Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Existence of Heterotic-String and Type-II-Superstring Field
  Theory Vertices   We consider two problems associated to the space of Riemann surfaces that are
closely related to string theory. We first consider the problem of existence of
heterotic-string and type-II-superstring field theory vertices in the product
of spaces of bordered surfaces parameterizing left- and right-moving sectors of
these theories. It turns out that this problem can be solved by proving the
existence of a solution to the BV quantum master equation in moduli spaces of
bordered spin-Riemann surfaces. We first prove that for arbitrary genus $g$,
$n_{\text{NS}}$ Neveu-Schwarz boundary components, and $n_{\text{R}}$ Ramond
boundary components such solutions exist. We also prove that these solutions
are unique up to homotopies in the category of BV algebras and are mapped to
fundamental classes of Deligne-Mumford stacks of associated punctured spin
curves. These results generalize the work of Costello on the existence of a
solution to the BV quantum master equations in moduli spaces of bordered
ordinary Riemann surfaces. Using this, we prove that heterotic-string and
type-II-superstring field theory vertices exist. Furthermore, we prove the
existence of a solution to the BV quantum master equation in spaces of bordered
$\mathscr{N}=1$ super-Riemann surfaces for arbitrary genus $g$, $n_{\text{NS}}$
Neveu-Schwarz boundary components, and $n_{\text{R}}$ Ramond boundary
components. Secondly, we turn to the moduli problem of stable $\mathscr{N}=1$
SUSY curves. Using Vaintrob's deformation theory of complex superspaces and
Deligne's model for the compactification of the space of $\mathscr{N}=1$ SUSY
curves, we prove the representability of this moduli problem by a proper smooth
Deligne-Mumford superstack. This is a generalization of the work of Deligne and
Mumford on the representability of the moduli problem of stable ordinary curves
by a Deligne-Mumford stack.

8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat