arXiv subjects

C. N. Pope

Publications and source records attributed to C. N. Pope.

At least 91 records · Page 5Linked to original sources

arXiv2011

Chiral Reductions in the Salam-Sezgin Model

Reductions from six to four spacetime dimensions are considered for a class of supergravity models based on the six-dimensional Salam-Sezgin model, which is a chiral theory with a gauged U(1) R-symmetry and a positive scalar-field potential. Reduction on a sphere and monopole background of such models naturally yields four-dimensional theories without a cosmological constant. The question of chirality preservation in such a reduction has been a topic of debate. In this article, it is shown that the possibilities of dimensional reduction bifurcate into two separate consistent dimensional-reduction schemes. One of these retains the massless SU(2) vector gauge triplet arising from the sphere's isometries, but it produces a non-chiral four-dimensional theory. The other consistent scheme sets to zero the SU(2) gauge fields, but retains the gauged U(1) from six dimensions and preserves chirality although the U(1) is spontaneously broken. Extensions of the Salam-Sezgin model to include larger gauge symmetries produce genuinely chiral models with unbroken gauge symmetries.

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arXiv2011

Critical and Non-Critical Einstein-Weyl Supergravity

We construct N=1 supersymmetrisations of some recently-proposed theories of critical gravity, conformal gravity, and extensions of critical gravity in four dimensions. The total action consists of the sum of three separately off-shell supersymmetric actions containing Einstein gravity, a cosmological term and the square of the Weyl tensor. For generic choices of the coefficients for these terms, the excitations of the resulting theory around an AdS_4 background describe massive spin-2 and massless spin-2 modes coming from the metric; massive spin-1 modes coming from a vector field in the theory; and massless and massive spin-3/2 modes (with two unequal masses) coming from the gravitino. These assemble into a massless and a massive N=1 spin-2 multiplet. In critical supergravity, the coefficients are tuned so that the spin-2 mode in the massive multiplet becomes massless. In the supersymmetrised extensions of critical gravity, the coefficients are chosen so that the massive modes lie in a "window" of lowest energies E_0 such that these ghostlike fields can be truncated by imposing appropriate boundary conditions at infinity, thus leaving just positive-norm massless supergravity modes.

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arXiv2011

Pseudo-Supergravity Extension of the Bosonic String

We construct a ``pseudo-supersymmetric" fermionic extension of the effective action of the bosonic string in arbitrary spacetime dimension D. The theory is invariant under pseudo-supersymmetry transformations up to the quadratic fermion order, which is sufficient in order to be able to derive Killing spinor equations in bosonic backgrounds, and hence to define BPS type solutions determined by a system of first-order equations. The pseudo-supersymmetric theory can be extended by coupling it to a Yang-Mills pseudo-supermultiplet. This also allows us to construct ``α' corrections'' involving quadratic curvature terms. An exponential dilaton potential term, associated with the conformal anomaly for a bosonic string outside its critical dimension, can also be pseudo-supersymmetrised.

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arXiv2011

Pseudo-supersymmetry, Consistent Sphere Reduction and Killing Spinors for the Bosonic String

Certain supergravity theories admit a remarkable consistent dimensional reduction in which the internal space is a sphere. Examples include type IIB supergravity reduced on S^5, and eleven-dimensional supergravity reduced on S^4 or S^7. Consistency means that any solution of the dimensionally-reduced theory lifts to give a solution in the higher dimension. Although supersymmetry seems to play a role in the consistency of these reductions, it cannot be the whole story since consistent sphere reductions of non-supersymmetric theories are also known, such as the reduction of the effective action of the bosonic string in any dimension D on either a 3-sphere or a (D-3)-sphere, retaining the gauge bosons of SO(4) or SO(D-2) respectively. We show that although there is no supersymmetry, there is nevertheless a natural Killing spinor equation for the D-dimensional bosonic string. A projection of the full integrability condition for these Killing spinors gives rise to the bosonic equations of motion (just as happens in the supergravity examples). Thus it appears that by extending the notion of supersymmetry to "pseudo-supersymmetry" in this way, one may be able to obtain a broader understanding of a relation between Killing spinors and consistent sphere reductions.

