Revisiting Supergravity and Super Yang-Mills Renormalization

Standard superspace Feynman diagram rules give one estimate of the onset of ultraviolet divergences in supergravity and super Yang-Mills theories. Newer techniques motivated by string theory but which also make essential use of unitarity cutting rules give another in certain cases. We trace the difference to the treatment of higher-dimensional gauge invariance in supersymmetric theories that can be dimensionally oxidized to pure supersymmetric gauge theories.Comment: 10 pages, Latex, uses aipproc macro

Counterterms, Holonomy and Supersymmetry

The divergence structure of supergravity has long been a topic of concern because of the theory's non-renormalizability. In the context of string theory, where perturbative finiteness should be achieved, the supergravity counterterm structures remain nonetheless of importance because they still occur, albeit with finite coefficients. The leading nonvanishing supergravity counterterms have a particularly rich structure that has a bearing on the preservation of supersymmetry in string vacua in the presence of perturbative string corrections. Although the holonomy of such manifolds is deformed by the corrections, a Killing spinor structure nevertheless can persist. The integrability conditions for the existence of such Killing spinors remarkably remain consistent with the perturbed effective field equations.Comment: To appear in the proceedings of Deserfest: A Celebration of the Life and Works of Stanley Deser, Ann Arbor, Michigan, 3-5 Apr 200

Heterotic Anomaly Cancellation in Five Dimensions

We study the constraints on five-dimensional N=1 heterotic M-theory imposed by a consistent anomaly-free coupling of bulk and boundary theory. This requires analyzing the cancellation of triangle gauge anomalies on the four-dimensional orbifold planes due to anomaly inflow from the bulk. We find that the semi-simple part of the orbifold gauge groups and certain U(1) symmetries have to be free of quantum anomalies. In addition there can be several anomalous U(1) symmetries on each orbifold plane whose anomalies are cancelled by a non-trivial variation of the bulk vector fields. The mixed U(1) non-abelian anomaly is universal and there is at most one U(1) symmetry with such an anomaly on each plane. In an alternative approach, we also analyze the coupling of five-dimensional gauged supergravity to orbifold gauge theories. We find a somewhat generalized structure of anomaly cancellation in this case which allows, for example, non-universal mixed U(1) gauge anomalies. Anomaly cancellation from the perspective of four-dimensional N=1 effective actions obtained from E_8xE_8 heterotic string- or M-theory by reduction on a Calabi-Yau three-fold is studied as well. The results are consistent with the ones found for five-dimensional heterotic M-theory. Finally, we consider some related issues of phenomenological interest such as model building with anomalous U(1) symmetries, Fayet-Illiopoulos terms and threshold corrections to gauge kinetic functions.Comment: 46 pages, Late

Invariants and divergences in half-maximal supergravity theories

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>1 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.Comment: 81 page

Anomalies and divergences in N=4 supergravity

The invariants in D=4, N=4 supergravity are discussed up to the three-loop order (where one expects a general R^4 structure). Because there is an anomaly in the rigid SL(2,R) symmetry of this theory, the analysis of possible restrictions on three-loop divergences due to duality needs careful treatment. We show that this anomalous symmetry is still strong enough at the three-loop order to require duality invariance of candidate counterterms. Provided one makes the additional assumption that there exists a full 16-supercharge off-shell formulation of the theory, counterterms at L \ge 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, subject to the assumption that a full off-shell quantisation formalism exists, such marginal invariants are not allowable as counterterms.Comment: 15 pages, version published in Phys. Lett.