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We find the classical supersymmetric vacuum states of a class of N =1 ∗ field theories obtained by mass deforming superconformal models with simple gauge groups and N =4 or N =2 supersymmetry. In particular, new classical vacuum states for mass-deformed N =4 models with Sp(2N) and SO(N) gauge symmetry are found. We also derive the classical vacua for various mass-deformed N =2 models with Sp(2N) and SU(N) gauge groups and antisymmetric (and symmetric) hypermultiplets. We suggest interpretations of the mass-deformed vacua in terms of three-branes expanded into five-brane configurations.

The renormalization group flows of the coupling constants for the gauged U(N) vector model, with N_f massless fermions in the defining representation, are studied in the large N limit, to all orders in the scalar coupling lambda, leading order in 1/N, and lowest two orders in the gauge coupling g^2. It is shown that the restrictions of asymptotic freedom, and the reality of the coupling constants throughout the flows, places important restrictions on N_f/N. For the case with massless mesons, these conditions are sufficiently restrictive to imply the existence of an infrared fixed-point (g_*,lambda_*) in both couplings. Thus, the consistent massless theory is scale invariant, and in a non-abelian Coulomb phase. The case of massive mesons, and of spontaneously broken symmetry is also discussed, with similar, but not identical, conclusions. Speculations related to the possibility that there is a non-perturbative (in g^2) breakdown of chiral symmetry are presented., 15 pages, plain Latex, one figure added

A new method to obtain the Picard-Fuchs equations of effective, N=2 supersymmetric gauge theories with massive matter hypermultiplets in the fundamental representation is presented. It generalises a previously described method to derive the Picard-Fuchs equations of both pure super Yang-Mills and supersymmetric gauge theories with massless matter hypermultiplets. The techniques developed are well suited to symbolic computer calculations., Comment: 29 pages, uses phyzzx.tex

A new method to obtain the Picard-Fuchs equations of effective $N = 2$ supersymmetric gauge theories in 4 dimensions is developed. It includes both pure super Yang-Mills and supersymmetric gauge theories with massless matter hypermultiplets. It applies to all classical gauge groups, and directly produces a decoupled set of second-order, partial differential equations satisfied by the period integrals of the Seiberg-Witten differential along the 1-cycles of the algebraic curves describing the vacuum structure of the corresponding $N = 2$ theory., Latex version, 43 pages, a few cosmetic changes and some references added

We examine the high energy (Regge) limit of gravitational scattering using a Wilson line approach previously used in the context of non-Abelian gauge theories. Our aim is to clarify the nature of the Reggeization of the graviton and the interplay between this Reggeization and the so-called eikonal phase which determines the spectrum of gravitational bound states. Furthermore, we discuss finite corrections to this picture. Our results are of relevance to various supergravity theories, and also help to clarify the relationship between gauge and gravity theories., 33 pages, 5 figures

We derive a linear relation between the one-loop five-point amplitude of N=8 supergravity and the one-loop five-point subleading-color amplitudes of N=4 supersymmetric Yang-Mills theory., Comment: 17 pages, 2 figures; v2: very minor corrections

We extend the analysis of Higgs-regulated planar amplitudes of N=4 supersymmetric Yang-Mills theory to four loops for the four-gluon amplitude and to two loops for the five-gluon amplitude. Our calculations are consistent with a proposed all-loop ansatz for planar MHV n-gluon amplitudes that is the analog of the BDS ansatz in dimensional regularization. In all cases considered, we have verified that the IR-finite parts of the logarithm of the amplitudes have the same dependence on kinematic variables as the corresponding functions in dimensionally-regulated amplitudes (up to overall additive constants, which we determine). We also study various Regge limits of N=4 SYM planar n-gluon amplitudes. Euclidean Regge limits of Higgs-regulated n \geq 4 amplitudes yield results similar in form to those found using dimensional regularization, but with different expressions for the gluon trajectory and Regge vertices resulting from the different regulator scheme. We also show that the Regge limit of the four-gluon amplitude is dominated at next-to-leading-log order by vertical ladder diagrams together with the class of vertical ladder diagrams with a single H-shaped insertion.

We compute the three-loop contribution to the N=4 supersymmetric Yang-Mills planar four-gluon amplitude using the recently-proposed Higgs IR regulator of Alday, Henn, Plefka, and Schuster. In particular, we test the proposed exponential ansatz for the four-gluon amplitude that is the analog of the BDS ansatz in dimensional regularization. By evaluating our results at a number of kinematic points, and also in several kinematic limits, we establish the validity of this ansatz at the three-loop level. We also examine the Regge limit of the planar four-gluon amplitude using several different IR regulators: dimensional regularization, Higgs regularization, and a cutoff regularization. In the latter two schemes, it is shown that the leading logarithmic (LL) behavior of the amplitudes, and therefore the lowest-order approximation to the gluon Regge trajectory, can be correctly obtained from the ladder approximation of the sum of diagrams. In dimensional regularization, on the other hand, there is no single dominant set of diagrams in the LL approximation. We also compute the NLL and NNLL behavior of the L-loop ladder diagram using Higgs regularization., Comment: 45 pages, 9 figures; v3: major revision (more stringent tests, discussion of order of limits in the Regge regime)

It is argued that the leading Skyrme model estimate of the electric dipole moment of the neutron in chiral perturbation theory should be Dn ∼ Ncmπ2 ln mπ. To obtain this result requires a careful quantization of the pion fluctuation about the rotating skyrmion, with appropriate attention to the derivative couplings and zero modes of the model.

Planar ${\cal N} =4$ super Yang-Mills SU(N) theory is expected to exhibit stringy behavior, anticipated by the 't Hooft genus expansion and the $AdS/CFT$ correspondence. We examine the Bern-Dixon-Smirnov (BDS) conjecture for $n$-gluon amplitudes in the context of single-Regge and multi-Regge limits and show that these amplitudes have the expected Regge form in the Euclidean region., 48 pages, 8 figures; Noted added commenting on related work which appeared after the initial posting. References and clarifications added, as well as typos corrected

We study the subleading-color (nonplanar) contributions to the four-gluon scattering amplitudes in N=4 supersymmetric SU(N) Yang-Mills theory. Using the formalisms of Catani and of Sterman and Tejeda-Yeomans, we develop explicit expressions for the infrared-divergent contributions of all the subleading-color L-loop amplitudes up to three loops, and make some conjectures for the IR behavior for arbitrary L. We also derive several intriguing relations between the subleading-color one- and two-loop four-gluon amplitudes and the four-graviton amplitudes of N=8 supergravity. The exact one- and two-loop N=8 supergravity amplitudes can be expressed in terms of the one- and two-loop N-independent N=4 SYM amplitudes respectively, but the natural generalization to higher loops fails, despite having a simple interpretation in terms of the 't Hooft picture. We also find that, at least through two loops, the subleading-color amplitudes of N=4 SYM theory have uniform transcendentality (as do the leading-color amplitudes). Moreover, the N=4 SYM Catani operators, which express the IR-divergent contributions of loop amplitudes in terms of lower-loop amplitudes, are also shown to have uniform transcendentality, and to be the maximum transcendentality piece of the QCD Catani operators., Comment: 30 pages; v2: corrections in sec. 6, minor addition in sec. 3.3

We present a matrix-model expression for the sum of instanton contributions to the prepotential of an N=2 supersymmetric U(N) gauge theory, with matter in various representations. This expression is derived by combining the renormalization-group approach to the gauge theory prepotential with matrix-model methods. This result can be evaluated order-by-order in matrix-model perturbation theory to obtain the instanton corrections to the prepotential. We also show, using this expression, that the one-instanton prepotential assumes a universal form., 20 pages, LaTeX, 2 figures

We give a unified analysis of four-dimensional elliptic models with N=2 supersymmetry and a simple gauge group, and their relation to M-theory. Explicit calculations of the Seiberg-Witten curves and the resulting one-instanton prepotential are presented. The remarkable regularities that emerge are emphasized. In addition, we calculate the prepotential in the Coulomb phase of the (asymptotically-free) Sp(2N) gauge theory with N_f fundamental hypermultiplets of arbitrary mass., 52 pages, latex, one eps figure, uses psfig.tex; revised version: typos corrected and references added

The one-instanton contribution to the prepotential for N=2 supersymmetric gauge theories with classical groups exhibits a universality of form. We extrapolate the observed regularity to SU(N) gauge theory with two antisymmetric hypermultiplets and N_f \leq 3 hypermultiplets in the defining representation. Using methods developed for the instanton expansion of non-hyperelliptic curves, we construct an effective quartic Seiberg-Witten curve that generates this one-instanton prepotential. We then interpret this curve in terms of an M-theoretic picture involving NS 5-branes, D4-branes, D6-branes, and orientifold sixplanes, and show that for consistency, an infinite chain of 5-branes and orientifold sixplanes is required, corresponding to a curve of infinite order., Comment: 30 pages; 3 figures; LaTeX; minor typos corrected

We consider N=2 supersymmetric Yang-Mills theories in four dimensions with gauge group SU(N) for N larger than two. Using the cubic curve for a matter hypermultiplet transforming in the symmetric representation, obtained from M-theory by Landsteiner and Lopez, we calculate the prepotential up to the one instanton correction. We treat the curve to be approximately hyperelliptic and perform a perturbation expansion for the Seiberg-Witten differential to get the one instanton contribution. We find that it reproduces the correct result for one-loop, and we obtain the prediction for that curve for the one instanton correction term., Comment: 31 p., plain latex

The discovery of integrable $N=2$ supersymmetric Landau-Ginzburg theories whose chiral rings are fusion rings suggests a close connection between fusion rings, the related Landau-Ginzburg superpotentials, and $N=2$ quantum integrability. We examine this connection by finding the natural $SO(N)_K$ analogue of the construction that produced the superpotentials with $Sp(N)_K$ and $SU(N)_K$ fusion rings as chiral rings. The chiral rings of the new superpotentials are not directly the fusion rings of any conformal field theory, although they are natural quotients of the tensor subring of the $SO(N)_K$ fusion ring. The new superpotentials yield solvable (twisted $N=2$) topological field theories. We obtain the integer-valued correlation functions as sums of $SO(N)_K$ Verlinde dimensions by expressing the correlators as fusion residues. The $SO(2n+1)_{2k+1}$ and $SO(2k+1)_{2n+1}$ related topological Landau-Ginzburg theories are isomorphic, despite being defined via quite different superpotentials., 34 pages, BRX-TH-348

We derive a compact all-loop-order expression for the IR-divergent part of the N=4 SYM four-gluon amplitude, which includes both planar and all subleading-color contributions, based on the assumption that the higher-loop soft anomalous dimension matrices are proportional to the one-loop soft anomalous dimension matrix, as has been recently conjectured. We also consider the Regge limit of the four-gluon amplitude, and we present evidence that the leading logarithmic growth of the subleading-color amplitudes is less severe than that of the planar amplitudes. We examine possible 1/N^2 corrections to the gluon Regge trajectory, previously obtained in the planar limit from the BDS ansatz. The double-trace amplitudes have Regge behavior as well, with a nonsense-choosing Regge trajectory and a Regge cut which first emerges at three loops., 29 pages; v2: corrections to sections 5.1 and 5.2, references added; v3: clarification in introduction, references added; v4: published version

We use matrix model technology to study the N=2 U(N) gauge theory with N_f massive hypermultiplets in the fundamental representation. We perform a completely perturbative calculation of the periods a_i and the prepotential F(a) up to the first instanton level, finding agreement with previous results in the literature. We also derive the Seiberg-Witten curve and differential from the large-M solution of the matrix model. We show that the two cases N_f, Comment: 22 pages, 2 figures; v3: added sec. 8, containing a derivation of the SW differential purely within the matrix model framework; references added

Meson hyperfine splittings give empirical evidence that the short-ranged part of the potential binding quarks has the behavior expected of single color gluon exchange in an asymptotically free theory. Since the interaction of light confined quarks depends on only one length scale, while that of heavy confined quarks depends on two length scales, it is argued that the spin-dependent interactions are qualitatively different in the cases. Phenomenological evidence suggests that the spin-dependent interactions of light quarks are short-ranged only, while that of heavy quarks are predominantly long-ranged. It is proposed that a measurement of the F∗-F mass-difference will help clarify the nature of a possible long-ranged spin-spin interaction of strange quarks.

The massless spectrum of closed strings on group manifolds Md × H described by a Wess-Zumino-Witten (WZW) action for the group H is studied. It is found that for certain groups H and central charge k of the associated Kac-Moody algebra, the massless spectrum does not coincide with the standard Kaluza-Klein spectrum. The nature of the extra, “accidental” massless states depends crucially on the multi-connectedness of H. In the presence of “accidental” gauge bosons, which requires multi-connected H, the gauge symmetry of the massless spectrum is enlarged to GL × GR, where H ⊂ G. A complete classification of “accidental” massless states is given for H = SU (2), SU (2) Z 2 , SU (3) and SU (3) Z 3 for every k.

We present a study of possible bound states in N = 8 supergravity. We find evidence for the existence of multiplets of two-body bound states and expect that many-body bound states may exist as well. Our study is based on a calculation of Regge trajectories in the two-body scattering amplitudes of the lagrangian field theory. We also study Regge trajectories in N = 4 Yang-Mills theory and find evidence for a possible spin zero, SU(4) and gauge singlet, massless bound state. If such a state actually exists and supersymmetry is not broken, it may be a member of a supersymmetric multiplet which includes the graviton.

A simple relativistic potential model is constructed in order to describe meson spectroscopy in a unified way, encompassing both light- and heavy-quark systems. A linear potential, transforming as the fourth component of a vector potential, is assumed in accordance with quark-confinement mechanisms appropriate to gauge theories. Scaling arguments are used to derive the Regge behavior of the model. We present evidence that the forces which confine quarks are essentially independent of quark species. The over-all systematics of our predictions for meson energy levels and leptonic decay widths give support to the usefulness of the model. We comment on the application of asymptotic freedom as a means of estimating decay rates which violate the Okubo - Zweig - Iizuka rule.

The systematics of L = 2 light meson spin dependent spectra is examined within the context of the spectroscopy of other meson states. A relatively model independent measure of the average quark velocity in light meson spectroscopy is presented. A qualitative picture of (q q ) valence quark spectra with relativistic kinematics seems to emerge from the data.

Recent results from quantum chromodynamics (QCD) are shown to be consistent with the generalized Breit-type phenomenological Hamiltonian previously proposed for the spin-dependent spectroscopy of quark-antiquark states. In particular, the concept of a short-distance and long-distance quark-gluon chromomagnetic moment, with different qualitative behavior for light and heavy quarks, is compatible with QCD. An induced axial-vector exchange, previously suggested by Feinberg and Sucher, also seems to be implied by the field-theoretic calculations.

Vacuum polarization at long distances for confined heavy-quark-antiquark (QQ-bar) pairs is considered. The vacuum-polarization-corrected static potential is shown to have a radial dependence which should allow interpolation between charmonium, upsilon states, and other heavy QQ-bar systems. It is argued that the static, confining potential cannot grow faster than a linear potential at large distances, within the framework of this analysis.

An arbitrary, renormalizable non-Abelian gauge theory with gauge group $\mathfrak{g}$, and arbitrary scalar and fermion representation structure is considered. It is shown that all the gauge vector mesons of the theory lie on a Regge trajectory if and only if $\mathfrak{g}$ is semisimple, i.e., Abelian subgroups are excluded. Implications for unified and grand unified theories of the weak and electromagnetic interactions are discussed. The photon, which does not Reggeize in the Weinberg-Salam theory, will lie on a Regge trajectory in a grand unified theory. If the Higgs-meson mass of the electroweak theory is large (\ensuremath{\gtrsim} 300 GeV, say), then Regge recurrences of the intermediate vector bosons should occur at energies of the order of 2-4 TeV. If the Higgs boson of the unified theory is light ( 100 GeV), then Regge recurrences of the gauge mesons are not expected for energies below the grand-unification mass of order ${{\ensuremath{\mu}}_{W}}^{2}$ $\mathrm{exp}(\frac{1}{{g}^{2}})$.

The accurately measured masses of D ∗∗ (2459) and D ∗∗ (2428), which recently became available, are used to discuss the effective spin-dependent quark—antiquark forces. A fairly model independent analysis indicates that the reduced matrix element of the Thomas term for the D ∗∗ multiplet is v 2 (L=1)⋍0 within errors, which supports the accepted idea that the Thomas term is repulsive at long distances, and attractive at short distances. If inverted multiplets are to be observed, one must find q Q states with larger spatial size than that of the D ∗∗ multiplet. Plausible candidates would be orbital excitations ( L ⩾2) of the q Q mesons, where q (Q) is a light (heavy) quark.

It is shown that the anomalous divergence of the supercurrent in a supersymmetric non-Abelian gauge theory may be removed at the one-loop level by coupling three scalar multiplets in the adjoint representation to the supersymmetric Yang-Mills multiplet.

It is demonstrated that an anomaly exists for the supercurrent in a supersymmetric non-Abelian gauge theory. Since no gauge particle is coupled to the current, the anomaly does not alter the renormalizability of the theory. Some consequences of the anomaly are discussed.

It is shown how to construct effective lagrangians to the two-loop level for non-abelian gauge theories, quantized in background field gauge. This construction is no more difficult than the analogous computation in abelian gauge theories when minimal subtraction is employed. It is argued that for three or more loops, one can no longer separate heavy or mixed light-heavy graphs in an intermediate renormalization, and the more general algorithm presented by us in an earlier work must be employed even in background field gauge.

Necessary group theoretic conditions for all elementary gauge bosons and fermions of an arbitrary renormalizable gauge theory to lie on Regge trajectories are reviewed. It is then argued that in properly unified gauge theories all particles of a given spin lie on Regge trajectories. This then implied that a properly unified gauge theory has no local U(1) factor groups, and no massive fermion singlets. A consideration of the general pattern of Regge and radial recurrences to be expected in quantum field theories suggests that the presence or absence of spin 3 2 quarks and/or leptons in the TeV region will provide crucial clues to enable one to distinguish between various classes of unified, grand unified, and subconstituent models. The correct interpretation of such excited fermions will require correlation with the Higgs boson mass and possible radial and Regge excitations of the weak vector bosons.

A Skyrme model calculation of weak radiative baryon decays is presented, based on a lagrangian describing weak nonleptonic decays of mesons previously discussed by Donoghue et al. There are no free parameters in the Skyrme model predictions for weak radiative decays, as all necessary parameters are obtained from other contexts. The predictions of the Skyrme model for the weak radiative baryon decays are in good agreement with experiment, except for Σ+ → Pγ, where however the model involves substantial cancellations among terms, which are sensitive to small changes of input parameters.

The low energy-effective action is computed to two-loop order for strings on group manifolds by compactification of the effective action of a closed boson string. By suitably chosen embeddings of the spin connection in the background gauge fields, one obtains the low energy effective actions of the Bose sector of the heterotic string and type II superstring.

Vacuum polarization at long distances for confined heavy-quark--antiquark (QQ-bar) pairs is considered. It is argued that the static confining potential cannot grow faster than a linear potential at large distances. The vacuum-polarization-corrected potential is a flavor-independent potential which allows interpolation between charmonium, UPSILON and other QQ-bar systems.

Evidence from meson spectroscopy is presented to support the view that the effective interaction between quark-antiquark pairs is a long-range scalar confining force, together with a short-range Coulomb-type vector exchange governed by the underlying quantum chromodynamics. As a result, it is prediced that the $^{3}P$-wave charmed mesons and mesons of the type ($b\overline{u}$) and ($b\overline{s}$) will be inverted multiplets. Discovery of such an effect would provide strong evidence for an effective scalar confining force. It is argued, on the basis of the systematics of the tensor force in the ordinary mesons, that there are important induced tensor forces in the $I=1$ and $I=\frac{1}{2}$ $P$-wave meson multiplets. A qualitative discussion suggests that the induced tensor forces are due to couplings of the $J=1$, $I=1$ and $I=\frac{1}{2}$ mesons to open decay channels. As a result, the ${A}_{1}$, $B$, ${Q}_{A}$, and ${Q}_{B}$ mesons appear to have substantial mixings with $(q\overline{q})(q\overline{q})$ configurations.

An arbitrary, renormalizable non-Abelian gauge theory with gauge group $\mathcal{G}$ and arbitrary scalar and fermion structure is considered. Necessary conditions for all the fermions of the theory to lie on Regge trajectories are derived. If no fermion transforms as a singlet under $\mathcal{G}$, then all fermions Reggeize. If some fermions transform as singlets under $\mathcal{G}$, then certain group-theoretic constraints on the fermion mass matrix must be satisfied if all fermions are to Reggeize. These methods are applied to the Weinberg-Salam and grand unified theories. As a by-product of this study, kinematical-singularity-free, signatured helicity amplitudes are constructed which allow for $P$ and $\mathrm{CP}$ violation. Such amplitudes may be useful for applications outside the context of the Regge program.

The supercurrent anomalies of the supercurrent S μ of the supersymmetric Yang-Mills theory in Wess-Zumino gauge are computed using the supersymmetric dimensional regulator of Siegel. It is shown that γ μ S μ =0 and ∂ μ S μ ≠0 in agreement with an earlier calculation based on the Adler-Rosenberg method. The problem of exhibiting the chiral anomaly and a regulator for local supersymmetry suggests that the interpretation of dimensional reduction in component language is incomplete.

Flavor-changing neutral currents are reconsidered allowing the possibility that superheavy quarks, with masses comparable to the weak-boson mass, exist in nature. It is argued that the natural conservation of these weak neutral currents cannot be imposed to order ..cap alpha..G/sub F/ in this case. Rather, the absence of strangeness-changing (and possibly charm-changing) neutral currents to this order suggests that the mixing angles between ordinary and superheavy quarks must be extremely small. Some phenomenological ramifications of this restriction are presented.

The large S-state hyperfine splittings and the spacing of the P-states of charmonium can be explained qualitatively by an effective quark-gluon anomalous magnetic moment of 1 quark magneton within the context of a nonrelativistic linear potential model.

It is shown by direct computation that the supersymmetry Ward identity for the supersymmetric Yang-Mills theory can be satisfied at the one-loop level in the Wess-Zumino gauge when one uses dimensional regularization with the prescription ${\ensuremath{\gamma}}^{\ensuremath{\mu}}{\ensuremath{\gamma}}_{\ensuremath{\mu}}=4$, and performs the Dirac algebra in four dimensions. The result is found to be valid for arbitrary covariant gauge-fixing functionals. A particular gauge, $\ensuremath{\xi}=\ensuremath{-}3$, is found for which the supersymmetry transformations of both renormalized and unrenormalized fields are finite and well defined. In this same gauge, one-loop renormalization constants for two-, three-, and four-point one-particle-irreducible Green's functions are found to be equal.

It is shown that an anomaly exists for the supercurrent of the supersymmetric vector multiplet when coupled to external supergravity fields. As a result, this anomaly will also be present in at least one of the O(1), O(2), or O(3) extended supergravity models.

The technique of Bjorken is combined with the Ward identities for the time-ordered products of currents to obtain a correlation between space-space equal-time commutators and the high-energy behavior of the hadron proper functions. The method is illustrated for the three-point function of conserved isovector currents.

New techniques are developed for treating the $n$-point functions of currents, which are interrelated by means of Ward identities obtained from the equal-time current commutation relations. The $n$-point functions are sorted out so as to define proper vertices which describe the reactions of particles of definite spin. A meson-dominance assumption is made by approximating the proper vertices by simple polynomials in momenta, with the coefficients determined by the Ward identities. The method is discussed in detail for $n=3$ and the currents of chiral $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$, and then applied to the decay processes ${A}_{1}\ensuremath{\rightarrow}\ensuremath{\rho}+\ensuremath{\pi}$ and $\ensuremath{\rho}\ensuremath{\rightarrow}\ensuremath{\pi}+\ensuremath{\pi}$.

The nonleptonic decay amplitudes of the $K$ mesons are calculated using current algebra and the spectral-function sum rules. The result is convergent in the intermediate-boson model, but not for a direct current-current interaction. Comparison with the observed rate for ${{K}_{1}}^{0}$ decay shows that the intermediate-boson mass is about 8 BeV.

The question of the Reggeization of the elementary particles in renormalizable gauge theories with the Higgs-Kibble mechanism is examined. It is concluded that the massive non-Abelian gauge vector mesons and $J=\frac{1}{2}$ fermions of these theoreis lie on Regge trajectories in every case in which a counting criterion due to Mandelstam is satisfied. Several explicit examples are presented which verify that the necessary factorization condition of the Born helicity matrices is satisfied at $J=1$ and $J=\frac{1}{2}$, supporting this conclusion.

A Skyrme-model calculation of weak radiative baryon octet and decuplet decays is presented, based on a Lagrangian describing weak nonleptonic decays of mesons previously discussed by Donoghue and collaborators. There are no free parameters in the Skyrme-model predictions for weak radiative decays, as all necessary parameters are obtained from other contexts. The predictions of the Skyrme model for the weak radiative baryon decays are in good qualitative agreement with experiment, except for ..sigma../sup +/..-->..p..gamma.., where however the model involves substantial cancellations among terms which are sensitive to small changes of input parameters.

Possible topological solitons (skyrmions) of four-dimensional supersymmetric nonlinear σ-models are investigated. The requirements of supersymmetry limit our study to the CP 1 model. A stable soliton seems possible, but in the absence of a demonstrated lower-bound for the mass, the stability of the soliton is unproved. The semi-classical spectrum of the CP 1 skyrmion, as well as its supersymmetric extension, is studied.

We describe here some recent work1 in which we undertook to investigate, based on the dynamics of N=8 supergravity, the existence of bound states in this system. We were motivated to some extent by the suggestion of Ellis, Gaillard, Maiani and Zumino2 (EGMZ) that N=8 supergravity could make contact with current particle phenomenology if one postulated a certain set of massless (before symmetry breaking) bound states transforming according to the local SU(8) invariance group that the theory may possess3. In their original proposal EGMZ assumed that these bound states had the quantum numbers of a so-called “current multiplet”: $${\left( { - 3/2} \right)_{\text{L}}},\;\left( { - 1} \right)_{\text{L}}^{\text{A}},\; \cdots \;\left( {5/2} \right)_{\text{L}}^{{\text{AB}}}\; \cdots \; + \left( {{\text{TCP}}\;{\text{conjugates}}} \right)$$ The particles of SU(5) GUT were to be found among these, following a sequence of symmetry breakings. It has also been argued” that in order to make the EGMZ scenario viable, one might have to postulate an infinite tower of massless particles.

Further discussion of the hadronic corrections to the van Royen--Weisskopf formula is presented.