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

Braneworld localisation in hyperbolic spacetime

We present a construction employing a type IIA supergravity and 3-form flux background together with an NS5-brane that localises massless gravity near the 5-brane worldvolume. The nonsingular underlying type IIA solution is a lift to 10D of the vacuum solution of the 6D Salam-Sezgin model and has a hyperbolic ${\cal H}^{(2,2)}\times S^1$ structure in the lifting dimensions. A fully back-reacted solution including the NS5-brane is constructed by recognising the 10D Salam-Sezgin vacuum solution as a "brane resolved through transgression." The background hyperbolic structure plays a key r\^ole in generating a mass gap in the spectrum of the transverse-space wave operator, which gives rise to the localisation of gravity on the 6D NS5-brane worldvolume, or, equally, in a further compactification to 4D. Also key to the successful localisation of gravity is the specific form of the corresponding transverse wavefunction Schr\"odinger problem, which asymptotically involves a $V=-1/(4\rho^2)$ potential, where $\rho$ is the transverse-space radius, and for which the NS5-brane source gives rise to a specific choice of self-adjoint extension for the transverse wave operator. The corresponding boundary condition as $\rho\to0$ ensures the masslessness of gravity in the effective braneworld theory. Above the mass gap, there is a continuum of massive states which give rise to small corrections to Newton's law.Comment: 32 pages, 2 figures; misprints corrected & some clarification adde

Conservation laws for self-adjoint first order evolution equations

In this work we consider the problem on group classification and conservation laws of the general first order evolution equations. We obtain the subclasses of these general equations which are quasi-self-adjoint and self-adjoint. By using the recent Ibragimov's Theorem on conservation laws, we establish the conservation laws of the equations admiting self-adjoint equations. We illustrate our results applying them to the inviscid Burgers' equation. In particular an infinite number of new symmetries of these equations are found and their corresponding conservation laws are established.Comment: This manuscript has been accepted for publication in Journal of Nonlinear Mathematical Physic

Form-field gauge symmetry in M-theory

We show how to cast an interacting system of M‐branes into manifestly gauge‐invariant form using an arrangement of higher‐dimensional Dirac surfaces. Classical M‐theory has a cohomologically nontrivial and noncommutative set of gauge symmetries when written using a “doubled” formalism containing 3‐form and 6‐form gauge fields. We show how the arrangement of Dirac surfaces allows an integral subgroup of these symmetries to be preserved at the quantum level. The proper context for discussing these large gauge transformations is relative cohomology, in which the 3‐form transformation parameters become exact when restricted to the five‐brane worldvolume. This structure yields the correct lattice of M‐theory brane charges

Quantum spacetime and the renormalization group: Progress and visions

The quest for a consistent theory which describes the quantum microstructure of spacetime seems to require some departure from the paradigms that have been followed in the construction of quantum theories for the other fundamental interactions. In this contribution we briefly review two approaches to quantum gravity, namely, asymptotically safe quantum gravity and tensor models, based on different theoretical assumptions. Nevertheless, the main goal is to find a universal continuum limit for such theories and we explain how coarse-graining techniques should be adapted to each case. Finally, we argue that although seemingly different, such approaches might be just two sides of the same coin.Comment: 14 pages, 4 figures, Proceedings of "Progress and Visions in Quantum Theory in View of Gravity: Bridging foundations of physics and mathematics", Leipzig, 201

Universal BPS structure of stationary supergravity solutions

We study asymptotically flat stationary solutions of four-dimensional supergravity theories via the associated G/H* pseudo-Riemannian non-linear sigma models in three spatial dimensions. The Noether charge C associated to G is shown to satisfy a characteristic equation that determines it as a function of the four-dimensional conserved charges. The matrix C is nilpotent for non-rotating extremal solutions. The nilpotency degree of C is directly related to the BPS degree of the corresponding solution when they are BPS. Equivalently, the charges can be described in terms of a Weyl spinor |C > of Spin*(2N), and then the characteristic equation becomes equivalent to a generalisation of the Cartan pure spinor constraint on |C>. The invariance of a given solution with respect to supersymmetry is determined by an algebraic `Dirac equation' on the Weyl spinor |C>. We explicitly solve this equation for all pure supergravity theories and we characterise the stratified structure of the moduli space of asymptotically Taub-NUT black holes with respect with their BPS degree. The analysis is valid for any asymptotically flat stationary solutions for which the singularities are protected by horizons. The H*-orbits of extremal solutions are identified as Lagrangian submanifolds of nilpotent orbits of G, and so the moduli space of extremal spherically symmetric black holes as a Lagrangian subvariety of the variety of nilpotent elements of Lie(G). We also generalise the notion of active duality transformations to an `almost action' of the three-dimensional duality group G on asymptotically flat stationary solutions.Comment: Few misprints correcte