## Publications

173 results found

Duff MJ, Stelle KS, 2020, Sir Thomas Walter Bannerman Kibble CBE, Publisher: arXiv

Professor Tom Kibble was an internationally-renowned theoretical physicistwhose contributions to theoretical physics range from the theory of elementaryparticles to modern early-universe cosmology. The unifying theme behind all hiswork is the theory of non-abelian gauge theories, the Yang-Mills extension ofelectromagnetism. One of Kibble's most important pieces of work in this areawas his study of the symmetry-breaking mechanism whereby the force-carryingvector particles in the theory can acquire a mass accompanied by the appearanceof a massive scalar boson. This idea, put forward independently by Brout andEnglert, by Higgs and by Guralnik, Hagen and Kibble in 1964, and generalised byKibble in 1967, lies at the heart of the Standard Model and all modern unifiedtheories of fundamental particles. It was vindicated in 2012 by the discoveryof the Higgs boson at CERN. According to Nobel Laureate Steven Weinberg, "TomKibble showed us why light is massless"; this is the fundamental basis ofelectromagnetism.

Erickson CW, Harrold AD, Leung R,
et al., 2020, Covert symmetry breaking, *The Journal of High Energy Physics*, Vol: 2020, Pages: 1-26, ISSN: 1029-8479

Reduction from a higher-dimensional to a lower-dimensional field theory can display special features when the zero-level ground state has nontrivial dependence on the reduction coordinates. In particular, a delayed ‘covert’ form of spontaneous symmetry breaking can occur, revealing itself only at fourth order in the lower-dimensional effective field theory action. This phenomenon is explored in a simple model of (d + 1)-dimensional scalar QED with one dimension restricted to an interval with Dirichlet/Robin boundary conditions on opposing ends. This produces an effective d-dimensional theory with Maxwellian dynamics at the free theory level, but with unusual symmetry breaking appearing in the quartic vector-scalar interaction terms. This simple model is chosen to illuminate the mechanism of effects which are also noted in gravitational braneworld scenarios.

Stelle KS, 2020, Mass gaps and braneworlds, *Journal of Physics A: Mathematical and Theoretical*, Vol: 53, ISSN: 1751-8113

Remembering the foundational contributions of Peter Freund to supergravity, and especially to the problems of dimensional compactification, reduction is considered with a non-compact space transverse to the lower dimensional theory. The known problem of a continuum of Kaluza–Klein states is avoided here by the occurrence of a mass gap between a single normalizable zero-eigenvalue transverse wavefunction and the edge of the transverse state continuum. This style of reduction does not yield a formally consistent truncation to the lower dimensional theory, so developing the lower-dimensional effective theory requires integrating out the Kaluza–Klein states lying above the mass gap.

Deser S, Stelle KS, 2019, Field redefinition's help in constructing non-abelian gauge theories, *Physics Letters B: Nuclear Physics and Particle Physics*, Vol: 798, Pages: 1-2, ISSN: 0370-2693

We study, using the example of general covariance, to what extent a would-be non-abelian extension of free field abelian gauge theory can be helped by a field redefinition; answer – not much! However, models resulting from dimensional reduction also include non-gauge fields needing to be integrated out, thereby offering a wider choice of redefinitions whose effects may indeed change the situation.

Lehners J-L, Stelle KS, 2019, Safe beginning for the Universe?, *Physical Review D: Particles, Fields, Gravitation and Cosmology*, Vol: 100, ISSN: 1550-2368

When general relativity is augmented by quadratic gravity terms, it becomes a renormalizable theory of gravity. This theory may admit a non-Gaussian fixed point as envisaged in the asymptotic safety program, rendering the theory trustworthy to energies up to the Planck scale and even beyond. We show that requiring physical solutions to have a finite action imposes a strong selection on big-bang-type universes. More precisely, we find that, in the approach to zero volume, both anisotropies and inhomogeneities are suppressed while the scale factor is required to undergo accelerated expansion. This provides initial conditions which are favorable to the onset of an inflationary phase while also providing a suitable starting point for the second law of thermodynamics in the spirit of the Weyl curvature hypothesis.

Lu H, Perkins A, Pope CN,
et al., 2017, Lichnerowicz modes and black hole families in Ricci quadratic gravity, *Physical Review D*, Vol: 96, ISSN: 2470-0010

A new branch of black hole solutions occurs along with the standard Schwarzschild branch in n-dimensional extensions of general relativity including terms quadratic in the Ricci tensor. The standard and new branches cross at a point determined by a static negative-eigenvalue eigenfunction of the Lichnerowicz operator, analogous to the Gross-Perry-Yaffe eigenfunction for the Schwarzschild solution in standard n=4 dimensional general relativity. This static eigenfunction has two roles: both as a perturbation away from Schwarzschild along the new black-hole branch and also as a threshold unstable mode lying at the edge of a domain of Gregory-Laflamme-type instability of the Schwarzschild solution for small-radius black holes. A thermodynamic analogy with the Gubser and Mitra conjecture on the relation between quantum thermodynamic and classical dynamical instabilities leads to a suggestion that there may be a switch of stability properties between the old and new black-hole branches for small black holes with radii below the branch crossing point.

Stelle KS, 2017, Abdus Salam and quadratic curvature gravity: classical solutions, *International Journal of Modern Physics A*, Vol: 32, ISSN: 0217-751X

In 1978, Salam and Strathdee suggested on the basis of Froissart boundedness that curvature-squared terms should be included in the gravitational Lagrangian. Despite the presence of ghosts in such theories, the subject has remained a persistent topic in approaches to quantum gravity and cosmology. In this article, the space of spherically symmetric solutions to such theories is explored, highlighting horizonless solutions, wormholes and non-Schwarzschild black holes.

Lu H, Perkins A, Pope CN,
et al., 2015, Spherically symmetric solutions in higher-derivative gravity, *Physical Review D*, Vol: 92, ISSN: 1550-7998

Extensions of Einstein gravity with quadratic curvature terms in the action arise in most effective theories of quantized gravity, including string theory. This article explores the set of static, spherically symmetric and asymptotically flat solutions of this class of theories. An important element in the analysis is the careful treatment of a Lichnerowicz-type “no-hair” theorem. From a Frobenius analysis of the asymptotic small-radius behavior, the solution space is found to split into three asymptotic families, one of which contains the classic Schwarzschild solution. These three families are carefully analyzed to determine the corresponding numbers of free parameters in each. One solution family is capable of arising from coupling to a distributional shell of matter near the origin; this family can then match onto an asymptotically flat solution at spatial infinity without encountering a horizon. Another family, with horizons, contains the Schwarzschild solution but includes also non-Schwarzschild black holes. The third family of solutions obtained from the Frobenius analysis is nonsingular and corresponds to “vacuum” solutions. In addition to the three families identified from near-origin behavior, there are solutions that may be identified as “wormholes,” which can match symmetrically onto another sheet of spacetime at finite radius.

Stelle KS, 2015, Black Holes in Supergravity, 1st Karl Schwarzschild Meeting (KSM) on Gravitational Physics, Publisher: SPRINGER-VERLAG BERLIN, Pages: 207-216, ISSN: 0930-8989

A brief review is given of the use of duality symmetries to form orbits of supergravity black-hole solutions and their relation to extremal (i.e. BPS) solutions at the limits of such orbits. An important technique in this analysis uses a timelike dimensional reduction and exchanges the stationary black-hole problem for a nonlinear sigma-model problem. Families of BPS solutions are characterized by nilpotent orbits under the duality symmetries, based upon a tri-graded or penta-graded decomposition of the corresponding duality group algebra.

Liu H, Perkins A, Pope CN,
et al., 2015, Black holes in D=4 higher-derivative gravity, *International Journal of Modern Physics A*, Vol: 30, ISSN: 0217-751X

Extensions of Einstein gravity with higher-order derivative terms are natural generalizations of Einstein’s theory of gravity. They may arise in string theory and other effective theories, as well as being of interest in their own right. In this paper we study static black-hole solutions in the example of Einstein gravity with additional quadratic curvature terms in four dimensions. A Lichnerowicz-type theorem simplifies the analysis by establishing that they must have vanishing Ricci scalar curvature. By numerical methods we then demonstrate the existence of further black-hole solutions over and above the Schwarzschild solution. We discuss some of their thermodynamic properties, and show that they obey the first law of thermodynamics.

