semi-classical analysis in topological quantum field theory. We develop a direct relationship between Fedosov's deformation quantization of a symplectic…