The non-minimal scalar multiplet: duality, σ-model, β-function

Abstract

We compute in superspace the one-loop beta-function for the nonlinear sigmamodel defined in terms of the nonminimal scalar multiplet. The recently proposed quantization of this complex linear superfield, viewed as the field strength of an unconstrained gauge spinor superfield, allows to handle efficiently the infinite tower of ghosts via the Batalin-Vilkovisky formalism. We find that the classical duality of the nonminimal scalar and chiral multiplets is maintained at the quantum one-loop level. † Onderzoeksdirecteur FWO, Belgium

Duality inN = 2 nonlinear sigma-models

“…We choose gauge-fixing functions independent of the background so that the ghosts couple to the quantum fields σ α andσα, but not to the physical background. Starting from the action (3.5) and performing the gauge-fixing as explained in [7,9] one obtains a final quadratic gauge-fixed action with all the diagonal terms invertible and an infinite number of nondiagonal terms mixing physical fields and ghosts. In order to perform perturbative calculations we need to compute the propagators for the prepotentials in (3.4) and these can be read from the gauge-fixed action once the diagonalization is performed.…”

“…The one-loop beta function is computed in Section 4 following Ref. [9]. The comparison with the standard one-loop result for the chiral sigma-model is then discussed.…”

Complex linear effective theory and supersymmetry breaking vacua

“…However, as was shown in Ref. [25], if the complex linear superfields prepotentials appear only through their field strengths (i.e. the superfields themselves) the ghosts decouple and one may ignore many of the complications originating in the infinite ghost sector.…”

“…It is possible that matter fields are not accommodated into a chiral multiplet, but rather into a complex linear multiplet for example, and the same goes for the supersymmetry breaking sector. The quantum properties of complex linear supermultiplets have been studied before [24][25][26][27] and it was shown that the general quantization procedure is rather involved. If one solves the constraints by introducing prepotentials one is faced with a theory with a gauge symmetry that needs to be fixed.…”

The nonminimal scalar multiplet coupled to supersymmetric Yang-Mills

“…First we notice that, since the quantum fields σ α ,σα always interact with the external background through their field-strengths Σ Q ,Σ Q , instead of the propagator in (16) it is sufficient to use the much simpler expression [5] <Σ…”