Supersymmetry counterterms revisited

Superspace power-counting rules give estimates for the loop order at which divergences can first appear in non-renormalisable supersymmetric field theories. In some cases these estimates can be improved if harmonic superspace, rather than ordinary superspace, is used. The new estimates are in agreement with recent results derived from unitarity calculations for maximally supersymmetric Yang-Mills theories in five and six dimensions. For N=8 supergravity in four dimensions, we speculate that the onset of divergences may correspondingly occur at the six loop order.Comment: 10 pages, plain Late

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.Comment: 12 pages. Minor changes to text. References adde

The Superparticle and the Lorentz Group

We present a unified group-theoretical framework for superparticle theories. This explains the origin of the ``twistor-like'' variables that have been used in trading the superparticle's $\kappa$-symmetry for worldline supersymmetry. We show that these twistor-like variables naturally parametrise the coset space ${\cal G}/{\cal H}$, where $\cal G$ is the Lorentz group $SO^\uparrow(1,d-1)$ and $\cal H$ is its maximal subgroup. This space is a compact manifold, the sphere $S^{d-2}$. Our group-theoretical construction gives the proper covariantisation of a fixed light-cone frame and clarifies the relation between target-space and worldline supersymmetries.Comment: 33 page

HKT and OKT Geometries on Soliton Black Hole Moduli Spaces

We consider Shiraishi's metrics on the moduli space of extreme black holes. We interpret the simplification in the pattern of N-body interactions that he observed in terms of the recent picture of black holes in four and five dimensions as composites, made up of intersecting branes. We then show that the geometry of the moduli space of a class of black holes in five and nine dimensions is hyper-K\"ahler with torsion, and octonionic-K\"ahler with torsion, respectively. For this, we examine the geometry of point particle models with extended world-line supersymmetry and show that both of the above geometries arise naturally in this context. In addition, we construct a large class of hyper-K\"ahler with torsion and octonionic-K\"ahler with torsion geometries in various dimensions. We also present a brane interpretation of our results.Comment: pages 55, phyzzx, some more references have been adde

Dirac Quantisation Conditions and Kaluza-Klein Reduction

We present the form of the Dirac quantisation condition for the p-form charges carried by p-brane solutions of supergravity theories. This condition agrees precisely with the conditions obtained in lower dimensions, as is necessary for consistency with Kaluza-klein dimensional reduction. These considerations also determine the charge lattice of BPS soliton states, which proves to be a universal modulus-independent lattice when the charges are defined to be the canonical charges corresponding to the quantum supergravity symmetry groups.Comment: 40 pages, Late

Harmonicity in N=4 supersymmetry and its quantum anomaly

The holomorphicity property of N=1 superpotentials or of N=2 F-terms involving vector multiplets is generalized to the case of N=4 1/2-BPS effective operators defined in harmonic superspace. The resulting harmonicity equations are shown to control the moduli dependence of the couplings of higher dimensional operators involving powers of the N=4 Weyl superfield, computed by N=4 topological amplitudes. These equations can also be derived on the string side, exhibiting an anomaly from world-sheet boundary contributions that leads to recursion relations for the non-analytic part of the couplings.Comment: 36 page

Instanton Cosmology and Domain Walls from M-theory and String Theory

The recent proposal by Hawking and Turok for obtaining an open inflationary universe from singular instantons makes use of low-energy effective Lagrangians describing gravity coupled to scalars and non-propagating antisymmetric tensors. In this paper we derive some exact results for Lagrangians of this type, obtained from spherical compactifications of M-theory and string theory. In the case of the S^7 compactification of M-theory, we give a detailed discussion of the cosmological solutions. We also show that the lower-dimensional Lagrangians admit domain-wall solutions, which preserve one half of the supersymmetry, and which approach AdS spacetimes near their horizons.Comment: 51 pages, Latex (3 times). Discussion and references adde

Canonical BRST Quantisation of Worldsheet Gravities

We reformulate the BRST quantisation of chiral Virasoro and $W_3$ worldsheet gravities. Our approach follows directly the classic BRST formulation of Yang-Mills theory in employing a derivative gauge condition instead of the conventional conformal gauge condition, supplemented by an introduction of momenta in order to put the ghost action back into first-order form. The consequence of these simple changes is a considerable simplification of the BRST formulation, the evaluation of anomalies and the expression of Wess-Zumino consistency conditions. In particular, the transformation rules of all fields now constitute a canonical transformation generated by the BRST operator $Q$, and we obtain in this reformulation a new result that the anomaly in the BRST Ward identity is obtained by application of the anomalous operator $Q^2$, calculated using operator products, to the gauge fermion.Comment: 27 pages. (Some factors of \hbar corrected

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.Comment: 56 pages, 1 figure, uses youngtab.sty. Contribution to the proceedings of the W.E. Heraeus Workhop "Quantum Gravity: Challenges and Perspectives", Bad Honnef, 14-16 April 2008. References and clarifying comments adde

Four dimensional "old minimal" N=2 supersymmetrization of R^4

We write in superspace the lagrangian containing the fourth power of the Weyl tensor in the "old minimal" d=4, N=2 supergravity, without local SO(2) symmetry. Using gauge completion, we analyze the lagrangian in components. We find out that the auxiliary fields which belong to the Weyl and compensating vector multiplets have derivative terms and therefore cannot be eliminated on-shell. Only the auxiliary fields which belong to the compensating nonlinear multiplet do not get derivatives and could still be eliminated; we check that this is possible in the leading terms of the lagrangian. We compare this result to the similar one of "old minimal" N=1 supergravity and we comment on possible generalizations to other versions of N=1,2 supergravity.Comment: 31 pages, no figures. Minor corrections. Details of the full calculation included as an appendix. Reference adde