Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Notes for a Quantum Index Theorem   We view DHR superselection sectors with finite statistics as Quantum Field
Theory analogs of elliptic operators where KMS functionals play the role of the
trace composed with the heat kernel regularization. We extend our local
holomorphic dimension formula and prove an analogue of the index theorem in the
Quantum Field Theory context. The analytic index is the Jones index, more
precisely the minimal dimension, and, on a 4-dimensional spacetime, the DHR
theorem gives the integrality of the index. We introduce the notion of
holomorphic dimension; the geometric dimension is then defined as the part of
the holomorphic dimension which is symmetric under charge conjugation. We apply
the AHKT theory of chemical potential and we extend it to the low dimensional
case, by using conformal field theory. Concerning Quantum Field Theory on
curved spacetime, the geometry of the manifold enters in the expression for the
dimension. If a quantum black hole is described by a spacetime with bifurcate
Killing horizon and sectors are localizable on the horizon, the logarithm of
the holomorphic dimension is proportional to the incremental free energy, due
to the addition of the charge, and to the inverse temperature, hence to the
surface gravity in the Hartle-Hawking KMS state. For this analysis we consider
a conformal net obtained by restricting the field to the horizon
(``holography''). Compared with our previous work on Rindler spacetime, this
result differs inasmuch as it concerns true black hole spacetimes, like the
Schwarzschild-Kruskal manifold, and pertains to the entropy of the black hole
itself, rather than of the outside system. An outlook concerns a possible
relation with supersymmetry and noncommutative geometry.

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The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
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The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs