Malcolm J. Perry

Strings in background fields

Abstract We formulate the propagation of strings in background fields, including the effects of metric, antisymmetric tensor, and dilaton expectation values, as well as gauge field backgrounds in the case of heterotic strings. The inclusion of background fermion fields is sketched. The equations of motion of all these fields are shown to be the consequence of (super) conformal invariance of the string.

Magnetic Monopoles in Kaluza-Klein Theories

Abstract We demonstrate that the five-dimensional Kaluza-Klein theory of unified gravity and electromagnetism admits soliton solutions. These are regular, static and stable solutions of the field equations which correspond, upon quantization, to particles. The solitons include magnetic monopoles, which obey the Dirac quantization condition, as well as magnetic dipoles which are topologically stable. The inertial mass of the solitons is typically of order mp/e, where mp is the Planck mass and e the electric charge. These solitons have bizarre gravitational interactions; in fact they exert no newtonian force on slowly moving test particles, thus they have zero gravitational mass. We explain how the inequality of the gravitational and inertial masses is due to the violation of Birkhoffs theorem in Kaluza-Klein theories and is consistent with the principle of equivalence.

Path Integrals and the Indefiniteness of the Gravitational Action

The Euclidean action for gravity is not positive definite unlike those of scalar and Yang-Mills fields. Indefiniteness arises because conformal transformations can make the action arbitrarily negative. In order to make the path integral converge one has to take the contour of integration for the conformal factor to be parallel to the imaginary axis. The path integral will then converge at least in the one-loop approximation if a certain positive action conjecture holds. We perform a zeta function regularization of the one-loop term for gravity and obtain a non-trivial scaling behaviour in cases in which the background metric has non-zero curvature tensor, and hence non-trivial topologies.

The first law of thermodynamics for Kerr–anti-de Sitter black holes

We obtain expressions for the mass and angular momenta of rotating black holes in anti-de Sitter backgrounds in four, five and higher dimensions. We verify explicitly that our expressions satisfy the first law of thermodynamics, thus allowing an unambiguous identification of the entropy of these black holes with of the area. We find that the associated thermodynamic potential equals the background-subtracted Euclidean action multiplied by the temperature. Our expressions differ from many given in the literature. We find that in more than four dimensions, only our expressions satisfy the first law of thermodynamics. Moreover, in all dimensions we show that our expression for the mass coincides with that given by the conformal conserved charge introduced by Ashtekar, Magnon and Das. We indicate the relevance of these results to the AdS/CFT correspondence.

Instantons and seven-branes in type IIB superstring theory

Abstract Instanton and seven-brane solutions of type IIB supergravity carrying charges in the Ramond-Ramond sector are constructed. The singular seven-brane has a quantized R ⊗ R ‘magnetic’ charge whereas its dual is the instanton, which is non-singular in the string frame and has an associated global ‘electric’ charge. The product of these charges is constrained by a Dirac quantization condition. The instanton has the form of a space-time wormhole in the string frame, and is responsible for the non-conservation of the Noether current.

Soft Hair on Black Holes

It has recently been shown that Bondi-van der Burg-Metzner-Sachs supertranslation symmetries imply an infinite number of conservation laws for all gravitational theories in asymptotically Minkowskian spacetimes. These laws require black holes to carry a large amount of soft (i.e., zero-energy) supertranslation hair. The presence of a Maxwell field similarly implies soft electric hair. This Letter gives an explicit description of soft hair in terms of soft gravitons or photons on the black hole horizon, and shows that complete information about their quantum state is stored on a holographic plate at the future boundary of the horizon. Charge conservation is used to give an infinite number of exact relations between the evaporation products of black holes which have different soft hair but are otherwise identical. It is further argued that soft hair which is spatially localized to much less than a Planck length cannot be excited in a physically realizable process, giving an effective number of soft degrees of freedom proportional to the horizon area in Planck units.

Generalized geometry and M theory

We reformulate the Hamiltonian form of bosonic eleven dimensional supergravity in terms of an object that unifies the three-form and the metric. For the case of four spatial dimensions, the duality group is manifest and the metric and C-field are on an equal footing even though no dimensional reduction is required for our results to hold. One may also describe our results using the generalized geometry that emerges from membrane duality. The relationship between the twisted Courant algebra and the gauge symmetries of eleven dimensional supergravity are described in detail.

Positive mass theorems for black holes

We extend Wittens proof of the positive mass theorem at spacelike infinity to show that the mass is positive for initial data on an asymptotically flat spatial hypersurface Σ which is regular outside an apparent horizonH. In addition, we prove that if a black hole has electromagnetic charge, then the mass is greater than the modulus of the charge. These results are also valid for the Bondi mass at null infinity. Finally, in the case of the Einstein equation with a negative cosmological constant, we show that a suitably defined mass is positive for data on an asymptotically anti-de Sitter surface Σ which is regular outside an apparent horizon.

String Theory Effective Actions

Abstract We show that the beta functions of the nonlinear sigma models which describe strings propagating in background fields can be used to construct the generating functional for on-shell S -matrix elements of the associated string theories.

Interacting chiral gauge fields in six dimensions and Born-Infeld theory

Abstract Dimensional reduction of a self-dual tensor gauge field in 6D gives an Abelian vector gauge field in 5D. We derive the conditions under which an interacting 5D theory of an Abelian vector gauge field is the dimensional reduction of a 6D Lorentz invariant interacting theory of a self-dual tensor. Then we specialize to the particular 6D theory that gives 5D Born-Infeld theory. The field equation and Lagrangian of this 6D theory are formulated with manifest 5D Lorentz invariance, while the remaining Lorentz symmetries are realized non-trivially. A string soliton with finite tension and self-dual charge is constructed.