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arXiv2011

More about Birkhoff's Invariant and Thorne's Hoop Conjecture for Horizons

A recent precise formulation of the hoop conjecture in four spacetime dimensions is that the Birkhoff invariant $β$ (the least maximal length of any sweepout or foliation by circles) of an apparent horizon of energy $E$ and area $A$ should satisfy $β\le 4 πE$. This conjecture together with the Cosmic Censorship or Isoperimetric inequality implies that the length $\ell$ of the shortest non-trivial closed geodesic satisfies $\ell^2 \le πA$. We have tested these conjectures on the horizons of all four-charged rotating black hole solutions of ungauged supergravity theories and find that they always hold. They continue to hold in the the presence of a negative cosmological constant, and for multi-charged rotating solutions in gauged supergravity. Surprisingly, they also hold for the Ernst-Wild static black holes immersed in a magnetic field, which are asymptotic to the Melvin solution. In five spacetime dimensions we define $β$ as the least maximal area of all sweepouts of the horizon by two-dimensional tori, and find in all cases examined that $ β(g) \le \frac{16 π}{3} E$, which we conjecture holds quiet generally for apparent horizons. In even spacetime dimensions $D=2N+2$, we find that for sweepouts by the product $S^1 \times S^{D-4}$, $β$ is bounded from above by a certain dimension-dependent multiple of the energy $E$. We also find that $\ell^{D-2}$ is bounded from above by a certain dimension-dependent multiple of the horizon area $A$. Finally, we show that $\ell^{D-3}$ is bounded from above by a certain dimension-dependent multiple of the energy, for all Kerr-AdS black holes.

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arXiv2011

Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume

In a theory where the cosmological constant $Λ$ or the gauge coupling constant $g$ arises as the vacuum expectation value, its variation should be included in the first law of thermodynamics for black holes. This becomes $dE= TdS + Ω_i dJ_i + Φ_αd Q_α+ Θd Λ$, where $E$ is now the enthalpy of the spacetime, and $Θ$, the thermodynamic conjugate of $Λ$, is proportional to an effective volume $V = -\frac{16 πΘ}{D-2}$ "inside the event horizon." Here we calculate $Θ$ and $V$ for a wide variety of $D$-dimensional charged rotating asymptotically AdS black hole spacetimes, using the first law or the Smarr relation. We compare our expressions with those obtained by implementing a suggestion of Kastor, Ray and Traschen, involving Komar integrals and Killing potentials, which we construct from conformal Killing-Yano tensors. We conjecture that the volume $V$ and the horizon area $A$ satisfy the inequality $R\equiv ((D-1)V/{\cal A}_{D-2})^{1/(D-1)}\, ({\cal A}_{D-2}/A)^{1/(D-2)}\ge1$, where ${\cal A}_{D-2}$ is the volume of the unit $(D-2)$-sphere, and we show that this is obeyed for a wide variety of black holes, and saturated for Schwarzschild-AdS. Intriguingly, this inequality is the "inverse" of the isoperimetric inequality for a volume $V$ in Euclidean $(D-1)$ space bounded by a surface of area $A$, for which $R\le 1$. Our conjectured {\it Reverse Isoperimetric Inequality} can be interpreted as the statement that the entropy inside a horizon of a given "volume" $V$ is maximised for Schwarzschild-AdS. The thermodynamic definition of $V$ requires a cosmological constant (or gauge coupling constant). However, except in 7 dimensions, a smooth limit exists where $Λ$ or $g$ goes to zero, providing a definition of $V$ even for asymptotically-flat black holes.

