We study the one-loop low-energy effective action for the higher-derivative superfield gauge theory coupled to a chiral matter. I. INTRODUCTIONThe use of higher-derivatives has been proposed as a way to tame the ultraviolet behavior of physically relevant models. Actually, a finite version of QED was put forward by Lee and Wick about fourty years ago [1]; that proposal was nevertheless beset by the presence of spurious degrees of freedom which induce indefinite metric in the space of states jeopardizing unitarity and so required special treatment. After a long story, recently the idea was revived in the so-called Lee-Wick standard model leading to some new insights in the hierachy problem [2]. Furthermore, following a similar thread, higher-curvature gravitational models were considered; in spite of the possible breaking of unitarity, they furnish renormalizable quantum gravity models [3] which may be useful for cosmological applications (for recent review work in this direction see [4]).In supersymmetric models, a higher-derivative regularization method was proposed in [5].Further, interest in the higher-derivative supersymmetric field theories increased not only due to their application within the regularization context (see [6] for many examples) but also in other contexts. For example, the higher-derivative supergravity model, which, in the *

In this paper, we deal with the f (R, Q) gravity whose action depends, besides of the scalar curvature R, on the higher-derivative invariant Q = R µν R µν . In order to compare this theory with the usual General Relativity (GR), we verify the consistency of Gödel-type solutions within the f (R, Q) gravity and discuss the related causality issues. Explicitly, we show that in the f (R, Q) gravity there are new Gödel-type completely causal solutions having no analogue in the general relativity. In particular, a remarkable Gödel-type solution corresponding to the conformally flat space and maximally symmetric for physically wellmotivated matter sources, with no necessity of cosmological constant, has been considered.We demonstrate that, in contrast to GR framework, f (R, Q) gravity supports new vacuum solutions with the requirement for the cosmological constant to be non-zero. Finally, causal solutions are obtained for a particular choice f (R, Q) = R + αR 2 + βQ. I. INTRODUCTIONThe GR is known to be the successful theory of gravity, its predictions are in accordance with tests realized in solar system, the so-called classical tests, for example, the precession of the perihelion of Mercury, as well as with the recent detection of gravitational waves [1][2][3]. Nonetheless, it turns out that the Einstein gravity fails in some aspects, which leads to interest to search for its possible consistent generalizations. Basically, there are two main problems having no solution within the framework of the GR: the first one takes place on a phenomenological perspective that arises as one of the most enigmatic problems in physics, the accelerated expansion of the Universe.It is confirmed by observational data from Type Ia supernovae [4][5][6], from cosmic microwave background (CMB) measurements [7][8][9] and studies of large structures [10,11]. The second reason, purely theoretical, is related to issues on quantization of gravity, since, as it is well known, the * Electronic address:

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Using the superfield formalism, we propose a non-local extension of the supersymmetric gauge theory coupled to massless chiral matter. Two different non-local models are considered. For these models, we explicitly calculate the one-loop Kälerian effective potential. * Electronic address: fisicofabricio@yahoo.com.br † Electronic address: jroberto@fisica.ufpb.br ‡ Electronic address: petrov@fisica.ufpb.br § Electronic address:

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