Unusual initial state interactions and Kinoshita diagram identities in perturbative QCD

Unlike in QED, algebraic identities for individual single-cut Kinoshita diagrams with all soft gluons are generally violated by initial state spectator interactions in light-cone time-ordered perturbation theory. At g⁴ order, identities insuring IR cancellation for the real graphs considered by Bodwin, Brodsky and Lepage for ππ→μ⁺μ^?+X when all gluons are soft can be obtained by summing over several of the corresponding single-cut diagrams. Although this fails for the two-loop virtual's diagrams considered by BBL, summing over a larger class of possible two-loop virtual spectator interactions having two Glauber singularities does restore IR finiteness when both gluons are soft.For individual single-cut Kinoshita diagrams with an arbitrary number ladder exchanges, algebraic identities for the (C_F)^n/2 contribution from the initial state are derived.     

QCD calculations in the light-cone gauge

The non-singlet quark structure function is calculated in the leading logarithm approximation in an axial gauge with n² = 0, the light-cone gauge. The choice n² = 0 leads to a simple identity for loop integrals involving the extra n · k denominators. We compare the results graph by graph with both Feynman gauge QCD and a scalar gluon theory. The leading diagrams are the same “rainbow” diagrams as for the case of the scalar theory.The techniques are also applied to quark-quark scattering at large transverse momentum. The leading diagrams have the same dressed ladder-form factor structure.     

Light-cone superspace and the ultraviolet finiteness of the N=4 model

Superspace in the light-cone frame takes a simple form. No auxiliary fields are necessary, and application to extended supersymmetries is straightforward. It is shown that the N=4 model, in a certain form of the light-cone gauge, is completely free of ultraviolet divergences in any order of perturbation theory. It follows that the β-function vanishes in any gauge, to all orders of perturbation theory. Our method differs from the conventional method in that we use only half the number of θ's as there are supersymmetry operators. All fields are unconstrained and independent of the $\text{θ}\text{'}\text{s}$.     

Electromagnetic mass shift of pions in unified gauge field theories and the light-cone

The electromagnetic mass shift of pions is discussed in unified gauge field theories of weak and electromagnetic interactions to second order of the electric charge and the pion mass, respectively. We calculate the contributions of the next to leading light-cone singularities (quark mass terms) and it is found that these do not contribute to the divergences in the mass shift provided the masses of the bare proton quark and neutron quark are equal. γ, Z, W, φ exchanges are taken into account. Different bare quark masses in general make the mass shift divergent. In the tadpole contribution, the Born term causes a divergence unless we extrapolate first to q² = 0.     

Ghost-free non-Abelian gauge theory: renormalization and gauge-invariance

Although it has been known for a long time that the special case n^μA_μ = 0 for an axial gauge of a vector field A_μ, characterized by a direction n_μ, is free from the peculiar loop complications inherent in all other known gauges of non-Abelian gauge theories, practical use of this ghost-free gauge has often met with some reserve. The reasons were always difficulties in the development of the theoretical formalism, all of which can be traced back to a singularity at n^μp_μ = 0 where p is some four-momentum. This paper, which is a sequel to an earlier one by one of the authors, is intended to show that within the functional integration formalism a consistent field theory can be developed. Here we first prove the gauge invariance of the renormalized theory, allowing for the presence of an arbitrary number of scalar and fermion fields with spontaneous symmetry breaking. Then it is shown that all on-shell elements for the physical S-matrix between properly selected physical sources are independent of n_μ (gauge invariant) and so are the renormalized masses.     

Type IIB Green-Schwarz superstrings in AdS 5 × S 5 from the supercoset approach

We consider superstrings moving in the AdS ₅ × S ⁵ space-time and find their Green-Schwarz action using the supercoset approach based on the supergroup PSU(2, 2|4). We describe several parametrizations of the relevant supercoset and present the action in different κ-symmetry gauges. In particular, we discuss a gauge where all the fermionic coordinates corresponding to the conformal (S) supercharges are gauged away and also a light-cone type gauge where half of the Q and S supercoordinates are gauged away. The resulting action contains terms that are quadratic and quartic in fermions. In the flat-space limit, it reduces to the standard light-cone Green-Schwarz action. We comment on the possibility of fixing the bosonic light-cone gauge and of reformulating the action in terms of two-dimensional Dirac spinors.     

A path-functional field theory of lattice gauge models and the large-N limit

We transform lattice gauge models to a theory of functional fields defined on a set of closed paths. Some relevant properties of the formalism are discussed in detail, with emphasis on symmetry and topological structure. We then investigate the large-N limit of the U(N) lattice gauge model in arbitrary dimensions using this formalism. Assuming the existence of the limit, we show, to arbitrary order of the strong coupling expansion parameter (g²N)^?, which is kept fixed, that for the leading contribution in the limit: (i) the flow of indices in color space can be represented by planar diagrams; (ii) when the diagrams are immersed in space-time they are random surfaces without handles; (iii) there are interactions of the surfaces which can be depicted as the formation of multisheet bubblesw in the surfaces. This formalism also makes it possible to set up a gauge-invariant mean-field approximation.     

Contact interactions in superstring theory

Contact interactions are shown to be required in superstring theory in order to ensure either world-sheet supersymmetry in a covariant formalism or spacetime supersymmetry in the light-cone gauge. These interactions only contribute for specific ranges of the momenta of the emitted particles. Their rôle is to ensure analyticity of S-matrix elements in much the same way as with contact terms in ordinary field theories with point particles. For tree diagrams the usual functional calculations, performed at sufficiently spacelike momentum transfer, give correct results. For other values of the momenta the correct answer is obtained either by analytic continuation or by adding the contribution of the contact interactions. In certain loop calculations the effect of the contact interactions must be taken into account. In the light-cone gauge formalism the contact terms ensure positivity of the hamiltonian.     

Multi-loops for light-cone gauge superstrings

After closure of the [10]-SUSY algebra, the full light-cone gauge field theory of superstrings is reduced to a set of general integral representations of first quantised form for multi-loop diagrams. These are then reduced further, by a limiting procedure, to an explicitly Lorentz-covariant expression for these diagrams. No summations over spin structures or odd supermoduli are required. The low energy cosmological constant and all N = 2 and 3amplitudesare zero at all loop orders.     

New avenues in supersymmetry and supergravity

We analyze the problem of constructing supersymmetric versions of gauge theories of particles and of gravity which have a closed supersymmetric algebra. Inparticular we present the basic no-go theorems that indicate that in four dimensions it is not possible to construct suitably extended supersymmetric versions of the above theories without drastic modification of the supersymmetric algebra. Two ways past the“N=3” barrier are discussed; that of central charges involved highly constrained versions which appearn difficult to quantize effectively, while the use of light-cone variables seems to be the most promising. We give light-cone gauge versions of supersymmetric Yang-Mills theories for all extended cases of interest and briefly consider their ultraviolet divergence properties.     

Wk structure of A SU(2)-level k from covariant construction of Kac-Moody algebras

The W_k structure underlying the transverse realization of affine SU(2) at level k is analyzed. The extension of the equivalence existing between the covariant and light-cone gauge realization of an affine Kac-Moody algebra to W_k algebras is given. Higher spin generators are extracted by the less singular terms in the operator product expansion of the parafermions constructed by means of the projection of the covariant on the light-cone gauge. These fields can be written in terms of only one free boson compactified on a circle.     

The general three-vertex,BRS identities and renormalizability of the light-cone gauge

The general one-loop three-vertexГ _μeλ ^abc (p, q, r) in the four-component formulation of the Yang-Mills theory is calculated in the light-cone gauge. The nonvanishing counter Lagrangian constructed from this three-vertex and the self-energy is proportional to the original Lagrangian, the single renormalization constant being -11g² C _YM Г(2?ω)/48π². Gauge dependent and nonlocal counterterms do not contribute to the renormalization constant, but are needed to verify the appropriate Slavnov-Taylor (ST) and Becchi-Rouet-Stora (BRS) identities.     

Spontaneously broken quark helicity symmetry

We discuss the origin of chiral-symmetry breaking in the light-cone representation of QCD. In particular, we show how quark helicity symmetry is spontaneously broken in SU (N) gauge theory with massless quarks if that theory has a condensate of fermion light-cone zero modes. The symmetry breaking appears as induced interactions in an effective light-cone Hamiltonian equation based on a trivial vacuum. The induced interaction is crucial for generating a splitting between pseudoscalar and vector meson masses, which we illustrate with spectrum calculations in some 1 + 1-dimensional reduced models of gauge theory.     

Proton decay in locally supersymmetric GUT

Proton decay is studied in the supergravity model with “the hidden sector” as the source of supersymmetry breaking. Each dimension-five operator is found to accompany ΔB ≠ 0 four-scalar interactions. The Higgs fermion exchange for loop diagrams at low energies can be as important as the gauge fermion exchange, if the associated Yukawa coupling is significant as suggested by the radiatively induced SU(2) × U(1) breaking mechanism. The experimental bound for p → K⁰μ⁺ gives the lower bound of the order of 10¹⁶ GeV for the mass of the baryon-number violating Higgs particle.