Topological Invariance of the Witten Index
نویسنده
چکیده
We discuss the Witten index in terms of Krein's spectral shift function, and prove invariance of the Witten index under suitable relative trace class hypotheses.
منابع مشابه
Witten index, axial anomaly, and Krein's spectral shift function in supersymmetric quantum mechanics
A new method is presented to study supersymmetric quantum mechanics. Using relative scattering techniques, basic relations are derived between Krein's spectral shift function, the Witten index, and the anomaly. The topological invariance of the spectral shift function is discussed. The power of this method is illustrated by treating various models and calculating explicitly the spectral shift f...
متن کاملInvariance of the barycentric subdivision of a simplicial complex
In this paper we prove that a simplicial complex is determined uniquely up to isomorphism by its barycentric subdivision as well as its comparability graph. We also put together several algebraic, combinatorial and topological invariants of simplicial complexes.
متن کاملOn Elliptic Genera and Theta-Functions
The main purpose of this paper is to give a simple and unified new proof of the Witten rigidity theorems, which were conjectured by Witten and first proved by Taubes [T], Bott-Taubes [BT], Hirzebruch [H] and Krichever [Kr]. Our proof shows that the modular invariance, which is the intrinsic symmetry of elliptic genera, actually implies their rigidity. Some new properties of elliptic genera and ...
متن کاملNew Proof of the Cobordism Invariance of the Index
We give a simple proof of the cobordism invariance of the index of an elliptic operator. The proof is based on a study of a Witten-type deformation of an extension of the operator to a complete Riemannian manifold. One of the advantages of our approach is that it allows to treat directly general elliptic operator which are not of Dirac type.
متن کامل2 00 2 Topological charge and topological susceptibility in connection with translation and gauge invariance
It is shown that the evaluation of the expectation value (EV) of topological charge density over θ-vacuum is reduced to investigation of the Chern-Simons term EV. An equation for this quantity is established and solved. EV of the topological charge density at an arbitrary θ occurs equal to zero and, as a consequence, topological susceptibility of both QCD and pure Yang-Mills vacua defined in a ...
متن کامل