In this work, we systematically analyze higher derivative terms in the supersymmetric effective actions for three dimensional scalar field theories using $\mathcal{N} =1$ superspace formalism. In these effective actions, we show that auxiliary fields do not propagate and their effective actions can be expressed in terms of the physical fields. So, the theory does not change its field content upon addition of higher derivative terms. We use derivative expansion to generate four, five and six dimensional terms for an interacting scalar field theory with $\mathcal{N} =1$ supersymmetry. We show that along with pure fermionic and bosonic terms, there are various five and six dimensional topological terms that mix bosonic and fermionic fields. Finally, we use these results to obtain higher derivative topological terms in the effective action for two M2-branes.
In this work, we consider local and nonlocal higher-derivative generalizations of the super-Chern-Simons theory and four-dimensional SQED. In contrast to previous studies, the models studied here also have higher-derivative terms in the matter sector. For these models, we calculate the one-loop superfield effective potential.
We consider a general non-Abelian renormalizable ${\cal N}=1$ supersymmetric gauge theory, regularized by higher covariant derivatives without breaking the BRST invariance, and calculate one-loop divergences for a general form of higher derivative regulator and of the gauge fixing term. It is demonstrated that the momentum integrals giving the one-loop $β$-function are integrals of double total derivatives independently of a particular choice of the higher derivative term. Evaluating them we reproduce the well-known result for the one-loop $β$-function. Also we find that the three-point ghost …
For a general ${\cal N}=1$ supersymmetric gauge theory regularized by higher covariant derivatives we prove in all orders that the $β$-function defined in terms of the bare couplings is given by integrals of double total derivatives with respect to loop momenta. With the help of the technique used for this proof it is possible to construct a method for obtaining these loop integrals, which essentially simplifies the calculations. As an illustration of this method, we find the expression for the three-loop contribution to the $β$-function containing the Yukawa couplings and compare it with the …
Structure of quantum corrections in ${\cal N}=1$ supersymmetric gauge theories is investigated in the case of using the regularization by higher covariant derivatives. It is demonstrated that this regularization allows revealing some interesting features which lead to the exact relations between the renormalization group functions. In particular, the NSVZ equation, which relates the $β$-function to the anomalous dimension of the matter superfields, naturally appears in this case. We briefly review the all-loop derivation of this equation and the construction of a simple renormalization prescri…
We consider the non-supersymmetric "magic" theories based on the split quaternion and the split complex division algebras. We show that these theories arise as "Ehlers" $SL(2,\mathbb{R})$ and $SL(3,\mathbb{R})$ truncations of the maximal supergravity theory, exploiting techniques related to very-extended Kac-Moody algebras. We also generalise the procedure to other $SL(n,\mathbb{R})$ truncations, resulting in additional classes of non-supersymmetric theories, as well as to truncations of non-maximal theories. Finally, we discuss duality orbits of extremal black-hole solutions in some of these …
We review recent developments in two-dimensional $\mathcal{N}=(2,2)$ supersymmetric gauge theories focusing on the implementation and applications of localization techniques.
