Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Physics and geometry of knots-quivers correspondence   The recently conjectured knots-quivers correspondence relates gauge theoretic
invariants of a knot $K$ in the 3-sphere to representation theory of a quiver
$Q_{K}$ associated to the knot. In this paper we provide geometric and physical
contexts for this conjecture within the framework of the large $N$ duality of
Ooguri and Vafa, that relates knot invariants to counts of holomorphic curves
with boundary on $L_{K}$, the conormal Lagrangian of the knot in the resolved
conifold, and corresponding M-theory considerations. From the physics side, we
show that the quiver encodes a 3d ${\mathcal N}=2$ theory $T[Q_{K}]$ whose low
energy dynamics arises on the worldvolume of an M5 brane wrapping the knot
conormal and we match the (K-theoretic) vortex partition function of this
theory with the motivic generating series of $Q_{K}$. From the geometry side,
we argue that the spectrum of (generalized) holomorphic curves on $L_{K}$ is
generated by a finite set of basic disks. These disks correspond to the nodes
of the quiver $Q_{K}$ and the linking of their boundaries to the quiver arrows.
We extend this basic dictionary further and propose a detailed map between
quiver data and topological and geometric properties of the basic disks that
again leads to matching partition functions. We also study generalizations of
A-polynomials associated to $Q_{K}$ and (doubly) refined version of LMOV
invariants.

30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom