arXiv subjects

Martin Cederwall

Publications and source records attributed to Martin Cederwall.

At least 73 records · Page 4Linked to original sources

arXiv2008

U-Duality and the Compactified Gauss-Bonnet Term

We present the complete toroidal compactification of the Gauss-Bonnet Lagrangian from D dimensions to (D-n) dimensions. Our goal is to investigate the resulting action from the point of view of the "U-duality" symmetry SL(n+1,R) which is present in the tree-level Lagrangian when D-n=3. The analysis builds upon and extends the investigation of the paper [arXiv:0706.1183], by computing in detail the full structure of the compactified Gauss-Bonnet term, including the contribution from the dilaton exponents. We analyze these exponents using the representation theory of the Lie algebra sl(n+1,R) and determine which representation seems to be the relevant one for quadratic curvature corrections. By interpreting the result of the compactification as a leading term in a large volume expansion of an SL(n+1,Z)-invariant action, we conclude that the overall exponential dilaton factor should not be included in the representation structure. As a consequence, all dilaton exponents correspond to weights of sl(n+1,R), which, nevertheless, remain on the positive side of the root lattice.

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arXiv2008

Pure Spinors and D=6 Super-Yang-Mills

Pure spinor cohomology has been used to describe maximally supersymmetric theories, like D=10 super-Yang-Mills and D=11 supergravity. Supersymmetry closes on-shell in such theories, and the fields in the cohomology automatically satisfy the equations of motion. In this paper, we investigate the corresponding structure in a model with off-shell supersymmetry, N=1 super-Yang-Mills theory in D=6. Here, fields and antifields are obtained as cohomologies in different complexes with respect to the BRST operator Q. It turns out to be natural to enlarge the pure spinor space with additional bosonic variables, subject to some constraints generalising the pure spinor condition, in order to accommodate the different supermultiplets in the same generalised pure spinor wave-function. We construct another BRST operator, s, acting in the cohomology of Q, whose cohomology implies the equations of motion. We comment on the possible use of similar approaches in other models.

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arXiv2007

M-branes on U-folds

We give a preliminary discussion of how the addition of extra coordinates in M-theory, which together with the original ones parametrise a U-fold, can serve as a tool for formulating brane dynamics with manifest U-duality. The redundant degrees of freedom are removed by generalised self-duality constraints or calibration conditions made possible by the algebraic structure of U-duality. This is the written version of an invited talk at the 7th International Workshop "Supersymmetries and Quantum Symmetries", Dubna, July 30-August 4, 2007.

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arXiv2007

A Note on Topological M5-branes and String-Fivebrane Duality

We derive the stability conditions for the M5-brane in topological M-theory using kappa-symmetry. The non-linearly self-dual 3-form on the world-volume is necessarily non-vanishing, as is the case also for the 2-form field strengths on coisotropic branes in topological string theory. It is demonstrated that the self-duality is consistent with the stability conditions, which are solved locally in terms of a tensor in the representation 6 of SU(3) in G_2. The double dimensional reduction of the M5-brane is the D4-brane, and its direct reduction is an NS5-brane. We show that the equation of motion for the 3-form on the NS5-brane wrapping a Calabi-Yau space is exactly the Kodaira-Spencer equation, providing support for a string-fivebrane duality in topological string theory.

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arXiv2007

Aspects of higher curvature terms and U-duality

We discuss various aspects of dimensional reduction of gravity with the Einstein-Hilbert action supplemented by a lowest order deformation formed as the Riemann tensor raised to powers two, three or four. In the case of R^2 we give an explicit expression, and discuss the possibility of extended coset symmetries, especially SL(n+1,Z) for reduction on an n-torus to three dimensions. Then we start an investigation of the dimensional reduction of R^3 and R^4 by calculating some terms relevant for the coset formulation, aiming in particular towards E_8(8)/(Spin(16)/Z_2) in three dimensions and an investigation of the derivative structure. We emphasise some issues concerning the need for the introduction of non-scalar automorphic forms in order to realise certain expected enhanced symmetries.

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arXiv2007

The octic E8 invariant

We give an explicit expression for the primitive E8-invariant tensor with eight symmetric indices. The result is presented in a manifestly Spin(16)/Z2-covariant notation.

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arXiv2005

Membranes for Topological M-Theory

We formulate a theory of topological membranes on manifolds with G_2 holonomy. The BRST charges of the theories are the superspace Killing vectors (the generators of global supersymmetry) on the background with reduced holonomy G_2. In the absence of spinning formulations of supermembranes, the starting point is an N=2 target space supersymmetric membrane in seven euclidean dimensions. The reduction of the holonomy group implies a twisting of the rotations in the tangent bundle of the branes with ``R-symmetry'' rotations in the normal bundle, in contrast to the ordinary spinning formulation of topological strings, where twisting is performed with internal U(1) currents of the N=(2,2) superconformal algebra. The double dimensional reduction on a circle of the topological membrane gives the strings of the topological A-model (a by-product of this reduction is a Green-Schwarz formulation of topological strings). We conclude that the action is BRST-exact modulo topological terms and fermionic equations of motion. We discuss the role of topological membranes in topological M-theory and the relation of our work to recent work by Hitchin and by Dijkgraaf et al.

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arXiv2005

U-duality covariant membranes

We outline a formulation of membrane dynamics in D=8 which is fully covariant under the U-duality group SL(2,Z) x SL(3,Z), and encodes all interactions to fields in the eight-dimensional supergravity, which is constructed through Kaluza-Klein reduction on T^3. Among the membrane degrees of freedom is an SL(2,R) doublet of world-volume 2-form potentials, whose quantised electric fluxes determine the membrane charges, and are conjectured to provide an interpretation of the variables occurring in the minimal representation of E_{6(6)} which appears in the context of automorphic membranes. We solve the relevant equations for the action for a restricted class of supergravity backgrounds. Some comments are made on supersymmetry and lower dimensions.

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arXiv2004

AdS twistors for higher spin theory

We construct spectra of supersymmetric higher spin theories in D=4, 5 and 7 from twistors describing massless (super-)particles on AdS spaces. A massless twistor transform is derived in a geometric way from classical kinematics. Relaxing the spin-shell constraints on twistor space gives an infinite tower of massless states of a ``higher spin particle'', generalising previous work of Bandos et al. This can generically be done in a number of ways, each defining the states of a distinct higher spin theory, and the method provides a systematic way of finding these. We reproduce known results in D=4, minimal supersymmetric 5- and 7-dimensional models, as well as supersymmetrisations of Vasiliev's Sp-models as special cases. In the latter models a dimensional enhancement takes place, meaning that the theory lives on a space of higher dimension than the original AdS space, and becomes a theory of doubletons. This talk was presented at the XIXth Max Born Symposium ``Fundamental Interactions and Twistor-Like Methods'', September 2004, in Wroclaw, Poland.

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arXiv2004

Thoughts on Membranes, Matrices and Non-Commutativity

We review the passage from the supermembrane to matrix theory via a consistent truncation following a non-commutative deformation in light-cone gauge. Some indications are given that there should exist a generalisation of non-commutativity involving a three-index theta on the membrane, and we discuss some possible ways of investigating the corresponding algebraic structure.

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arXiv2004

Supersymmetric Corrections to Eleven-Dimensional Supergravity

In this paper we study eleven-dimensional supergravity in its most general form. This is done by implementing manifest supersymmetry (and Lorentz invariance) through the use of the geometric (torsion and curvature) superspace Bianchi identities. These identities are solved to linear order in a deformation parameter introduced via the dimension zero supertorsion given in its most general form. The theory so obtained is referred to as the deformed theory (to avoid the previously used term "off-shell"). An important by-product of this result is that any higher derivative correction to ordinary supergravity of the same dimension as R^4, but not necessarily containing it, derived e.g. from M-theory, must appear in a form compatible with the equations obtained here. Unfortunately we have not yet much to say about the explicit structure of these corrections in terms of the fields in the massless supermultiplet. Our results are potentially powerful since if the dimension zero torsion could be derived by other means, our reformulation of the Bianchi identities as a number of algebraic relations implies that the full theory would be known to first order in the deformation, including the dynamics. We mention briefly some methods to derive the information needed to obtain explicit answers both in the context of supergravity and ten-dimensional super-Yang-Mills where the situation is better understood. Other relevant aspects like spinorial cohomology, the role of the 3- and 6-form potentials and the connection of these results to M2 and M5 branes are also commented upon.

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arXiv2003

M5-branes and Matrix Theory

We consider supermembranes ending on M5-branes, with the aim of deriving the appropriate matrix theories describing different situations. Special attention is given to the case of non-vanishing (selfdual) C-field. We identify the relevant deformation of the six-dimensional super-Yang-Mills theory whose dimensional reduction is the matrix theory for membranes in the presence of M5-branes. Possible applications and limitations of the models are discussed.

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arXiv2002

Open and Winding Membranes, Affine Matrix Theory and Matrix String Theory

We examine the structure of winding toroidal and open cylindrical membranes, especially in cases where they are stretched between boundaries. Non-zero winding or stretching means that there are linear terms in the mode expansion of the coordinates obeying Dirichlet boundary conditions. A linear term acts as an outer derivation on the subalgebra of volume-preserving diffeomorphisms generated by single-valued functions, and obstructs the truncation to matrix theory obtained via non-commutativity with rational parameter. As long as only one of the two membrane directions is stretched, the possible consistent truncation is to coordinates taking values in representations of an affine algebra. We show that this consistent truncation of the supermembrane gives a precise microscopic derivation of matrix string theory with the representation content appropriate for the physical situation. The matrix superstring theory describing parallel M5-branes is derived. We comment on the possible applications of the construction to membrane quantisation in certain M-theory backgrounds.

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arXiv2002

Spinorial cohomology of abelian d=10 super-Yang-Mills at alpha'^3

We compute the spinorial cohomology of ten-dimensional abelian SYM at order alpha'^3 and we find that it is trivial. Consequently, linear supersymmetry alone excludes the presence of alpha'^3-order corrections. Our result lends support to the conjecture that there may be a unique supersymmetric deformation of ordinary ten-dimensional abelian SYM.

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arXiv2001

Spinorial cohomology and maximally supersymmetric theories

Fields in supersymmetric gauge theories may be seen as elements in a spinorial cohomology. We elaborate on this subject, specialising to maximally supersymmetric theories, where the superspace Bianchi identities, after suitable conventional constraints are imposed, put the theories on shell. In these cases, the spinorial cohomologies describe in a unified manner gauge transformations, fields and possible deformations of the models, e.g. string-related corrections in an alpha' expansion. Explicit cohomologies are calculated for super-Yang-Mills theory in D=10, for the N=(2,0) tensor multiplet in D=6 and for supergravity in D=11, in the latter case from the point of view of both the super-vielbein and the super-3-form potential. The techniques may shed light on some questions concerning the alpha'-corrected effective theories, and result in better understanding of the role of the 3-form in D=11 supergravity.

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arXiv2001

Deformation independent open brane metrics and generalized theta parameters

We investigate the consequences of generalizing certain well established properties of the open string metric to the conjectured open membrane and open Dp-brane metrics. By imposing deformation independence on these metrics their functional dependence on the background fields can be determined including the notorious conformal factor. In analogy with the non-commutativity parameter $Θ^{μν}$ in the string case, we also obtain `generalized' theta parameters which are rank q+1 antisymmetric tensors (polyvectors) for open Dq-branes and rank 3 for the open membrane case. The expressions we obtain for the open membrane quantities are expected to be valid for general background field configurations, while the open D-brane quantities are only valid for one parameter deformations. By reducing the open membrane data to five dimensions, we show that they, modulo a subtlety with implications for the relation between OM-theory and NCYM, correctly generate the open string and open D2-data.

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arXiv2001

Superspace Methods in String Theory, Supergravity and Gauge Theory

In these two lectures, delivered at the XXXVII Karpacz Winter School, February 2001, I review some applications of superspace in various topics related to string theory and M-theory. The first lecture is mainly devoted to descriptions of brane dynamics formulated in supergravity backgrounds. The second lecture concerns the use of superspace techniques for determining consistent interactions in supersymmetric gauge theory and supergravity, e.g. alpha'-corrections from string/M-theory.

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arXiv2001

Holographic Noncommutativity

We examine noncommutative Yang-Mills and open string theories using magnetically and electrically deformed supergravity duals. The duals are near horizon regions of Dp-brane bound state solutions which are obtained by using O(p+1,p+1) transformations of Dp-branes. The action of the T-duality group implies that the noncommutativity parameter is constant along holographic RG-flows. The moduli of the noncommutative theory, i.e., the open string metric and coupling constant, as well as the zero-force condition are shown to be invariant under the O(p+1,p+1) transformation, i.e., deformation independent. We find sufficient conditions, including zero force and constant dilaton in the ISO(3,1)-invariant D3 brane solution, for exact S-duality between noncommutative Yang-Mills and open string theories. These results are used to construct noncommutative field and string theories with N=1 supersymmetry from the T^(1,1) and Pilch-Warner solutions. The latter has a non-trivial zero-force condition due to the warping.

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