Chapter 5
Supersymmetry Breaking
Throughout these lecture notes, we have discussed the superfield methodology for
studying supersymmetric field theories. However, it is known that, actually the supersymmetry is broken at observed scales of energy. There are two ways to describe
the breaking of any symmetry including the supersymmetry, those are—explicit and
spontaneous breaking. The detailed discussions of the supersymmetry breaking are
presented in famous review papers, such as [114, 115], and, of course, in classical supersymmetry textbooks like [23, 32, 43]. Here we do not intend to give a
detailed discussion of the supersymmetry breaking, following a more modest aim—
to present a brief description of some ways to describe these phenomena in terms
of the superfield methodology. Here we concentrate on the theories defined in the
four-dimensional space-time.
5.1 Explicit Supersymmetry Breaking
To break the supersymmetry, continuing within the framework of the superfield
approach, we suggest that the classical action of the theory involves a small additive
term whose presence breaks the supersymmetry. Proceeding on the base of the superfield description, at least formally, we can introduce such an additive term through an
introduction of a special extra “superfield” possessing a broken component structure,
with a corresponding non-trivial component of this superfield is a constant. Actually
such a superfield, called a spurion, represents itself as a some generalization of a
coupling constant (actually, this is a soft supersymmetry breaking if the divergences
continue to be logarithmic; we also note that additive supersymmetry-breaking terms
are small). There is a natural restriction on the structure of such terms, indeed, it is
easy to see that only logarithmic divergences can emerge within quantum corrections
in Wess-Zumino and SYM theories: while for the Wess-Zumino model it follows
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
A. Petrov, Quantum Superfield Supersymmetry, Fundamental Theories of Physics 202,
https://doi.org/10.1007/978-3-030-68136-4_5
143
Supersymmetry Breaking
Throughout these lecture notes, we have discussed the superfield methodology for
studying supersymmetric field theories. However, it is known that, actually the supersymmetry is broken at observed scales of energy. There are two ways to describe
the breaking of any symmetry including the supersymmetry, those are—explicit and
spontaneous breaking. The detailed discussions of the supersymmetry breaking are
presented in famous review papers, such as [114, 115], and, of course, in classical supersymmetry textbooks like [23, 32, 43]. Here we do not intend to give a
detailed discussion of the supersymmetry breaking, following a more modest aim—
to present a brief description of some ways to describe these phenomena in terms
of the superfield methodology. Here we concentrate on the theories defined in the
four-dimensional space-time.
5.1 Explicit Supersymmetry Breaking
To break the supersymmetry, continuing within the framework of the superfield
approach, we suggest that the classical action of the theory involves a small additive
term whose presence breaks the supersymmetry. Proceeding on the base of the superfield description, at least formally, we can introduce such an additive term through an
introduction of a special extra “superfield” possessing a broken component structure,
with a corresponding non-trivial component of this superfield is a constant. Actually
such a superfield, called a spurion, represents itself as a some generalization of a
coupling constant (actually, this is a soft supersymmetry breaking if the divergences
continue to be logarithmic; we also note that additive supersymmetry-breaking terms
are small). There is a natural restriction on the structure of such terms, indeed, it is
easy to see that only logarithmic divergences can emerge within quantum corrections
in Wess-Zumino and SYM theories: while for the Wess-Zumino model it follows
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
A. Petrov, Quantum Superfield Supersymmetry, Fundamental Theories of Physics 202,
https://doi.org/10.1007/978-3-030-68136-4_5
143