Vector-multiplet effective action in the non-anticommutative charged hypermultiplet model

Abstract

We investigate the quantum aspects of a charged hypermultiplet in deformed N =(1, 1) superspace with singlet non-anticommutative deformation of supersymmetry. This model is a "star" modification of the hypermultiplet interacting with a background Abelian vector superfield. We prove that this model is renormalizable in the sense that the divergent part of the effective action is proportional to the N =(1, 0) non-anticommutative super Yang-Mills action. We also calculate the finite part of the low-energy effective action depending on the vector multiplet, which corresponds to the (anti)holomorphic potential. The holomorphic piece is just deformed to the star-generalization of the standard holomorphic potential, while the antiholomorphic piece is not. We also reveal the component structure and find the deformation of the mass and the central charge.

Gauge theory in deformed % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXgatC % vAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wz % ZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbb % L8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpe % pae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaam % aaeaqbaaGcbaWefv3ySLgznfgDOfdarCqr1ngBPrginfgDObYtUvga % iyaacqWFneVtaaa!4628! $$ \mathcal{N} $$ = (1, 1) superspace

“…Up to now, the case of extended quantum supersymmetry has been studied only for the particular case of chiral singlet Q-deformations (in the harmonic superspace approach) [32,33]. In particular, it was found that the non-anticommutative models of the abelian gauge superfield and the neutral hypermultiplet are renormalizable.…”

“…In [33] we also studied the quantum structure of the non-anticommutative charged hypermultiplet model introduced in [29]. This model is of interest because in the undeformed limit it remains interacting, becoming the N =(1, 1) supersymmetric extension of electrody-namics.…”

“…It is well known that the low-energy effective action of the latter model is described by a holomorphic potential which plays an important role in N =2 Seiberg-Witten theory [5]. In [33], by quantum superfield calculations in harmonic superspace, it was established that this non-anticommutative model is renormalizable in the standard sense. In addition, finite contributions to the low-energy effective action were obtained including the holomorphic potential, which turned out to be deformed in the naive sense.…”

“…The review is mostly based on our papers [21,26,29,32,33]. We shall keep to the notation used in these works.…”

Gauge theory in deformed N=(1,1) superspace

“…The renormalizability and other quantum aspects of theories with non-anticommutative Qdeformations of N =(1/2, 1/2) supersymmetry were considered in detail in [15]- [20]. Up to now, the case of extended quantum supersymmetry has been studied only for the particular case of chiral singlet Q-deformations (in the harmonic superspace approach) [32,33]. In particular, it was found that the non-anticommutative models of the abelian gauge superfield and the neutral hypermultiplet are renormalizable.…”