Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $\beta$-function of supersymmetric theories from vacuum supergraphs:
  a three-loop example   We verify a method which allows to obtain the $\beta$-function of
supersymmetric theories regularized by higher covariant derivatives by
calculating only specially modified vacuum supergraphs. With the help of this
method for a general renormalizable ${\cal N}=1$ supersymmetric gauge theory a
part of the three-loop $\beta$-function depending on the Yukawa couplings is
constructed in the general $\xi$-gauge. The result is written in the form of an
integral of double total derivatives with respect to the loop momenta. It is
demonstrated that all gauge dependent terms cancel each other in agreement with
the general statements. Taking into account that the result in the Feynman
gauge (found earlier) coincides with the one obtained by the standard
technique, this fact confirms the correctness of the considered method by a
highly nontrivial multiloop calculation.

8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
2
The categories of this paper are: math
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas