Domain Walls and Spaces of Special Holonomy

We review the relations between a family of domain-wall solutions to M-theory and gravitational instantons with special holonomy. When oxidized into the maximal-dimension parent supergravity, the transverse spaces of these domain walls become cohomogeneity-one spaces with generalized Heisenberg symmetries and a homothetic conformal symmetry. These metrics may also be obtained as scaling limits of generalized Eguchi-Hanson metrics, or, with appropriate discrete identifications, from generalized Atiyah-Hitchin metrics, thus providing field-theoretic realizations of string-theory orientifolds

Domain Walls and the Universe

D=11 supergravity possesses D=5 Calabi-Yau compactified solutions that may be identified with the vacua of the Horava-Witten orbifold construction for M--theory/heterotic duality. The simplest of these solutions naturally involves two 3-brane domain walls, which may be identified with the orbifold boundary planes; this solution also possesses an unbroken $Z_2$ symmetry. Consideration of nearby excited solutions, truncated to the zero-mode and $Z_2$ invariant sector, yields an effective D=4 heterotic theory displaying chirality and N=1, D=4 supersymmetry

Non-critical d=2d=2 Gravities and Integrable Models

We review the origin of anomaly-induced dynamics in theories of $d=2$ gravity from a BRST viewpoint and show how quantum canonical transformations may be used to solve the resulting Liouville or Toda models for the anomalous modes

Symmetry Orbits of Supergravity Black Holes - In Honor of Andrei Slavnov's 75th Birthday

Black hole solutions of supergravity theories form families that realizing the deep nonlinear duality symmetries of these theories. They form orbits under the action of these symmetry groups, with extremal (i.e. BPS) solutions at the limits of such orbits. An important technique in the analysis of such solution families employs timelike dimensional reduction and exchanges the stationary black-hole problem for a nonlinear sigma-model problem. Families of extremal or BPS solutions are characterized by nilpotent orbits under the duality symmetries, based upon a tri-graded or penta-graded decomposition of the corresponding duality-group algebra

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