516 research outputs found
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.
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