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C. M. Hull

Publications and source records attributed to C. M. Hull.

At least 37 records · Page 2Linked to original sources
arXiv2005

Higher-Spin Gauge Fields and Duality

We review the construction of free gauge theories for gauge fields in arbitrary representations of the Lorentz group in $D$ dimensions. We describe the multi-form calculus which gives the natural geometric framework for these theories. We also discuss duality transformations that give different field theory representations of the same physical degrees of freedom, and discuss the example of gravity in $D$ dimensions and its dual realisations in detail.

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arXiv2002

Gauged D=9 Supergravities and Scherk-Schwarz Reduction

Generalised Scherk-Schwarz reductions in which compactification on a circle is accompanied by a twist with an element of a global symmetry G typically lead to gauged supergravities and are classified by the monodromy matrices, up to conjugation by the global symmetry. For compactifications of IIB supergravity on a circle, G=SL(2,R) and there are three distinct gauged supergravities that result, corresponding to monodromies in the three conjugacy classes of SL(2,R). There is one gauging of the compact SO(2) subgroup of the SL(2,R) and two distinct gaugings of non-compact SO(1,1) subgroups, embedded differently in SL(2,R). The non-compact gaugings can be obtained from the compact one via an analytic continuation of the kind used in D=4 gauged supergravities. For the superstring, the monodromy must be in SL(2,Z), and the distinct theories correspond to SL(2,Z) conjugacy classes. The theories consist of two infinite classes with quantised mass parameter m=1,2,3,..., three exceptional theories corresponding to elliptic conjugacy classes, and a set of sporadic theories corresponding to hyperbolic conjugacy classes.

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arXiv2002

New Gauged N=8, D=4 Supergravities

New gaugings of four dimensional N=8 supergravity are constructed, including one which has a Minkowski space vacuum that preserves N=2 supersymmetry and in which the gauge group is broken to $SU(3)xU(1)^2$. Previous gaugings used the form of the ungauged action which is invariant under a rigid $SL(8,R)$ symmetry and promoted a 28-dimensional subgroup ($SO(8),SO(p,8-p)$ or the non-semi-simple contraction $CSO(p,q,8-p-q)$) to a local gauge group. Here, a dual form of the ungauged action is used which is invariant under $SU^*(8)$ instead of $SL(8,R)$ and new theories are obtained by gauging 28-dimensional subgroups of $SU^*(8)$. The gauge groups are non-semi-simple and are different real forms of the $CSO(2p,8-2p)$ groups, denoted $CSO^*(2p,8-2p)$, and the new theories have a rigid SU(2) symmetry. The five dimensional gauged N=8 supergravities are dimensionally reduced to D=4. The $D=5,SO(p,6-p)$ gauge theories reduce, after a duality transformation, to the $D=4,CSO(p,6-p,2)$ gauging while the $SO^*(6)$ gauge theory reduces to the $D=4, CSO^*(6,2)$ gauge theory. The new theories are related to the old ones via an analytic continuation. The non-semi-simple gaugings can be dualised to forms with different gauge groups.

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arXiv2001

De Sitter Space from Warped Supergravity Solutions

The solutions of 10 and 11 dimensional supergravity that are warped products of de Sitter space with a non-compact `internal' space are investigated. A convenient form of the metric is found and it is shown that in each case the internal space is asymptotic to a cone over a product of spheres. A consistent truncation gives gauged supergravities with non-compact gauge groups. The BPS domain wall solutions of the non-compact gauged supergravities are lifted to warped solutions in 10 or 11 dimensions.

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arXiv2001

De Sitter Space in Supergravity and M Theory

Two ways in which de Sitter space can arise in supergravity theories are discussed. In the first, it arises as a solution of a conventional supergravity, in which case it necessarily has no Killing spinors. For example, de Sitter space can arise as a solution of N=8 gauged supergravities in four or five dimensions. These lift to solutions of 11-dimensional supergravity or D=10 IIB supergravity which are warped products of de Sitter space and non-compact spaces of negative curvature. In the second way, de Sitter space can arise as a supersymmetric solution of an unconventional supergravity theory, which typically has some kinetic terms with the `wrong' sign; such solutions are invariant under a de Sitter supergroup. Such solutions lift to supersymmetric solutions of unconventional supergravities in D=10 or D=11, which nonetheless arise as field theory limits of theories that can be obtained from M-theory by timelike T-dualities and related dualities. Brane solutions interpolate between these solutions and flat space and lead to a holographic duality between theories in de Sitter vacua and Euclidean conformal field theories. Previous results are reviewed and generalised, and discussion is included of Kaluza-Klein theory with non-compact internal spaces, brane and cosmological solutions, and holography on de Sitter spaces and product spaces.

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arXiv2001

Duality in Gravity and Higher Spin Gauge Fields

Dual field theory realisations are given for linearised gravity in terms of gauge fields in exotic representations of the Lorentz group. The field equations and dual representations are discussed for a wide class of higher spin gauge fields. For non-linear Einstein gravity, such transformations can be implemented locally in light-cone gauge, or partially implemented in the presence of a Killing vector. Sources and the relation to Kaluza-Klein monopoles are discussed.

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arXiv2000

Conformal Non-Geometric Gravity in Six Dimensions and M-Theory above the Planck Energy

The proposal that a strong coupling limit of the five-dimensional type II string theory (M-theory compactified on a 6-torus) in which the Planck length becomes infinite could give a six-dimensional superconformal phase of M-theory is reviewed. This limit exists for the free theory, giving a 6-dimensional theory with (4,0) supersymmetry compactified on a circle whose radius gives the 5-dimensional Planck length. The free 6-dimensional theory has a fourth rank tensor gauge field with the symmetries of the Riemann tensor instead of a symmetric tensor gauge field, but its dimensional reduction gives conventional linearised gravity in five dimensions. The possibility of an interacting form of this theory existing and the consequences it would have for the geometric picture of gravity are discussed.

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arXiv2000

Symmetries and Compactifications of (4,0) Conformal Gravity

The free (4,0) superconformal theory in 6 dimensions and its toroidal dimensional reductions are studied. The reduction to four dimensions on a 2-torus has an $SL(2,\Z)$ duality symmetry that acts non-trivially on the linearised gravity sector, interchanging the linearised Einstein equations and Bianchi identities and giving a self-duality between strong and weak coupling regimes. The possibility of this extending to an interacting form of the theory is discussed and implications for the non-geometric picture of gravity that could emerge are considered.

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arXiv2000

BPS Supermultiplets in Five Dimensions

BPS representations of 5-dimensional supersymmetry algebras are classified. For BPS states preserving 1/2 the supersymmetry, there are two distinct classes of multiplets for N=4 supersymmetry and three classes for N=8 supersymmetry. For N=4 matter theories, the two 1/2 supersymmetric BPS multiplets are the massive vector multiplet and the massive self-dual 2-form multiplet. Some applications to super-Yang-Mills, supergravity and little string theories are considered.

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arXiv2000

Strongly Coupled Gravity and Duality

A strong coupling limit of theories whose low-energy effective field theory is 5-dimensional N=8 supergravity is proposed in which the gravitational coupling becomes large. It is argued that, if this limit exists, it should be a 6-dimensional theory with (4,0) supersymmetry compactified on a circle whose radius gives the 5-dimensional Planck length. The sector corresponding to the D=5 supergravity multiplet is a (4,0) D=6 superconformal field theory based on the (4,0) multiplet with 27 self-dual 2-forms, 42 scalars and, instead of a graviton, a fourth-rank tensor gauge field satisfying a self-duality constraint. The superconformal field theory has 32 supersymmetries and 32 conformal supersymmetries and its dimensional reduction gives the maximal supergravity in five dimensions. Electromagnetic duality generalises to a gravitational triality.

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arXiv1999

Duality and Strings, Space and Time

Duality symmetries in M--theory and string theory are reviewed, with particular emphasis on the way in which string winding modes and brane wrapping modes can lead to new spatial dimensions. Brane world-volumes wrapping around Lorentzian tori can give rise to extra time dimensions and in this way dualities can change the number of time dimensions as well as the number of space dimensions. This suggests that brane wrapping modes and spacetime momenta should be on an equal footing and M--theory should not be formulated in a spacetime of definite dimension or signature.

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arXiv1999

The Geometry of Supersymmetric Quantum Mechanics

One-dimensional sigma-models with N supersymmetries are considered. For conventional supersymmetries there must be N-1 complex structures satisfying a Clifford algebra and the constraints on the target space geometry can be formulated in terms of these. In the cases in which the complex structures are simultaneously integrable, a conventional extended superspace formulation is given, with the geometry determined by a 2-form potential for N=2, by a 1-form potential for N=3 and a scalar potential for N=4; for N>4 it is given by a scalar potential satisfying differential constraints. This gives explicit constructions of models with N=3 but not N=4 supersymmetry and of N=4 models in which the complex structures do not satisfy a quaternionic algebra. Generalisations with central terms in the superalgebra are also considered.

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arXiv1999

Spacetime-Filling Branes and Strings with Sixteen Supercharges

We discuss branes whose worldvolume dimension equals the target spacetime dimension, i.e. ``spacetime-filling branes''. In addition to the D9-branes, there are 9-branes in the NS-NS sectors of both the IIA and IIB strings. The worldvolume actions of these branes are constructed, via duality, from the known actions of branes with codimension larger than zero. Each of these types of branes is used in the construction of a string theory with sixteen supercharges by modding out a type II string by an appropriate discrete symmetry and adding 32 9-branes. These constructions are related by a web of dualities and each arises as a different limit of the Horava-Witten construction.

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arXiv1998

The Non-Perturbative SO(32) Heterotic String

The SO(32) heterotic string can be obtained from the type IIB string by gauging a discrete symmetry that acts as $(-1)^{F_L}$ on the perturbative string states and reverses the parity of the D-string. Consistency requires the presence of 32 NS 9-branes -- the S-duals of D9-branes -- which give SO(32) Chan-Paton factors to open D-strings. At finite string coupling, there are SO(32) charges tethered to the heterotic string world-sheet by open D-strings. At zero-coupling, the D-string tension becomes infinite and the SO(32) charges are pulled onto the world-sheet, and give the usual SO(32) world-sheet currents of the heterotic string.

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arXiv1998

Massive String Theories From M-Theory and F-Theory

The massive IIA string theory whose low energy limit is the massive supergravity theory constructed by Romans is obtained from M-theory compactified on a 2-torus bundle over a circle in a limit in which the volume of the bundle shrinks to zero. The massive string theories in 9-dimensions given by Scherk-Schwarz reduction of IIB string theory are interpreted as F-theory compactified on 2-torus bundles over a circle. The M-theory solution that gives rise to the D8-brane of the massive IIA theory is identified. Generalisations of Scherk-Schwarz reduction are discussed.

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arXiv1998

Duality and the Signature of Space-Time

Versions of M-theory are found in spacetime signatures (9,2) and (6,5), in addition to the usual M-theory in 10+1 dimensions, and these give rise to type IIA string theories in 10-dimensional spacetime signatures (10,0),(9,1),(8,2),(6,4) and (5,5), and to type IIB string theories in signatures (9,1),(7,3) and (5,5). The field theory limits are 10 and 11 dimensional supergravities in these signatures. These theories are all linked by duality transformations which can change the number of time dimensions as well as the number of space dimensions, so that each should be a different limit of the same underlying theory.

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arXiv1998

Matrix Theory, U-Duality and Toroidal Compactifications of M-Theory

Using U-duality, the properties of the matrix theories corresponding to the compactification of M-theory on $T^d$ are investigated. The couplings of the $d+1$ dimensional effective Super-Yang-Mills theory to all the M-theory moduli is deduced and the spectrum of BPS branes in the SYM gives the corresponding spectrum of the matrix theory.Known results are recovered for $d\le 5$ and predictions for $d>5$ are proposed. For $d>3$, the spectrum includes $d-4$ branes arising from YM instantons, and U-duality interchanges momentum modes with brane wrapping modes.For $d=6$, there is a generalised $þ$-angle which couples to instantonic 3-branes and which combines with the SYM coupling constant to take values in $SL(2,\R)/U(1)$, acted on by an $SL(2,\Z)$ subgroup of the U-duality group $E_6(\Z)$. For $d=4,7,8$, there is an $SL(d+1)$ symmetry, suggesting that the matrix theory could be a scale-invariant $d+2$ dimensional theory on $T^{d+1} \times \R$ in these cases, as is already known to be the case for $d=4$; evidence is found suggesting this happens for $d=8$ but not $d=7$.

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