N=2 supergravity counterterms, off and on shell

Abstract

We study N=2 supergravity deformed by a genuine supersymmetric completion of the λR 4 term, using the underlying off shell N=2 superconformal framework. The gauge-fixed superconformal model has unbroken local supersymmetry of N=2 supergravity with higher derivative deformation. Elimination of auxiliary fields leads to the deformation of the supersymmetry rules as well as to the deformation of the action, which becomes a Born-Infeld with higher derivative type action. We find that the gravitino supersymmetry deformation starts from λ ∂ 4 F 3 and has higher graviphoton couplings. In the action there are terms λ 2 ∂ 8 F 6 and higher, in addition to original on shell counterterm deformation. These deformations are absent in the on shell superspace and in the candidate on shell counterterms of N=4, 8 supergravities, truncated down to N=2. We conclude therefore that the undeformed on shell superspace candidate counterterms break the N=2 part of local supersymmetry.

New higher-derivative invariants in N = 2 supergravity and the Gauss-Bonnet term

“…The N = 2 supercurrent must be a real conformal primary w = 2 superfield, and the unique such superfield one may construct in conformal supergravity is ∇ αβ W αβ . 16 Moreover, J W must also obey the constraint (5.15), which one can check is indeed satisfied for J W ∝ ∇ αβ W αβ . Remarkably, we may now apply the same argument to the variation of the kinetic multiplet action S − NL .…”

“…of BPS black holes. Actions of this class have also been used recently to study supergravity counterterms and the relation between off-shell and on-shell results [16]. Furthermore, in [17], higher-derivative actions were constructed in projective superspace by allowing vector multiplets and/or tensor multiplets to be contained in similar homogeneous functions of other multiplets.…”

Nonlinear (super)symmetries and amplitudes

“…The construction of supergravity counterterms, as initiated in [38,39], based on on-shell classical superspace, appears to be naive in this respect. Namely, it was more recently shown in [40], using N = 2 supergravity with higher derivatives, that when auxiliary fields are integrated out, the supersymmetry transformations of the physical fields are deformed due to presence of higher derivative terms. This fact makes the predictions of counterterms, based on on-shell classical superspace for N ≥ 3, inconclusive.…”

Majorana Fermions, Supersymmetry Breaking, and Born-Infeld Theory

“…For various recent developments on BI theory, supersymmetry, and e.m. duality, see e.g. [30,31,32,33,34].…”