arXiv subjects

Martin Cederwall

Publications and source records attributed to Martin Cederwall.

At least 55 records · Page 3Linked to original sources

arXiv2014

T-duality and non-geometric solutions from double geometry

Although the introduction of generalised and extended geometry has been motivated mainly by the appearance of dualities upon reductions on tori, it has until now been unclear how (all) the duality transformations arise from first principles in extended geometry. A proposal for solving this problem is given in the framework of double field theory. It is based on a clearly defined extension of the definition of gauge symmetry by isometries of an underlying pseudo-Riemannian manifold. The ensuing relation between transformations of coordinates and fields, which is now derived from first principles, differs from earlier proposals.

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arXiv2014

The geometry behind double geometry

Generalised diffeomorphisms in double field theory rely on an O(d,d) structure defined on tangent space. We show that any (pseudo-)Riemannian metric on the doubled space defines such a structure, in the sense that the generalised diffeomorphisms defined using such a metric form an algebra, provided a covariant section condition is fulfilled. Consistent solutions of the section condition gives further restrictions. The case previously considered corresponds to a flat metric. The construction makes it possible to apply double geometry to a larger class of manifolds. Examples of curved defining metrics are given. We also comment on the role of the defining geometry for the symmetries of double field theory, and on the continuation of the present construction to the U-duality setting.

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arXiv2014

Global aspects of double geometry

We consider the concept of a generalised manifold in the O(d,d) setting, i.e., in double geometry. The conjecture by Hohm and Zwiebach for the form of finite generalised diffeomorphisms is shown to hold. Transition functions on overlaps are defined. Triple overlaps are trivial concerning their action on coordinates, but non-trivial on fields, including the generalised metric. A generalised manifold is an ordinary manifold, but the generalised metric on the manifold carries a gerbe structure. We show how the abelian behaviour of the gerbe is embedded in the non-abelian T-duality group. We also comment on possibilities and difficulties in the U-duality setting.

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arXiv2013

Pure spinor superfields -- an overview

Maximally supersymmetric theories do not allow off-shell superspace formulations with traditional superfields containing a finite set of auxiliary fields. It has become clear that off-shell supersymmetric action formulations of such models can be achieved by the introduction of pure spinors. In this talk, an overview of this formalism is given, with emphasis on D=10 super-Yang-Mills theory and D=11 supergravity. This a somewhat expanded version of a talk presented at the workshop "Breaking of supersymmetry and ultraviolet divergences in extended supergravity" (BUDS), Laboratori Nazionali di Frascati, March 25-28, 2013.

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arXiv2013

Exceptional geometry and tensor fields

We present a tensor calculus for exceptional generalised geometry. Expressions for connections, torsion and curvature are given a unified formulation for different exceptional groups E_n(n). We then consider "tensor gauge fields" coupled to the exceptional generalised gravity. Many of the properties of forms on manifolds are carried over to these fields.

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arXiv2013

Non-gravitational exceptional supermultiplets

We examine non-gravitational minimal supermultiplets which are based on the tensor gauge fields appearing as matter fields in exceptional generalised geometry. When possible, off-shell multiplets are given. The fields in the multiplets describe non-gravitational parts of the internal dynamics of compactifications of M-theory. In flat backgrounds, they enjoy a global U-duality symmetry, but also provide multiplets with a possibility of coupling to a generalised exceptional geometry.

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arXiv2013

Loop amplitudes in maximal supergravity with manifest supersymmetry

We present a description for amplitude diagrams in maximal supergravities obtained by dimensional reduction from D=11, derived from a field theory point of view using the pure spinor formalism. The advantages of this approach are the manifest supersymmetry present in the formalism, and the limited number of interaction terms in the action. Furthermore, we investigate the conditions set by this description in order for amplitudes in maximal supergravity to be finite in the ultraviolet limit. Typically, there is an upper limit to the dimension, set by the loop order, which for an arbitrary number of loops is no larger than two. In four dimensions, the non-renormalisation power of the formalism fails for the 7-loop contribution to the 4-point amplitude, all of which is in clear agreement with previous work.

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arXiv2012

The gauge structure of generalised diffeomorphisms

We investigate the generalised diffeomorphisms in M-theory, which are gauge transformations unifying diffeomorphisms and tensor gauge transformations. After giving an En(n)-covariant description of the gauge transformations and their commutators, we show that the gauge algebra is infinitely reducible, i.e., the tower of ghosts for ghosts is infinite. The Jacobiator of generalised diffeomorphisms gives such a reducibility transformation. We give a concrete description of the ghost structure, and demonstrate that the infinite sums give the correct (regularised) number of degrees of freedom. The ghost towers belong to the sequences of rep- resentations previously observed appearing in tensor hierarchies and Borcherds algebras. All calculations rely on the section condition, which we reformulate as a linear condition on the cotangent directions. The analysis holds for n < 8. At n = 8, where the dual gravity field becomes relevant, the natural guess for the gauge parameter and its reducibility still yields the correct counting of gauge parameters.

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arXiv2012

The geometry of pure spinor space

We investigate the complex geometry of D=10 pure spinor space. The Kähler structure and the corresponding metric giving rise to the desired Calabi-Yau property are determined, and an explicit covariant expression for the Laplacian is given. The metric is not that of a cone obtained by embedding pure spinor space in a flat space of unconstrained spinors. Some directions for future studies, concerning regularisation and generalisation to eleven dimensions, are briefly discussed.

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arXiv2011

Pure spinor superfields and Born-Infeld theory

We present a method for introducing and analysing higher-derivative deformations of maximally supersymmetric field theories. Such terms are built in the pure spinor superfield framework, using a set of operators representing physical fields. The action for abelian Born-Infeld theory becomes polynomial in this language, and contains only a four-point interaction in addition to the free action. Simplifications also occur in the non-abelian case.

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arXiv2011

D=3, N=8 conformal supergravity and the Dragon window

We give a superspace description of D=3, N=8 supergravity. The formulation is off-shell in the sense that the equations of motion are not implied by the superspace constraints (but an action principle is not given). The multiplet structure is unconventional, which we connect to the existence of a "Dragon window", that is modules occurring in the supercurvature but not in the supertorsion. According to Dragon's theorem this cannot happen above three dimensions. We clarify the relevance of this window for going on the conformal shell, and discuss some aspects of coupling to conformal matter.

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arXiv2010

From supergeometry to pure spinors

In this talk, we review how the superspace formulation of maximally supersymmetric field theories (including supergravity) naturally leads to introduction of pure spinors and pure spinor superfields, and why the formalism provides off-shell formulations. This approach to pure spinor superfields thus stresses field-theoretic aspects rather than the first-quantised ones normally used e.g. in superstring theory. We discuss how the BRST operator arises and the principles behind constructions of actions, as well as the general Batalin-Vilkovisky framework. D=11 supergravity and its recently constructed supersymmetric action are taken as an example throughout the talk. This is the written version of a lecture given at the 6th Mathematical Physics Meeting, Belgrade, September 2010.

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arXiv2009

D=11 supergravity with manifest supersymmetry

The complete supersymmetric action for eleven-dimensional supergravity is presented. The action is polynomial in the scalar fermionic pure spinor superfield, and contains only a minor modification to the recently proposed three-point coupling.

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arXiv2009

Towards a manifestly supersymmetric action for 11-dimensional supergravity

We investigate the possibility of writing a manifestly supersymmetric action for 11-dimensional supergravity. The construction involves an explicit relation between the fields in the super-vielbein and the super-3-form, and uses non-minimal pure spinors. A simple cubic interaction term for a single scalar superfield is found.

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arXiv2009

Pure spinor superfields, with application to D=3 conformal models

I review and discuss the construction of supersymmetry multiplets and manifestly supersymmetric Batalin-Vilkovisky actions using pure spinors, with emphasis on models with maximal supersymmetry. The special cases of D=3, N=8 (Bagger-Lambert-Gustavsson) and N=6 (Aharony-Bergman-Jafferis-Maldacena) conformal models are treated in detail. Most of the material is covered by the papers arXiv:0808.3242 and arXiv:0809.0318. This is the written version of a talk given at 4th Baltic-Nordic workshop "Algebra, Geometry and Mathematical Physics", Tartu, Estonia, October 9-11, 2008, to appear in the Proceedings of the Estonian Academy of Sciences, vol 4, 2010.

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arXiv2008

Superfield actions for N=8 and N=6 conformal theories in three dimensions

The manifestly supersymmetric pure spinor formulations of the Bagger-Lambert-Gustavsson models with N=8 supersymmetry and the Aharony-Bergman-Jafferis-Maldacena models with N=6 supersymmetry are given. The structures of the pure spinors are investigated in both cases, and non-degenerate measures are formed using non-minimal sets of variables, allowing for the formulation of an action principle.

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arXiv2008

N=8 superfield formulation of the Bagger-Lambert-Gustavsson model

We reformulate the Bagger-Lambert-Gustavsson model using an N=8 superspace, thus making the full supersymmetry manifest. The formulation is based on appropriate "pure spinor wave functions" for the Chern-Simons and matter multiplets. The Lagrangian has an extremely simple structure, essentially containing a Chern-Simons-like term for the gauge field wave function and a minimally coupled matter wave function. No higher order interactions than cubic are present. The consistency of the setup relies on an interplay between the algebraic structures of the 3-algebra and of the pure spinors.

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arXiv2008

The B-model on the A-model NS5-brane

We formulate the dynamics for the NS5-brane of the A-model, via the 'maximal form' method, which couples all background fields to the world-volume. This procedure provides the extra one- and five-forms fields of the extended Hitchin model. The generalised B-model emerges as the world-volume theory of this brane. The starting point of the construction is an embedding of the brane in a superspace geometry with 16 fermionic directions. The correspondence with Hitchin's formulation in terms of pure spinors is explained.

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