Invariants and divergences in half-maximal supergravity theories

Abstract

The invariants in half-maximal supergravity theories in D = 4, 5 are discussed in detail up to dimension eight (e.g. R 4 ). In D = 4, owing to the anomaly in the rigid SL(2, R) duality symmetry, the restrictions on divergences need careful treatment. In pure N = 4 supergravity, this anomalous symmetry still implies duality invariance of candidate counterterms at three loops. Provided one makes the additional assumption that there exists a full 16-supercharge off-shell formulation of the theory, counterterms at L ≥ 2 loops would also have to be writable as full-superspace integrals. At the three-loop order such a duality-invariant full-superspace integral candidate counterterm exists, but its duality invariance is marginal in the sense that the full-superspace counter-Lagrangian is not itself duality-invariant. We show that such marginal invariants are not allowable as counterterms in a 16-supercharge off-shell formalism. It is not possible to draw the same conclusion when vector multiplets are present because of the appearance of F 4 terms in the SL(2, R)anomaly. In D = 5 there is no one-loop anomaly in the shift invariance of the dilaton, and we argue that this implies finiteness at two loops, again subject to the assumption that 16 supercharges can be preserved off-shell.

Manifesting enhanced cancellations in supergravity: integrands versus integrals

“…These cancellations go beyond those presently understood from standard-symmetry argumentation [11][12][13][14] and therefore appear to require novel explanations.…”

“…recent examples of enhanced cancellations have as yet no standard symmetry explanation, despite attempts [11][12][13][14] and insight from string theory [15]. These examples include N = 5 supergravity at four loops in D = 4 [9], N = 4 supergravity at three loops in D = 4 [8], and half-maximal supergravity at two loops in D = 5 [10].…”

“…Enhanced cancellations become more interesting beyond one loop where they correspond to a variety of ultraviolet cancellations for which standard-symmetry explanations are not known [11][12][13][14]. We therefore turn to half-maximal supergravity at two loops.…”

“…[16][17][18]) rely on the ability to make the integrand manifestly ultraviolet finite by power counting. The difficulty in finding a standard-symmetry based explanation for enhanced cancellations [11][12][13][14] in gravity theories is presumably tied to our difficulty in identifying the cancellations at the integrand level. This greatly complicates any all-order understanding of the divergence properties of supergravity theories.…”

Superforms in five-dimensional, N = 1 superspace

“…(1) a highly efficient derivation of supergravity density measures [16][17][18][19], (2) a superspace formulation for 4D, N = 8 supergravity counterterms [20], (3) a covariant formulation of 4D, N = 4 supergravity anomalies/divergences [21,22], (4) complete formulations of integration on supermanifolds with boundaries [23], (5) a supergravity derivation of a minimal unitary representation of the string effective action [24,25], and (6) establishing the relationship between superspace integration theory and the picturechanging formalism of superstring theory [26].…”