Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: S-duality transformation of $\mathcal{N}$ $=4$ SYM theory at the
  operator level   We consider the S-duality transformation of gauge invariant operators and
states in $\mathcal{N}$ $=4$ SYM theory. The transformation is realized through
an operator $ S $ which is the $ SL(2,Z) $ canonical transformation in loop
space with the gauge invariant electric and the magnetic flux operators
composing the canonical variables. Based on $ S $, S-duals for all of the
physical operators and states can be defined. The criterion for the theory to
be S-duality invariant is that the superconformal charges and their S-duals
differ by a $ U(1)_{Y} $ phase. The verification can be done by checking the S
transformation for supersymmetry and special supersymmetry variations of the
loop operators. The fact that supercharges preserved by BPS Wilson operators
and the S-dual BPS 't Hooft operators differ by a $4d $ chiral rotation could
in some sense serve as a proof.

31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
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The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org