arXiv subjects

C. M. Hull

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

At least 55 records · Page 3Linked to original sources

arXiv1998

Branes, Times and Dualities

Dualities link M-theory, the 10+1 dimensional strong coupling limit of the IIA string, to other 11-dimensional theories in signatures 9+2 and 6+5, and to type II string theories in all 10-dimensional signatures. We study the Freund-Rubin-type compactifications and brane-type solutions of these theories, and find that branes with various world-volume signatures are possible. For example, the 9+2 dimensional M* theory has membrane-type solutions with world-volumes of signature (3,0) and (1,2), and a solitonic solution with world-volume signature (5,1).

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arXiv1998

Timelike T-Duality, de Sitter Space, Large $N$ Gauge Theories and Topological Field Theory

T-Duality on a timelike circle does not interchange IIA and IIB string theories, but takes the IIA theory to a type $IIB^*$ theory and the IIB theory to a type $IIA^*$ theory. The type $II^*$ theories admit E-branes, which are the images of the type II D-branes under timelike T-duality and correspond to imposing Dirichlet boundary conditions in time as well as some of the spatial directions. The effective action describing an E$n$-brane is the $n$-dimensional Euclidean super-Yang-Mills theory obtained by dimensionally reducing 9+1 dimensional super-Yang-Mills on $9-n$ spatial dimensions and one time dimension. The $IIB^*$ theory has a solution which is the product of 5-dimensional de Sitter space and a 5-hyperboloid, and the E4-brane corresponds to anon-singular complete solution which interpolates between this solution and flat space. This leads to a duality between the large $N$ limit of the Euclidean 4-dimensional U(N) super-Yang-Mills theory and the $IIB^*$ string theory in de Sitter space, and both are invariant under the same de Sitter supergroup. This theory can be twisted to obtain a large $N$ topological gauge theory and its topological string theory dual. Flat space-time may be an unstable vacuum for the type $II^*$ theories, but they have supersymmetric cosmological solutions.

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arXiv1998

Decoupling Limits in M-Theory

Limits of a system of N Dn-branes in which the bulk and string degrees of freedom decouple to leave a `matter' theory are investigated and, for n>4, either give a free theory or require taking $N \to \infty$. The decoupled matter theory is described at low energies by the $N \to \infty$ limit of n+1 dimensional \sym, and at high energies by a free type II string theory in a curved space-time. Metastable bound states of D6-branes with mass $M$ and D0-branes with mass $m$ are shown to have an energy proportional to $M^{1/3}m^{2/3}$ and decouple, whereas in matrix theory they only decouple in the large N limit.

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arXiv1998

Geometric Actions for D-Branes and M-Branes

New forms of Born-Infeld, D-brane and M theory five-brane actions are found which are quadratic in the abelian field strength. The gauge fields couple both to a background or induced metric and a new auxiliary metric, whose elimination reproduces the non-polynomial Born-Infeld action. This is similar to the introduction of an auxiliary metric to simplify the Nambu-Goto string action. This simplifies the quantisation and dualisation of the gauge fields.

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arXiv1998

Duality and Moduli Spaces for Time-Like Reductions

We consider the dimensional reduction/compactification of supergravity, string and M-theories on tori with one time-like circle. We find the coset spaces in which the massless scalars take their values, and identify the discrete duality groups.

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arXiv1997

Conformal Invariance and Duality in Self-Dual Gravity and (2,1) Heterotic String Theory

A system of gravity coupled to a 2-form gauge field, a dilaton and Yang-Mills fields in $2n$ dimensions arises from the (2,1) sigma model or string. The field equations imply that the curvature with torsion and Yang-Mills field strength are self-dual in four dimensions, or satisfy generalised self-duality equations in $2n$ dimensions. The Born-Infeld-type action describing this system is simplified using an auxiliary metric and shown to be classically Weyl invariant only in four dimensions. A dual form of the action is found (no isometries are required). In four dimensions, the dual geometry is self-dual gravity without torsion coupled to a scalar field. In $D>4$ dimensions, the dual geometry is hermitian and determined by a $D-4$ form potential $K$, generalising the Kähler potential of the four dimensional case, with the fundamental 2-form given by $\tilde J= i*\partial \bar \partial K$. The coupling to Yang-Mills is through a term $K\wedge tr (F\wedge F)$ and leads to a Uhlenbeck-Yau field equation $\tilde J^{ij}F_{ij}=0$.

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arXiv1997

The Gauged (2,1) Heterotic Sigma-Model

The geometry of (2,1) supersymmetric sigma-models with isometry symmetries is discussed. The gauging of such symmetries in superspace is then studied. We find that the coupling to the (2,1) Yang-Mills supermultiplet can be achieved provided certain geometric conditions are satisfied. We construct the general gauged action, using an auxiliary vector to generate the full non-polynomial structure.

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arXiv1997

U-Duality and BPS Spectrum of Super Yang-Mills Theory and M-Theory

It is shown that the BPS spectrum of Super-Yang-Mills theory on $T^d\times \R$, which fits into representations of the U-duality group for M-theory compactified on $T^{d}$, in accordance with the matrix-theory conjecture, in fact fits into representations of the U-duality group for M-theory on $T^{d+1}$, the extra dualities realised as generalised Nahm transformations. The spectrum of BPS M-branes is analysed, new branes are discussed and matrix theory applications described.

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arXiv1997

Higher Dimensional Yang-Mills Theories and Topological Terms

Higher dimensional generalisations of self-duality conditions and of theta angle terms are analysed in Yang-Mills theories. For the theory on a torus, the torus metric and various antisymmetric tensors are viewed as coupling constants related by U-duality, arising from background expectation values of supergravity fields for D-brane or matrix theories. At certain special points in the moduli space of coupling constants certain branes or instantons are found to dominate the functional integral. The possibility of lifting chiral or supersymmetric theories to higher dimensions is discussed.

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arXiv1997

Non-Abelian Gravity and Antisymmetric Tensor Gauge Theory

A non-abelian generalisation of a theory of gravity coupled to a 2-form gauge field and a dilaton is found, in which the metric and 3-form field strength are Lie algebra-valued. In the abelian limit, the curvature with torsion is self-dual in four dimensions, or has SU(n) holonomy in $2n$ dimensions. The coupling to self-dual Yang-Mills fields in 4 dimensions, or their higher dimensional generalisation, is discussed. The abelian theory is the effective action for (2,1) strings, and the non-abelian generalisation is relevant to the study of coincident branes in the (2,1) string approach to M-theory. The theory is local when expressed in terms of a vector pre-potential.

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arXiv1997

Gravitational Duality, Branes and Charges

It is argued that D=10 type II strings and M-theory in D=11 have D-5 branes and 9-branes that are not standard p-branes coupled to anti-symmetric tensors. The global charges in a D-dimensional theory of gravity consist of a momentum $P_M$ and a dual D-5 form charge $K_{M_1...M_{D-5}}$, which is related to the NUT charge. On dimensional reduction, P gives the electric charge and K the magnetic charge of the graviphoton. The charge K is constructed and shown to occur in the superalgebra and BPS bounds in $D\ge 5$, and leads to a NUT-charge modification of the BPS bound in D=4. $K$ is carried by Kaluza-Klein monopoles, which can be regarded as D-5 branes. Supersymmetry and U-duality imply that the type IIB theory has (p,q) 9-branes. Orientifolding with 32 (0,1) 9-branes gives the type I string, while modding out by a related discrete symmetry with 32 (1,0) 9-branes gives the SO(32) heterotic string. Symmetry enhancement, the effective world-volume theories and the possibility of a twelve dimensional origin are discussed.

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arXiv1997

Intrinsic Geometry of D-Branes

We obtain forms of Born-Infeld and D-brane actions that are quadratic in derivatives of $X$ and linear in $F_{μν}$ by introducing an auxiliary `metric' which has both symmetric and anti-symmetric parts, generalising the simplification of the Nambu-Goto action for $p$-branes using a symmetric metric. The abelian gauge field appears as a Lagrange multiplier, and solving the constraint gives the dual form of the $n$ dimensional action with an $n-3$ form gauge field instead of a vector gauge field. We construct the dual action explicitly, including cases which could not be covered previously. The generalisation to supersymmetric D-brane actions with local fermionic symmetry is also discussed.

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arXiv1997

Geometry, Isometries and Gauging of (2,1) Heterotic Sigma-Models

The geometry of (2,1) supersymmetric sigma-models is reviewed and the conditions under which they have isometry symmetries are analysed. Certain potentials are constructed that play an important role in the gauging of such symmetries. The gauged action is found for a special class of models.

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arXiv1997

Actions For (2,1) Sigma-Models and Strings

Effective actions are derived for (2,0) and (2,1) superstrings by studying the corresponding sigma-models. The geometry is a generalisation of Kahler geometry involving torsion and the field equations imply that the curvature with torsion is self-dual in four dimensions, or has SU(n,m) holonomy in other dimensions. The Yang-Mills fields are self-dual in four dimensions and satisfy a form of the Uhlenbeck-Yau equation in higher dimensions. In four dimensions with Euclidean signature, there is a hyperkahler structure and the sigma-model has (4,1) supersymmetry, while for signature (2,2) there is a hypersymplectic structure consisting of a complex structure squaring to -1 and two real structures squaring to 1. The theory is invariant under a twisted form of the (4,1) superconformal algebra which includes an SL(2,R) Kac-Moody algebra instead of an SU(2) Kac-Moody algebra. Kahler and related geometries are generalised to ones involving real structures.

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arXiv1996

The Geometry of $N=2$ Strings with Torsion

$N=2$ string theories are formulated in space-times with 2 space and 2 time dimensions. If the world-sheet matter system consists of 2 chiral superfields, the space-time is Kahler and the dynamics are those of anti-self-dual gravity. If instead one chiral superfield and one twisted chiral superfield are used, the space-time is a hermitian manifold with torsion and a dilaton. The string spectrum consists of a scalar, which is a potential $K$ determining the metric, torsion and dilaton. The dynamics imply that the curvature with torsion is anti-self-dual, and an action is found for the potential $K$. It is argued that any $N=2$ sigma-model with twisted chiral multiplets in any dimension can be deformed to a conformally invariant theory if the lowest order contribution to the conformal anomaly vanishes. If there are isometries, more general geometries are possible in which the dilaton is the Killing potential for a holomorphic Killing vector.

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arXiv1996

Duality in the Type--II Superstring Effective Action

We derive the T-duality transformations that transform a general d=10 solution of the type-IIA string with one isometry to a solution of the type-IIB string with one isometry and vice versa. In contrast to other superstring theories, the T-duality transformations are not related to a non-compact symmetry of a d=9 supergravity theory. We also discuss S-duality in d=9 and d=10 and the relationship with eleven-dimensional supergravity theory. We apply these dualities to generate new solutions of the type IIA and type IIB superstrings and of eleven-dimensional supergravity.

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arXiv1996

Enhanced Gauge Symmetries in Superstring Theories

Certain four-dimensional $N=4$ supersymmetric theories have special vacua in which massive charged vector supermultiplets become massless, resulting in an enhanced non-abelian gauge symmetry. We show here that any two $N=4$ theories having the same Bogomolnyi spectrum at corresponding points of their moduli spaces have the same enhanced symmetry groups. In particular, the $K_3\times T^2$ compactified type II string is argued to have the same enhanced symmetry groups as the $T^6$-compactified heterotic string, giving further evidence for our conjecture that these two string theories are equivalent. A feature of the enhanced symmetry phase is that for every electrically charged state whose mass tends to zero as an enhanced symmetry point is approached, there are magnetically charged and dyonic states whose masses also tend to zero, a result that applies equally to N=4 super Yang-Mills theory. These extra non-perturbative massless states in the $K_3$ compactification result from $p$-branes wrapping around collapsed homology two-cycles of $K_3$. Finally, we show how membrane `wrapping modes' lead to symmetry enhancement in D=11 supergravity, providing further evidence that the $K_3$-compactified D=11 supergravity is the effective field theory of the strong coupling limit of the $T^3$-compactified heterotic string.

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arXiv1996

String Dynamics at Strong Coupling

The dynamics of superstring, supergravity and M theories and their compactifications are probed by studying the various perturbation theories that emerge in the strong and weak coupling limits for various directions in coupling constant space. The results support the picture of an underlying non-perturbative theory that, when expanded perturbatively in different coupling constants, gives different perturbation theories, which can be perturbative superstring theories or superparticle theories. The $p$-brane spectrum is considered in detail and a criterion found to establish which $p$-branes govern the strong coupling dynamics. In many cases there are competing conjectures in the literature, and this analysis decides between them. In other cases, new results are found. The chiral six-dimensional theory resulting from compactifying the type IIB string on $K_3$ is studied in detail and it is found that certain strong coupling limits appear to give new theories, some of which hint at the possibility of a twelve-dimensional origin.

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