Search

A given field theory action determines a set of field equations but other actions may yield equivalent field equations; if so they are on-shell equivalent. They may also be off-shell equivalent, being related by the elimination of auxiliary fields or by local field redefinitions, but this is not guaranteed, as we demonstrate by consideration of the linearized limit of 3D massive gravity models. Failure to appreciate this subtlety has led to incorrect conclusions in recent studies of the "Minimal Massive Gravity" model., Comment: 17 pages, published version

We discuss a non-relativistic contraction of massive and massless field theories minimally coupled to gravity. Using the non-relativistic limiting procedure introduced in our previous work, we (re-)derive non-relativistic field theories of massive and massless spins 0 to 3/2 coupled to torsionless Newton-Cartan backgrounds. We elucidate the relativistic origin of the Newton-Cartan central charge gauge field $m_\mu$ and explain its relation to particle number conservation., Comment: 19 pages

For models of gravity coupled to hyperbolic sigma models, such as the metric-scalar sector of IIB supergravity, we show how smooth trajectories in the `augmented target space' connect FLRW cosmologies to non-extremal D-instantons through a cosmological singularity. In particular, we find closed cyclic universes that undergo an endless sequence of big-bang to big-crunch cycles separated by instanton `phases'. We also find `big-bounce' universes in which a collapsing closed universe bounces off its cosmological singularity to become an open expanding universe., Comment: 21 pages, 4 figures. v2: minor changes

We construct maximal D = 8 gauged supergravities by the reduction of D = I I supergravity over three-dimensional group manifolds. Such manifolds are classified into two classes, A and B, and eleven types. This Bianchi classification carries over to the gauged supergravities. The class A theories have 1/2 BPS domain wall solutions that uplift to purely gravitational solutions consisting of 7D Minkowski and a 4D Euclidean geometry. These geometries are generically singular. The two regular exceptions correspond to the near-horizon limit of the single- or double-centre Kaluza-Klein monopole. In contrast, the class B supergravities are defined by a set of equations of motion that cannot be integrated to an action and allow for no 1/2 BPS domain walls.

We construct five massive deformations of the unique nine–dimensional N = 2 supergravity, each with two parameters. All of these deformations have a higher–dimensional origin via Scherk–Schwarz reduction and correspond to gauged supergravities. The gauge groups we encounter are SO(2), SO(1, 1)+, R, R+ and the unique two–dimensional non–Abelian Lie group CR1, which consists of scalings and translations in one dimension. We make a systematic search for two classes of vacuum solutions: maximally symmetric solutions with constant scalars and half-supersymmetric domain wall solutions. In the first category we find explicit solutions in the form of (non-supersymmetric) de Sitter space solutions. In the second category we find precisely the three classes of domain wall solutions that were given in an earlier work.

We investigate half-supersymmetric domain wall solutions of four maximally supersymmetric D = 9 massive supergravity theories obtained by Scherk-Schwarz reduction of D = 10 IIA and IIB supergravity. One of the theories does not have a superpotential and does not allow domain wall solutions preserving any supersymmetry. The other three theories have superpotentials leading to half-supersymmetric domain wall solutions, one of which has zero potential but non-zero superpotential. The uplifting of these domain wall solutions to ten dimensions leads to three classes of half-supersymmetric type IIB 7-brane solutions. All solutions within each class are related by SL(2, R) transformations. The three classes together contain solutions carrying all possible (quantized) 7-brane charges. One class contains the well-known D7-brane solution and its dual partners and we provide the explicit solutions for the other two classes. The domain wall solution with zero potential lifts up to a half-supersymmetric conical spacetime.

We present an alternative to Topologically Massive Gravity (TMG) with the same "minimal" bulk properties; i.e. a single local degree of freedom that is realized as a massive graviton in linearization about an anti-de Sitter (AdS) vacuum. However, in contrast to TMG, the new "minimal massive gravity" has both a positive energy graviton and positive central charges for the asymptotic AdS-boundary conformal algebra., Comment: 21 pages. v2 includes additional references and an extended discussion of the unusual features of the MMG equation. Typos corrected in v3 and a "note added" concerning matter coupling. More sign corrections in v4 plus additional "note added"

We construct a supersymmetric extension of three-dimensional Newton-Cartan gravity by gauging a super-Bargmann algebra. In order to obtain a non-trivial supersymmetric extension of the Bargmann algebra one needs at least two supersymmetries leading to a N = 2 super-Bargmann algebra. Due to the fact that there is a universal Newtonian time, only one of the two supersymmetries can be gauged. The other supersymmetry is realized as a fermionic Stueckelberg symmetry and only survives as a global supersymmetry. We explicitly show how, in the frame of a Galilean observer, the system reduces to a supersymmetric extension of the Newton potential. The corresponding supersymmetry rules can only be defined, provided we also introduce a 'dual Newton potential'. We comment on the four-dimensional case.

This book is written for both physicists and mathematicians. It contains a detailed investigation of nonlinear extensions of two-dimensional conformal symmetries, i.e. the Virasoro symmetries. These extended conformal symmetries, generically called symmetries, generate so-called algebras which are defined by nonlinear relations. The algebras have attracted the attention of both physicists and mathematicians. From the mathematician's point of view they form interesting extensions of the usual linear algebras. From the physicist's point of view they could be used for the construction of new string theories in the same way that the Virasoro symmetries underlie the usual string theories. The book contains an overview of the author's work on the simplest example of a algebra: the algebra. For this special case many results are derived thereby clarifying the general case. Many explicit expressions are given, often via tables in the different appendices, that have sometimes been obtained by using a computer. In the introduction the authors first discuss the case of the linear Virasoro algebra to clarify and emphasize the common features of and the differences with the case of the nonlinear algebra. They discuss, in the first part of the book, the structure of the modules and use these results to compute (partly via conjectures) the semi-infinite cohomology of the algebra with values in the tensor product of c = 2 and c = 98 Fock modules. This case is relevant for the study of a noncritical string propagating in four dimensions. The second part of the book focuses on the geometrical structure underlying the operator cohomology. It turns out that this structure is described by Batalin - Vilkovisky (BV) algebras which have been introduced independently by mathematicians and physicists at around the same time. The authors first derive some general results on BV algebras. This part of the book can be read independently of the rest. They next discuss the BV algebra of the string that occurred in the first part of the book. The precise connection between the cohomology and the BV algebras is made via a claim which the authors themselves consider as perhaps the most important result in the book. In short, the authors are well able to present their results in a clear and precise way. I highly recommend this book both to the physicist who is interested in the precise mathematical properties of symmetries and to the mathematician who wants to learn more about the physical applications of algebras.

The book starts with a nice historical introduction to the subject of zeta functions, zeta function regularization and its applications in physics. The author emphasizes some of the advantages of the zeta function regularization method. In particular, the zeta function regularization can conveniently be applied in a curved spacetime. Anybody who wants to get a quick overview of the state of the art in the zeta function regularization method is recommended to read this introduction. Apart from the introduction the main virtue of this book is to provide help to any physics student and/or researcher who encounters zeta functions in his/her work. For this purpose the book provides the reader first of all with many technical details about zeta functions and some of their most important properties. Crucial amongst these properties is the existence of the so-called zeta function regularization theorem. This theorem is discussed and explained in the first part of the book. At a more advanced level, the author emphasizes the importance of a non-trivial extension of the celebrated Chowla--Selberg formula. This extension was invented by the author and plays an important role in some of the physics applications discussed later in the book. The second and main part of the book is devoted to illustrate the zeta function regularization method by giving ten physical applications. These applications cover such a wide range of topics as the Casimir effect, Kaluza--Klein compactification, two- and three-dimensional quantum gravity, extended objects like strings and membranes, critical behaviour of a field theory at non-zero temperature and topological mass generation. It is needless to say that all these applications give an impressive overview of the universality and power of the zeta function regularization method. I like in particular the discussion of the Casimir effect which is done in quite some detail. Apart from the technical discussion the author also explains why the Casimir effect only received so much attention many years after its discovery. Finally, I should note that it is interesting that the book discusses an application to the theory of membranes and, more generally p-branes, which has received such renewed interest in the past year. In short, I can recommend this book to anybody who encounters zeta functions in research and/or education. Undoubtedly, this book will be of great help in taking away some of the confusion on this topic.

We construct a new off-shell invariant in N=2, D=5 supergravity whose leading term is the square of the Riemann tensor. It contains a gravitational Chern-Simons term involving the vector field that belongs to the supergravity multiplet. The action is obtained by mapping the transformation rules of a spin connection with bosonic torsion and a set of curvatures to the fields of the Yang-Mills multiplet with gauge group SO(4,1). We also employ the circle reduction of an action that describes locally supersymmetric Yang-Mills theory in six dimensions.

We show how the Newton-Cartan formulation of Newtonian gravity can be obtained from gauging the Bargmann algebra, i.e., the centrally extended Galilean algebra. In this gauging procedure several curvature constraints are imposed. These convert the spatial (time) translational symmetries of the algebra into spatial (time) general coordinate transformations, and make the spin connection gauge fields dependent. In addition we require two independent Vielbein postulates for the temporal and spatial directions. In the final step we impose an additional curvature constraint to establish the connection with (on-shell) Newton-Cartan theory. We discuss a few extensions of our work that are relevant in the context of the AdS-CFT correspondence., Latex, 20 pages, typos corrected, published version

We construct, at the linearized level, the three-dimensional (3D) N = 4 supersymmetric "general massive supergravity" and the maximally supersymmetric N = 8 "new massive supergravity". We also construct the maximally supersymmetric linearized N = 7 topologically massive supergravity, although we expect N = 6 to be maximal at the non-linear level., Comment: 33 pages