Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Superconformal vertex algebras in differential geometry. I   We show how to construct an N=1 superconformal vertex algebra (SCVA) from any
Riemannian manifold. When the Riemannian manifold has special holonomy groups,
we discuss the extended supersymmetry. When the manifold is complex or
K\"{a}hler, we also generalize the construction to obtain N=2 SCVA's. We study
the BRST cohomology groups of the topological vertex algebras obtained by the
$A$ twist and the $B$ twist from these N=2 SCVA's. We show that for one of
them, the BRST cohomologies are isomorphic to $H^*(M, \Lambda^*(T^*M))$ and
$H^*(M, \Lambda^*(TM))$ respectively. This provides a mathematical formulation
of the $A$ theory and $B$ theory in physics literature. The connection with
elliptic genera is also discussed. Furthermore, when the manifold is
hyperk\"{a}hler, we generalize our constructions to obtain N=4 SCVA's. A
heuristic relationship with super loop space is also discussed.

30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat