arXiv subjects

K. S. Stelle

Publications and source records attributed to K. S. Stelle.

At least 37 records · Page 2Linked to original sources

arXiv2015

Black Holes in Higher-Derivative Gravity

Extensions of Einstein gravity with higher-order derivative terms 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. 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.

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arXiv2014

Symmetry Orbits of Supergravity Black Holes - In Honor of Andrei Slavnov's 75th Birthday

Black hole solutions of supergravity theories form families that realizing the deep nonlinear "duality" symmetries of these theories. They form orbits under the action of these symmetry groups, with extremal (i.e. BPS) solutions at the limits of such orbits. An important technique in the analysis of such solution families employs timelike dimensional reduction and exchanges the stationary black-hole problem for a nonlinear sigma-model problem. Families of extremal or 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.

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arXiv2013

Invariants and divergences in half-maximal supergravity theories

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>1 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.

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arXiv2013

Anomalies and divergences in N=4 supergravity

The invariants in D=4, N=4 supergravity are discussed up to the three-loop order (where one expects a general R^4 structure). Because there is an anomaly in the rigid SL(2,R) symmetry of this theory, the analysis of possible restrictions on three-loop divergences due to duality needs careful treatment. We show that this anomalous symmetry is still strong enough at the three-loop order to require duality invariance of candidate counterterms. Provided one makes the additional assumption that there exists a full 16-supercharge off-shell formulation of the theory, counterterms at L \ge 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, subject to the assumption that a full off-shell quantisation formalism exists, such marginal invariants are not allowable as counterterms.

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arXiv2012

String Theory, Unification and Quantum Gravity

An overview is given of the way in which the unification program of particle physics has evolved into the proposal of superstring theory as a prime candidate for unifying quantum gravity with the other forces and particles of nature. A key concern with quantum gravity has been the problem of ultraviolet divergences, which is naturally solved in string theory by replacing particles with spatially extended states as the fundamental excitations. String theory turns out, however, to contain many more extended-object states than just strings. Combining all this into an integrated picture, called M-theory, requires recognition of the rôle played by a web of nonperturbative duality symmetries suggested by the nonlinear structures of the field-theoretic supergravity limits of string theory.

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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

The vanishing volume of D=4 superspace

The volume of on-shell D=4, N=8 superspace is shown to vanish. Despite this, it is shown that there is a fully supersymmetric and duality-invariant candidate d^8 R^4 counterterm corresponding to an anticipated seven-loop logarithmic divergence in D=4. We construct this counterterm explicitly and also give the complete nonlinear extension of the 1/8-BPS d^6 R^4 invariant. Similar results are derived for N=4,5 & 6.

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arXiv2011

Ectoplasm with an Edge

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.

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arXiv2010

D=7 / D=6 Heterotic Supergravity with Gauged R-Symmetry

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 Horava-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 Kahler 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.

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arXiv2010

Integral invariants in maximally supersymmetric Yang-Mills theories

Integral invariants in maximally supersymmetric Yang-Mills theories are discussed in spacetime dimensions $4\leq D\leq 10$ 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 $D\leq 8$, 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.

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arXiv2010

On duality symmetries of supergravity invariants

The role of duality symmetries in the construction of counterterms for maximal supergravity theories is discussed in a field-theoretic context from different points of view. These are: dimensional reduction, the question of whether appropriate superspace measures exist and information about non-linear invariants that can be gleaned from linearised ones. The former allows us to prove that F-term counterterms cannot be E7(7)-invariant in D=4, N=8 supergravity or E6(6)-invariant in D=5 maximal supergravity. This is confirmed by the two other methods which can also be applied to D=4 theories with fewer supersymmetries and allow us to prove that N=6 supergravity is finite at three and four loops and that N=5 supergravity is three-loop finite.

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arXiv2009

A note on the UV behaviour of maximally supersymmetric Yang-Mills theories

The question of whether BPS invariants are protected in maximally supersymmetric Yang-Mills theories is investigated from the point of view of algebraic renormalisation theory. The protected invariants are those whose cohomology type differs from that of the action. It is confirmed that one-half BPS invariants ($F^4$) are indeed protected while the double-trace one-quarter BPS invariant ($d^2F^4$) is not protected at two loops in D=7, but is protected at three loops in D=6 in agreement with recent calculations. Non-BPS invariants, i.e. full superspace integrals, are also shown to be unprotected.

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arXiv2009

BPS Branes in Supergravity

This review considers the properties of classical solutions to supergravity theories with partially unbroken supersymmetry. These solutions saturate Bogomol'ny-Prasad-Sommerfield bounds on their energy densities and are the carriers of the $p$-form charges that appear in the supersymmetry algebra. The simplest such solutions have the character of $(p+1)$-dimensional Poincaré-invariant hyperplanes in spacetime, i.e. $p$-branes. Topics covered include the relations between mass densities, charge densities and the preservation of unbroken supersymmetry; interpolating-soliton structure; diagonal and vertical Kaluza-Klein reduction families; multiple-charge solutions and the four D=11 elements; duality-symmetry multiplets; charge quantisation; low-velocity scattering and the geometry of worldvolume supersymmetric $σ$-models; and the target-space geometry of BPS instanton solutions obtained by the dimensional reduction of static $p$-branes.

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arXiv2009

Universal BPS structure of stationary supergravity solutions

We study asymptotically flat stationary solutions of four-dimensional supergravity theories via the associated G/H* pseudo-Riemannian non-linear sigma models in three spatial dimensions. The Noether charge C associated to G is shown to satisfy a characteristic equation that determines it as a function of the four-dimensional conserved charges. The matrix C is nilpotent for non-rotating extremal solutions. The nilpotency degree of C is directly related to the BPS degree of the corresponding solution when they are BPS. Equivalently, the charges can be described in terms of a Weyl spinor |C > of Spin*(2N), and then the characteristic equation becomes equivalent to a generalisation of the Cartan pure spinor constraint on |C>. The invariance of a given solution with respect to supersymmetry is determined by an algebraic `Dirac equation' on the Weyl spinor |C>. We explicitly solve this equation for all pure supergravity theories and we characterise the stratified structure of the moduli space of asymptotically Taub-NUT black holes with respect with their BPS degree. The analysis is valid for any asymptotically flat stationary solutions for which the singularities are protected by horizons. The H*-orbits of extremal solutions are identified as Lagrangian submanifolds of nilpotent orbits of G, and so the moduli space of extremal spherically symmetric black holes as a Lagrangian subvariety of the variety of nilpotent elements of Lie(G). We also generalise the notion of active duality transformations to an `almost action' of the three-dimensional duality group G on asymptotically flat stationary solutions.

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arXiv2009

M-theory on Calabi-Yau Five-Folds

We study the compactification of M-theory on Calabi-Yau five-folds and the resulting 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 N=2 super-space action. We find that the Kahler 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 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 N=2 supersymmetry and supergravity to the level of generality required for our purposes.

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arXiv2009

The ultra-violet question in maximally supersymmetric field theories

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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arXiv2008

Gravitational multi-NUT solitons, Komar masses and charges

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.

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arXiv2007

Kaluza-Klein Induced Supersymmetry Breaking for Braneworlds in Type IIB Supergravity

We consider Z_2-symmetric braneworlds arising from 5-sphere compactifications with 5-form flux in type IIB supergravity. This Kaluza-Klein reduction produces a D=5 theory which supports 1/2-supersymmetric Z_2-symmetric domain-wall solutions. However, upon lifting such solutions back to D=10, one finds that supersymmetry is broken by 5-sphere Kaluza-Klein effects. This happens owing to the action on the Killing spinor of the Z_2 \subset SO(1,9) symmetry, which requires an orientation-reversing transformation in the 5-sphere directions together with the flip of the orbifold coordinate. We study the consequences of this supersymmetry breaking for the masses of fermion fluctuation modes about the brane background and find a natural two-scale hierarchy: some bulk modes have characteristic masses of order 1/L_5 but other modes more closely associated to the branes have an additional factor exp(-ρ/L_5), where L_5 is the AdS_5 length parameter and ρis the orbifold size.

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