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arXiv2011

The General Supersymmetric Solution of Topologically Massive Supergravity

We find the general fully non-linear solution of topologically massive supergravity admitting a Killing spinor. It is of plane-wave type, with a null Killing vector field. Conversely, we show that all solutions with a null Killing vector are supersymmetric for one or the other choice of sign for the Chern-Simons coupling constant μ. If μdoes not take the critical value μ=\pm 1, these solutions are asymptotically regular on a Poincaré patch, but do not admit a smooth global compactification with boundary S^1\times\R. In the critical case, the solutions have a logarithmic singularity on the boundary of the Poincaré patch. We derive a Nester-Witten identity, which allows us to identify the associated charges, but we conclude that the presence of the Chern-Simons term prevents us from making a statement about their positivity. The Nester-Witten procedure is applied to the BTZ black hole.

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arXiv2011

Critical Gravity in Four Dimensions

We study four-dimensional gravity theories that are rendered renormalisable by the inclusion of curvature-squared terms to the usual Einstein action with cosmological constant. By choosing the parameters appropriately, the massive scalar mode can be eliminated and the massive spin-2 mode can become massless. This "critical" theory may be viewed as a four-dimensional analogue of chiral topologically massive gravity, or of critical "New Massive Gravity" with a cosmological constant, in three dimensions. We find that the on-shell energy for the remaining massless gravitons vanishes. There are also logarithmic spin-2 modes, which have positive energy. The mass and entropy of standard Schwarzschild type black holes vanish. The critical theory might provide a consistent toy model for quantum gravity in four dimensions.

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arXiv2011

Critical Points of D-Dimensional Extended Gravities

We study the parameter space of D-dimensional cosmological Einstein gravity together with quadratic curvature terms. In D>4 there are in general two distinct (anti)-de Sitter vacua. We show that for appropriate choice of the parameters there exists a critical point for one of the vacua, for which there are only massless tensor, but neither massive tensor nor scalar, gravitons. At criticality, the linearized excitations have vanishing energy (as do black hole solutions). A further restriction of the parameters gives a one-parameter cosmological Einstein plus Weyl^2 model with a unique vacuum, whose Λis determined.

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arXiv2010

Kohn's Theorem, Larmor's Equivalence Principle and the Newton-Hooke Group

We consider non-relativistic electrons, each of the same charge to mass ratio, moving in an external magnetic field with an interaction potential depending only on the mutual separations, possibly confined by a harmonic trapping potential. We show that the system admits a "relativity group" which is a one-parameter family of deformations of the standard Galilei group to the Newton-Hooke group which is a Wigner-Inonu contraction of the de Sitter group. This allows a group-theoretic interpretation of Kohn's theorem and related results. Larmor's Theorem is used to show that the one-parameter family of deformations are all isomorphic. We study the "Eisenhart" or "lightlike" lift of the system, exhibiting it as a pp-wave. In the planar case, the Eisenhart lift is the Brdicka-Eardley-Nappi-Witten pp-wave solution of Einstein-Maxwell theory, which may also be regarded as a bi-invariant metric on the Cangemi-Jackiw group.

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arXiv2010

Universal Area Product Formulae for Rotating and Charged Black Holes in Four and Higher Dimensions

We present explicit results for the product of all horizon areas for general rotating multi-charge black holes, both in asymptotically flat and asymptotically anti-de Sitter spacetimes in four and higher dimensions. The expressions are universal, and depend only on the quantized charges, quantized angular momenta and the cosmological constant. If the latter is also quantized these universal results may provide a "looking glass" for probing the microscopics of general black holes.

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arXiv2010

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 $\ft14$ 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.

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arXiv2010

Massive Three-Dimensional Supergravity From R+R^2 Action in Six Dimensions

We obtain a three-parameter family of massive N=1 supergravities in three dimensions from the 3-sphere reduction of an off-shell N=(1,0) six-dimensional Poincare supergravity that includes a curvature squared invariant. The three-dimensional theory contains an off-shell supergravity multiplet and an on-shell scalar matter multiplet. We then generalise this in three dimensions to an eight-parameter family of supergravities. We also find a duality relationship between the six-dimensional theory and the N=(1,0) six-dimensional theory obtained through a T^4 reduction of the heterotic string effective action that includes the higher-order terms associated with the supersymmetrisation of the anomaly-cancelling \tr(R\wedge R) term.

