4.12 Conclusions
141
ric matter. One more reason of the interest to SYM theories is caused by the fact that
namely the N = 4 SYM theory is the first known explicitly finite four-dimensional
theory without higher derivatives. It is interesting to note that this finiteness can
be apparently extended to the noncommutative generalization of this theory, see
[104]. Moreover, we explicitly demonstrated that our methodology can be applied
not only to usual Wess-Zumino and supergauge theories but can be also extended
to their nontrivial generalizations including non-polynomial and higher-derivative
ones, which play important role for constructing various low-energy effective models (as we already argued, such effective models can arise, for example, when some
of superfields, for example heavy ones, are integrated out). It is interesting to note
that the superfield approach is very efficient for performing quantum calculations
even in nonlocal supersymmetric theories, i.e. those ones involving infinite orders in
derivatives. The examples of such studies are presented in [112] (see also references
therein).
At the same time, the natural question is—whether perturbative treating of superfield models based on other multiplets is possible and can be realized? An important
example of such a multiplet is the spinor chiral superfield representing the so-called
tensor multiplet defined in [23], whose importance is motivated by the fact that its
component content includes the Kalb-Ramond antisymmetric tensor field, therefore
it can play a fundamental role within study of effective theories arising in the string
context. An important property of this superfield consists in the fact that its free
Lagrangian possesses the gauge symmetry. First perturbative studies of field theory
models involving this superfield have been performed in [113], where the one-loop
effective action in a theory involving a spinor chiral superfield and a usual real gauge
scalar superfield coupled to a chiral matter has been calculated.
And, besides of considering these superfields, studies of the supergravity multiplet certainly have a fundamental role. A detailed discussion of the supergravity
is presented in [23]; here, because of restricted volume of our review, we will not
discuss it.
141
ric matter. One more reason of the interest to SYM theories is caused by the fact that
namely the N = 4 SYM theory is the first known explicitly finite four-dimensional
theory without higher derivatives. It is interesting to note that this finiteness can
be apparently extended to the noncommutative generalization of this theory, see
[104]. Moreover, we explicitly demonstrated that our methodology can be applied
not only to usual Wess-Zumino and supergauge theories but can be also extended
to their nontrivial generalizations including non-polynomial and higher-derivative
ones, which play important role for constructing various low-energy effective models (as we already argued, such effective models can arise, for example, when some
of superfields, for example heavy ones, are integrated out). It is interesting to note
that the superfield approach is very efficient for performing quantum calculations
even in nonlocal supersymmetric theories, i.e. those ones involving infinite orders in
derivatives. The examples of such studies are presented in [112] (see also references
therein).
At the same time, the natural question is—whether perturbative treating of superfield models based on other multiplets is possible and can be realized? An important
example of such a multiplet is the spinor chiral superfield representing the so-called
tensor multiplet defined in [23], whose importance is motivated by the fact that its
component content includes the Kalb-Ramond antisymmetric tensor field, therefore
it can play a fundamental role within study of effective theories arising in the string
context. An important property of this superfield consists in the fact that its free
Lagrangian possesses the gauge symmetry. First perturbative studies of field theory
models involving this superfield have been performed in [113], where the one-loop
effective action in a theory involving a spinor chiral superfield and a usual real gauge
scalar superfield coupled to a chiral matter has been calculated.
And, besides of considering these superfields, studies of the supergravity multiplet certainly have a fundamental role. A detailed discussion of the supergravity
is presented in [23]; here, because of restricted volume of our review, we will not
discuss it.