Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebra of the infrared and secondary polytopes   We study algebraic structures ($L_\infty$ and $A_\infty$-algebras) introduced
by Gaiotto, Moore and Witten in their recent work devoted to certain
supersymmetric 2-dimensional massive field theories.
  We show that such structures can be systematically produced in any number of
dimensions by using the geometry of secondary polytopes, esp. their
factorization properties. In particular, in 2 dimensions, we produce, out of a
polyhedral "coefficient system", a dg-category $R$ with a semi-orthogonal
decomposition and an $L_\infty$-algebra $\mathfrak g$. We show that $\mathfrak
g$ is quasi-isomorphic to the ordered Hochschild complex of $R$, governing
deformations preserving the semi-orthogonal decomposition.
  This allows us to give a more precise mathematical formulation of the
(conjectural) alternative description of the Fukaya-Seidel category of a Kahler
manifold endowed with a holomorphic Morse function.

34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg