arXiv subjects
Publications and source records attributed to P. K. Townsend.
The superfield equations of massive IIA supergravity, in the form of constraints on the superspace geometry, are shown to be implied by $κ$-symmetry of the topologically massive D-2-brane.
Lecture notes for a 'Part III' course 'Black Holes' given in DAMTP, Cambridge. The course covers some of the developments in Black Hole physics of the 1960s and 1970s.
Generalized membrane solutions of D=11 supergravity, for which the transverse space is a toric hyper-K{\" a}hler manifold, are shown to have IIB duals representing the intersection of parallel 3-branes with 5-branes whose orientations are determined by their $Sl(2;\bZ)$ charge vectors. These IIB solutions, which generically preserve 3/16 of the supersymmetry, can be further mapped to solutions of D=11 supergravity representing the intersection of parallel membranes with any number of fivebranes at arbitrary angles. Alternatively, a subclass (corresponding to non-singular D=11 solutions) can be mapped to solutions representing the intersection on a string of any number of D-5-branes at arbitrary angles, again preserving 3/16 supersymmetry, as we verify in a special case by a quaternionic extension of the analysis of Berkooz, Douglas and Leigh. We also use similar methods to find new 1/8 supersymmetric solutions of orthogonally intersecting branes.
A manifestly S-dual, and `12 dimensional', IIB superstring action with an $Sl(2;\bR)$ doublet of `Born-Infeld' fields is presented. The M-theory origin of the 12th dimension is the M-2-brane tension, which can be regarded as the flux of a 3-form worldvolume field strength. The latter is required by the fact that the M-2-brane can have a boundary on an M-5-brane.
We present a manifestly Lorentz invariant, spacetime supersymmetric, and `$κ$-invariant' worldvolume action for all type II Dirichlet p-branes, $p\le9$, in a general type II supergravity background, including massive backgrounds in the IIA case. The $p=0,2$ cases are rederived from D=11. The $p=9$ case provides a supersymmetrization of the D=10 Born-Infeld action.
The M-theory interpretation of certain D=10 IIA p-branes implies the existence of worldvolume Kaluza-Klein modes which are expected to appear as 0-brane/p-brane bound states preserving 1/4 of the spacetime supersymmetry. We construct the corresponding solutions of the effective supergravity theory for $p=1,4$, and show that no such solution exists for $p=8$.
We show how toroidally-compactified eleven-dimensional supergravity can be consistently truncated to yield a variety of maximally-supersymmetric ``massive'' supergravities in spacetime dimensions $D\le 8$. The mass terms arise as a consequence of making a more general ansatz than that in usual Kaluza-Klein dimensional reduction, in which one or more axions are given an additional linear dependence on one of the compactification coordinates. The lower-dimensional theories are nevertheless consistent truncations of eleven-dimensional supergravity. Owing to the fact that the generalised reduction commutes neither with U-duality nor with ordinary dimensional reduction, many different massive theories can result. The simplest examples arise when just a single axion has the additional linear coordinate dependence. We find five inequivalent such theories in D=7, and 71 inequivalent ones in D=4. The massive theories admit no maximally-symmetric vacuum solution, but they do admit $(D-2)$-brane solutions, i.e. domain walls, which preserve half the supersymmetry. We present examples of these solutions, and their oxidations to D=11. Some of the latter are new solutions of D=11 supergravity.
Some aspects of the role of p-branes in non-perturbative superstring theory and M-theory are reviewed. It is then shown how the Chern-Simons terms in D=10 and D=11 supergravity theories determine which branes can end on which, i.e. the `brane boundary rules'.
We examine $(D-2)$-brane solutions in supergravities, showing that they fall into four categories depending on the details of the dilaton coupling. In general they describe domain walls, although in one of the four categories the metric describes anti-de Sitter spacetime. We study this case, and its $S^1$ dimensional reduction to a more conventional domain wall in detail, focussing in particular on the manner in which the unbroken supersymmetry of the anti-de Sitter solution is partially broken by the dimensional reduction to the domain wall.
The `electromagnetic' $Sl(2;\bZ)$ duality group in spacetime dimension $D=4k$ can be given a Kaluza-Klein interpretation in $D=4k+2$ as the modular group of a compactifying torus. We show how dyonic $2(k-1)$-branes in $D=4k$ can be interpreted as self-dual $(2k-1)$-branes in $D=4k+2$ wound around the homology cycles of the torus. In particular, dyons of the D=4 N=4 heterotic string theory are interpreted as winding modes of a D=6 self-dual string, while D=8 dyonic membranes are interpreted as wound 3-branes of D=10 IIB superstring theory. We also discuss the T-dual IIA interpretations of D=8 dyonic membranes.
We present a version of ten-dimensional IIA supergravity containing a 9-form potential for which the field equations are equivalent to those of the standard, massless, IIA theory for vanishing 10-form field strength, $F_{10}$, and to those of the `massive' IIA theory for non-vanishing $F_{10}$. We present a multi 8-brane solution of these equations that generalizes the 8-brane of Polchinski and Witten. We show that this solution is T-dual to a new multi 7-brane solution of $S^1$ compactified IIB supergravity, and that the latter is T-dual to the IIA 6-brane. When combined with the $Sl(2;\Z)$ U-duality of the type IIB superstring, the T-duality between type II 7-branes and 8-branes implies a quantization of the cosmological constant of type IIA superstring theory. These results are made possible by the construction of a new {\it massive} N=2 D=9 supergravity theory. We also discuss the 11-dimensional interpretation of these type II p-branes.
We present the magnetic duals of Güven's electric-type solutions of D=11 supergravity preserving $1/4$ or $1/8$ of the D=11 supersymmetry. We interpret the electric solutions as $n$ orthogonal intersecting membranes and the magnetic solutions as $n$ orthogonal intersecting 5-branes, with $n=2,3$; these cases obey the general rule that $p$-branes can self-intersect on $(p-2)$-branes. On reduction to $D=4$ these solutions become electric or magnetic dilaton black holes with dilaton coupling constant $a=1$ (for $n=2$) or $a=1/\sqrt{3}$ (for $n=3$). We also discuss the reduction to D=10.
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.
The 2-brane and 4-brane solutions of ten dimensional IIA supergravity have a dual interpretation as Dirichlet-branes, or `D-branes', of type IIA superstring theory and as `M-branes' of an $S^1$-compactified eleven dimensional supermembrane theory, or M-theory. This eleven-dimensional connection is used to determine the ten-dimensional Lorentz covariant worldvolume action for the Dirichlet super 2-brane, and its coupling to background spacetime fields. It is further used to show that the 2-brane can carry the Ramond-Ramond charge of the Dirichlet 0-brane as a topological charge, and an interpretation of the 2-brane as a 0-brane condensate is suggested. Similar results are found for the Dirichlet 4-brane via its interpretation as a double-dimensional reduction of the eleven-dimensional fivebrane. It is suggested that the latter be interpreted as a D-brane of an open eleven-dimensional supermembrane.
We construct a new class of $(p,q)$-extended Poincaré supergravity theories in 2+1 dimensions as Chern-Simons theories of supersymmetry algebras with both central and automorphism charges. The new theories have the advantage that they are limits of corresponding $(p,q)$ adS supergravity theories and, for not too large a value of $N=p+q$, that they have a natural formulation in terms of off-shell superfields, in which context the distinction between theories having the same value of $N$ but different $(p,q)$ arises because of inequivalent conformal compensator superfields. We also show that, unlike previously constructed N-extended Poincaré supergravity theories, the new (2,0) theory admits conical spacetimes with Killing spinors. Many of our results on (2,0) Poincaré supergravity continue to apply in the presence of coupling to N=2 supersymmetric sigma-model matter.
We present dyonic multi-membrane solutions of the N=2 D=8 supergravity theory that serves as the effective field theory of the $T^2$-compactified type II superstring theory. The `electric' charge is fractional for generic asymptotic values of an axion field, as for D=4 dyons. These membrane solutions are supersymmetric, saturate a Bogomolnyi bound, fill out orbits of an $Sl(2;\Z)$ subgroup of the type II D=8 T-duality group, and are non-singular when considered as solutions of $T^3$-compactified D=11 supergravity. On $K_3$ compactification to D=4, the conjectured type II/heterotic equivalence allows the $Sl(2;\Z)$ group to be reinterpreted as the S-duality group of the toroidally compactified heterotic string and the dyonic membranes wrapped around homology two-cycles of $K_3$ as S-duals of perturbative heterotic string states.
We present a version of ten-dimensional IIA supergravity containing a 9-form potential for which the field equations are equivalent to those of the standard, massless, IIA theory for vanishing 10-form field strength, $F_{10}$, and to those of the `massive' IIA theory for non-vanishing $F_{10}$. We exhibit a multi 8-brane solution of this theory which preserves half the supersymmetry. We propose this solution as the effective field theory realization of the Dirichlet 8-brane of type IIA superstring theory.
A review is given of the implications of supersymmetric black holes for the non-perturbative formulation of toroidally compactified superstrings, with particular emphasis on symmetry enhancement at special vacua and S-duality of the heterotic string.