Lu H, Perkins A, Pope CN,
et al., 2015, Black holes in higher derivative gravity, *Physical Review Letters*, Vol: 114, ISSN: 1079-7114

Extensions of Einstein gravity with higher-order derivative terms arise in string theory and othereffective theories, as well as being of interest in their own right. In this Letter we study static black-holesolutions in the example of Einstein gravity with additional quadratic curvature terms. A Lichnerowicztypetheorem simplifies the analysis by establishing that they must have vanishing Ricci scalar curvature.By numerical methods we then demonstrate the existence of further black-hole solutions over and above theSchwarzschild solution. We discuss some of their thermodynamic properties, and show that they obey thefirst law of thermodynamics.

Stelle KS, 2015, Symmetry orbits of supergravity black holes, *THEORETICAL AND MATHEMATICAL PHYSICS*, Vol: 182, Pages: 130-140, ISSN: 0040-5779

Crampton B, Pope CN, Stelle KS, 2014, Braneworld localisation in hyperbolic spacetime, *Journal of High Energy Physics*, Pages: 1-26, ISSN: 1126-6708

We present a construction employing a type IIA supergravity and 3-form fluxbackground together with an NS5-brane that localises massless gravity near the5-brane worldvolume. The nonsingular underlying type IIA solution is a lift to10D of the vacuum solution of the 6D Salam-Sezgin model and has a hyperbolic${\cal H}^{(2,2)}\times S^1$ structure in the lifting dimensions. A fullyback-reacted solution including the NS5-brane is constructed by recognising the10D Salam-Sezgin vacuum solution as a "brane resolved through transgression."The background hyperbolic structure plays a key r\^ole in generating a mass gapin the spectrum of the transverse-space wave operator, which gives rise to thelocalisation of gravity on the 6D NS5-brane worldvolume, or, equally, in afurther compactification to 4D. Also key to the successful localisation ofgravity is the specific form of the corresponding transverse wavefunctionSchr\"odinger problem, which asymptotically involves a $V=-1/(4\rho^2)$potential, where $\rho$ is the transverse-space radius, and for which theNS5-brane source gives rise to a specific choice of self-adjoint extension forthe transverse wave operator. The corresponding boundary condition as$\rho\to0$ ensures the masslessness of gravity in the effective braneworldtheory. Above the mass gap, there is a continuum of massive states which giverise to small corrections to Newton's law.

Bossard G, Howe PS, Stelle KS, 2013, Invariants and divergences in half-maximal supergravity theories, *The Journal of High Energy Physics*, Vol: 117, Pages: 1-76, ISSN: 1029-8479

The invariants in half-maximal supergravity theories in D = 4, 5 are discussed in detail up to dimension eight (e.g. R 4). In D = 4, owing to the anomaly in the rigid SL(2, R) duality symmetry, the restrictions on divergences need careful treatment. In pure N=4 supergravity, this anomalous symmetry still implies duality invariance of candidate counterterms at three loops. Provided one makes the additional assumption that there exists a full 16-supercharge off-shell formulation of the theory, counterterms at L ≥ 2 loops would also have to be writable as full-superspace integrals. At the three-loop order such a duality-invariant full-superspace integral candidate counterterm exists, but its duality invariance is marginal in the sense that the full-superspace counter-Lagrangian is not itself duality-invariant. We show that such marginal invariants are not allowable as counterterms in a 16-supercharge off-shell formalism. It is not possible to draw the same conclusion when vector multiplets are present because of the appearance of F 4 terms in the SL(2, R) anomaly. In D = 5 there is no one-loop anomaly in the shift invariance of the dilaton, and we argue that this implies finiteness at two loops, again subject to the assumption that 16 supercharges can be preserved off-shell.

Bossard G, Howe PS, Stelle KS, 2013, Anomalies and divergences in N=4 supergravity, *PHYSICS LETTERS B*, Vol: 719, Pages: 424-429, ISSN: 0370-2693

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- Citations: 21

Stelle KS, 2013, String Theory, Unification and Quantum Gravity, *Lecture Notes in Physics*, Vol: 99999999, Pages: 3-30, ISSN: 0075-8450

An overview is given of the way in which the unification program of particlephysics has evolved into the proposal of superstring theory as a primecandidate for unifying quantum gravity with the other forces and particles ofnature. A key concern with quantum gravity has been the problem of ultravioletdivergences, which is naturally solved in string theory by replacing particleswith spatially extended states as the fundamental excitations. String theoryturns out, however, to contain many more extended-object states than juststrings. Combining all this into an integrated picture, called M-theory,requires recognition of the r\^ole played by a web of nonperturbative dualitysymmetries suggested by the nonlinear structures of the field-theoreticsupergravity limits of string theory.

Stelle KS, 2012, ULTRAVIOLET INFINITIES AND COUNTERTERMS IN SUPERSYMMETRIC THEORIES, *INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS*, Vol: 9, ISSN: 0219-8878

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- Citations: 4

Pope CN, Pugh TG, Stelle KS, 2012, Chiral reductions in the Salam-Sezgin model, *The Journal of High Energy Physics*, Vol: 2012, Pages: 1-32, ISSN: 1029-8479

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 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) R from six dimensions and preserves chirality although the U(1) R is spontaneously broken. Extensions of the Salam-Sezgin model to include larger gauge symmetries produce genuinely chiral models with unbroken gauge symmetries.

Bossard G, Howe PS, Stelle KS,
et al., 2011, The vanishing volume of D=4 superspace, *CLASSICAL AND QUANTUM GRAVITY*, Vol: 28, ISSN: 0264-9381

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- Citations: 62

Howe PS, Pugh TG, Stelle KS,
et al., 2011, Ectoplasm with an edge, *The Journal of High Energy Physics*, Vol: 2011, Pages: 1-23, ISSN: 1029-8479

The construction of supersymmetric invariant actions on a spacetime manifold with a boundary is carried out using the “ectoplasm” formalism for the construction of closed forms in superspace. Non-trivial actions are obtained from the pull-backs to the bosonic bodies of closed but non-exact forms in superspace; finding supersymmetric invariants thus becomes a cohomology problem. For a spacetime with a boundary, the appropriate mathematical language changes to relative cohomology, which we use to give a general formulation of off-shell supersymmetric invariants in the presence of boundaries. We also relate this construction to the superembedding formalism for the construction of brane actions, and we give examples with bulk spacetimes of dimension 3, 4 and 5. The closed superform in the 5D example needs to be constructed as a Chern-Simons type of invariant, obtained from a closed 6-form displaying Weil triviality.

Bossard G, Howe PS, Lindstrom U,
et al., 2011, Integral invariants in maximally supersymmetric Yang-Mills theories, *The Journal of High Energy Physics*, Vol: 2011, Pages: 1-21, ISSN: 1029-8479

Integral invariants in maximally supersymmetric Yang-Mills theories are discussed in spacetime dimensions 4 ≤ D ≤ 10 for SU(k) gauge groups. It is shown that, in addition to the action, there are three special invariants in all dimensions. Two of these, the single-and double-trace F 4 invariants, are of Chern-Simons type in D = 9, 10 and BPS type in D ≤ 8, while the third, the double-trace of two derivatives acting on F 4, can be expressed in terms of a gauge-invariant super-D -form in all dimensions. We show that the super-ten-forms for D = 10 F 4 invariants have interesting cohomological properties and we also discuss some features of other invariants, including the single-trace d 2 F 4, which has a special form in D = 10. The implications of these results for ultra-violet divergences are discussed in the framework of algebraic renormalisation.

Stelle KS, 2011, Non-renormalization theorems in maximal supergravity, *PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS*, Vol: 272, Pages: 246-255, ISSN: 0081-5438

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- Citations: 1

Pugh TG, Sezgin E, Stelle KS, 2011, D=7/D=6 heterotic supergravity with gauged R-symmetry, *The Journal of High Energy Physics*, Vol: 2011, Pages: 1-41, ISSN: 1029-8479

We construct a family of chiral anomaly-free supergravity theories in D =6 starting from D = 7 supergravity with a gauged noncompact R-symmetry, employing a HoĊava-Witten bulk-plus-boundary construction. The gauged noncompact R-symmetry yields a positive (de Sitter sign) D = 6 scalar field potential. Classical anomaly inflow which is needed to cancel boundary-field loop anomalies requires careful consideration of the gravitational, gauge, mixed and local supersymmetry anomalies. Coupling of boundary hypermultiplets requires care with the Sp(1) gauge connection required to obtain quaternionic Kähler target manifolds in D = 6. This class of gauged R-symmetry models may be of use as starting points for further compactifications to D = 4 that take advantage of the positive scalar potential, such as those proposed in the scenario of supersymmetry in large extra dimensions.

Bossard G, Howe PS, Stelle KS, 2011, On duality symmetries of supergravity invariants, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 45

Bossard G, Howe PS, Stelle KS, 2009, A note on the UV behaviour of maximally supersymmetric Yang-Mills theories, *PHYSICS LETTERS B*, Vol: 682, Pages: 137-142, ISSN: 0370-2693

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- Citations: 41

Bossard G, Nicolai H, Stelle KS, 2009, Universal BPS structure of stationary supergravity solutions, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 68

Bossard G, Nicolai H, Stelle KS, 2009, Gravitational multi-NUT solitons, Komar masses and charges, *General Relativity and Gravitation*, Vol: 41, Pages: 1367-1379, ISSN: 0001-7701

Generalising expressions given by Komar, we give precise definitions of gravitational mass and solitonic NUT charge and we apply these to the description of a class of Minkowski-signature multi-Taub–NUT solutions without rod singularities. A Wick rotation then yields the corresponding class of Euclidean-signature gravitational multi-instantons.

Haupt AS, Lukas A, Stelle KS, 2009, M-theory on Calabi-Yau Five-Folds, *The Journal of High Energy Physics*, Vol: 2009, Pages: 1-82, ISSN: 1029-8479

We study the compactification of M-theory on Calabi-Yau five-folds and the resulting Script N = 2 super-mechanics theories. By explicit reduction from 11 dimensions, including both bosonic and fermionic terms, we calculate the one-dimensional effective action and show that it can be derived from an Script N = 2 super-space action. We find that the Kähler and complex structure moduli of the five-fold reside in 2a and 2b super-multiplets, respectively. Constrained 2a super-multiplets arise from zero-modes of the M-theory three-form and lead to cross-couplings between 2a and 2b multiplets. Fermionic zero modes which arise from the (1,3) sector of the 11-dimensional gravitino do not have bosonic super-partners and have to be described by purely fermionic super-multiplets in one dimension. We also study the inclusion of flux and discuss the consistency of the scalar potential with one-dimensional Script N = 2 supersymmetry and how it can be described in terms of a superpotential. This superpotential can also be obtained from a Gukov-type formula which we present. Supersymmetric vacua, obtained by solving the F-term equations, always have vanishing vacuum energy due to the form of this scalar potential. We show that such supersymmetric solutions exist for particular examples. Two substantial appendices develop the topology and geometry of Calabi-Yau five-folds and the structure of one-dimensional Script N = 2 supersymmetry and supergravity to the level of generality required for our purposes.

Stelle KS, 2009, Is N=8 supergravity a finite field theory?, 4th EU RTN Workshop on Constituents, Fundamental Forces and Symmetries of the Universe, Publisher: WILEY-V C H VERLAG GMBH, Pages: 446-450, ISSN: 0015-8208

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- Citations: 5

Bossard G, Howe PS, Stelle KS, 2009, The ultra-violet question in maximally supersymmetric field theories, 405th WE Heraeus Seminar on Quantum Gravity, Publisher: SPRINGER/PLENUM PUBLISHERS, Pages: 919-981, ISSN: 0001-7701

We discuss various approaches to the problem of determining which supersymmetric invariants are permitted as counterterms in maximally supersymmetric super Yang–Mills and supergravity theories in various dimensions. We review the superspace non-renormalisation theorems based on conventional, light-cone, harmonic and certain non-Lorentz covariant superspaces, and we write down explicitly the relevant invariants. While the first two types of superspace admit the possibility of one-half BPS counterterms, of the form F 4 and R 4 respectively, the last two do not. This suggests that UV divergences begin with one-quarter BPS counterterms, i.e. d 2 F 4 and d 4 R 4, and this is supported by an entirely different approach based on algebraic renormalisation. The algebraic formalism is discussed for non-renormalisable theories and it is shown how the allowable supersymmetric counterterms can be determined via cohomological methods. These results are in agreement with all the explicit computations that have been carried out to date. In particular, they suggest that maximal supergravity is likely to diverge at four loops in D = 5 and at five loops in D = 4, unless other infinity suppression mechanisms not involving supersymmetry or gauge invariance are at work.

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