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arXiv2010

Inconsistency of Breathing Mode Extensions of Maximal Five-Dimensional Supergravity Embedding

Recent work on consistent Kaluza-Klein reductions on Einstein-Sasaki spaces prompted an intriguing conjecture that there might exist a consistent $S^5$ reduction of type IIB supergravity to give five-dimensional ${\cal N}=8$ gauged supergravity coupled to a massive supermultiplet that includes the breathing-mode scalar. Motivated by this, we investigate the possibility of augmenting the usual ${\cal N}=8$ supergravity reduction to include a breathing-mode scalar, and we show that this is in fact inconsistent. The standard reduction to the massless ${\cal N}=8$ supermultiplet depends for its consistency on a delicate interplay between properties of the ten-dimensional type IIB theory and properties of the Killing vectors on $S^5$. Our calculations show that turning on the breathing-mode is sufficient to destroy the balance, and hence render the reduction inconsistent.

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arXiv2010

Deforming the Maxwell-Sim Algebra

The Maxwell alegbra is a non-central extension of the Poincaré algebra, in which the momentum generators no longer commute, but satisfy $[P_μ,P_ν]=Z_{μν}$. The charges $Z_{μν}$ commute with the momenta, and transform tensorially under the action of the angular momentum generators. If one constructs an action for a massive particle, invariant under these symmetries, one finds that it satisfies the equations of motion of a charged particle interacting with a constant electromagnetic field via the Lorentz force. In this paper, we explore the analogous constructions where one starts instead with the ISim subalgebra of Poincaré, this being the symmetry algebra of Very Special Relativity. It admits an analogous non-central extension, and we find that a particle action invariant under this Maxwell-Sim algebra again describes a particle subject to the ordinary Lorentz force. One can also deform the ISim algebra to DISim$_b$, where $b$ is a non-trivial dimensionless parameter. We find that the motion described by an action invariant under the corresponding Maxwell-DISim algebra is that of a particle interacting via a Finslerian modification of the Lorentz force.

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arXiv2010

Classification of solutions in topologically massive gravity

We study exact solutions of three-dimensional gravity with a cosmological constant and a gravitational Chern-Simons term: the theory known as topologically massive gravity. After reviewing the algebraic classification, we show that if a solution has curvature of algebraic type D, then it is biaxially squashed AdS_3. Applying the classification, we provide a comprehensive review of the literature, showing that most known solutions are locally equivalent to biaxially squashed AdS_3 or to AdS pp-waves.

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arXiv2010

Kundt spacetimes as solutions of topologically massive gravity

We obtain new solutions of topologically massive gravity. We find the general Kundt solutions, which in three dimensions are spacetimes admitting an expansion-free null geodesic congruence. The solutions are generically of algebraic type II, but special cases are types III, N or D. Those of type D are the known spacelike-squashed AdS_3 solutions, and of type N are the known AdS pp-waves or new solutions. Those of types II and III are the first known solutions of these algebraic types. We present explicitly the Kundt solutions that are CSI spacetimes, for which all scalar polynomial curvature invariants are constant, whereas for the general case we reduce the field equations to a series of ordinary differential equations. The CSI solutions of types II and III are deformations of spacelike-squashed AdS_3 and the round AdS_3, respectively.

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arXiv2010

Topologically Massive Gravity from the Heterotic String

Topologically massive gravity (TMG) in three dimensions provides an interesting toy model for constructing a quantum theory of gravity. Although it can be thought of as standing as a theory in its own right, it is also of interest to see whether it can be described within the larger framework of string theory or M-theory. In this paper, we show that it can be embedded within the heterotic string, via a compactification on $S^3\times T^4$. Since all solutions of TMG can now be lifted to ten dimensions, this allows us to give a string and brane interpretation to quantities such as the central charges in the conformal field theory on the boundary of TMG, and the entropy of the BTZ black hole solution.

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