Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Implications of ANEC for SCFTs in four dimensions   We explore consequences of the Averaged Null Energy Condition (ANEC) for
scaling dimensions $\Delta$ of operators in four-dimensional $\mathcal{N}=1$
superconformal field theories. We show that in many cases the ANEC bounds are
stronger than the corresponding unitarity bounds on $\Delta$. We analyze in
detail chiral operators in the $(\frac12 j,0)$ Lorentz representation and prove
that the ANEC implies the lower bound $\Delta\ge\frac32j$, which is stronger
than the corresponding unitarity bound for $j>1$. We also derive ANEC bounds on
$(\frac12 j,0)$ operators obeying other possible shortening conditions, as well
as general $(\frac12 j,0)$ operators not obeying any shortening condition. In
both cases we find that they are typically stronger than the corresponding
unitarity bounds. Finally, we elucidate operator-dimension constraints that
follow from our $\mathcal{N}=1$ results for multiplets of $\mathcal{N}=2,4$
superconformal theories in four dimensions. By recasting the ANEC as a convex
optimization problem and using standard semidefinite programming methods we are
able to improve on previous analyses in the literature pertaining to the
nonsupersymmetric case.

37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an