On confinement in a light-cone Hamiltonian for QCD

The canonical front form Hamiltonian for non-Abelian SU(N) gauge theory in 3+1 dimensions and in the light-cone gauge is mapped non-perturbatively on an effective Hamiltonian which acts only in the Fock space of a quark and an antiquark. Emphasis is put on the many-body aspects of gauge field theory, and it is shown explicitly how the higher Fock-space amplitudes can be retrieved self-consistently from solutions in the -space. The approach is based on the novel method of iterated resolvents and on discretized light-cone quantization driven to the continuum limit. It is free of the usual perturbative Tamm-Dancoff truncations in particle number and coupling constant and respects all symmetries of the Lagrangian including covariance and gauge invariance. Approximations are done to the non-truncated formalism. Together with vertex as opposed to Fock-space regularization, the method allows to apply the renormalization programme non-perturbatively to a Hamiltonian. The conventional QCD scale is found arising from regulating the transversal momenta. It conspires with additional mass scales to produce possibly confinement. Received: 27 March 1998 / Revised version: 3 June 1998 / Published online: 16 September 1998     

On the Light-Cone Expansion in Gauge Field Theories (QED)

The techniques for the derivation of light-cone expansions in scalar field theories are generalized to nonscalar, especially gauge field theories. For this reason the smallness of the remainder is proved in an arbitrary renormalizable theory provided an infrared regularization is present. Then we apply the formalism to derive a light-cone expansion for the product of two scalar currents in Quantum Electrodynamics in leading order. Thereby the gauge-invariance of the underlying theory is used from the very beginning by the application of the known solutions of the Ward identities. As a result of that, one obtains two gauge-invariant light cone operators, and the corresponding coefficient functions are independent one from another.     

Four-photon scattering amplitude in bosonic open string field theory

The covariant string field theory, which is formulated as a natural generalization of the light-cone gauge approach, is used to calculate three- and four-photon scattering amplitudes explicitly at tree level. The results are found to be consistent with the first quantized covariant approach.     

Generalized Parton Distributions of the Pion on the Transverse Lattice

The quark-generalized parton distributions of the pion are calculated from light-cone wavefunctions in transverse lattice gauge theory at large N_c. The pion effective size is found to decrease with increasing momentum transfer. An analytic ansatz, consistent with finite bound-state light-cone energy conditions, is given for the light-cone momentum dependence of the wavefunctions. This leads to simple, universal predictions for the behaviour of the distributions near the endpoints, complementing numerical DLCQ data.     

Gauge invariant finite size spectrum of the giant magnon

It is shown that the finite size corrections to the spectrum of the giant magnon solution of classical string theory, computed using the uniform light-cone gauge, are gauge invariant and have physical meaning. This is seen in two ways: from a general argument where the single magnon is made gauge invariant by putting it on an orbifold as a wrapped state obeying the level matching condition as well as all other constraints, and by an explicit calculation where it is shown that physical quantum numbers do not depend on the uniform light-cone gauge parameter. The resulting finite size effects are exponentially small in the R-charge and the exponent (but not the prefactor) agrees with gauge theory computations using the integrable Hubbard model.     

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.     

Cubic interaction vertices for fermionic and bosonic arbitrary spin fields

Using the light-cone gauge approach to relativistic field dynamics, we study arbitrary spin fermionic and bosonic fields propagating in flat space of dimension greater than or equal to four. Generating functions of parity invariant cubic interaction vertices for totally symmetric and mixed-symmetry massive and massless fields are obtained. For the case of totally symmetric fields, we derive restrictions on the allowed values of spins and the number of derivatives. These restrictions provide a complete classification of parity invariant cubic interaction vertices for totally symmetric fermionic and bosonic fields. As an example of application of the light-cone formalism, we obtain simple expressions for the Yang–Mills and gravitational interactions of massive arbitrary spin fermionic fields. For some particular cases, using our light-cone cubic vertices, we discuss the corresponding manifestly Lorentz invariant and on-shell gauge invariant cubic vertices.     

Non-leading terms in the light-cone expansion and electromagnetic mass differences

In this note it is shown to what extent non-leading terms in the FGM light-cone expansion (of conserved currents) are determined by the requirement of gauge invariance. A consistent short distance limit of the light-cone expansion is only obtained by taking these secondary terms into account. In this way the expression for the logarithmically divergent term in electromagnetic mass differences is rederived.     

Properties of the covariant formulation of superstring theories

The covariant two-dimensional action principle that describes the dynamics of free superstrings in a Minkowski background is reviewed. Covariant gauge conditions are formulated, which simplify the equations of motion of the superspace coordinates to free equations. In this gauge there are bosonic and fermionic constraints whose generators give a supersymmetric generalization of the Virasoro algebra. As in certain supersymmetric field theories, closure of the algebra requires using the equations of motion. Covariant constrained bracket relations are obtained for the classical theory, but it is very difficult to extend them to quantum mechanical commutation relations. Interaction vertices satisfying supersymmetry and the necessary gauge conditions are constructed. They reduce in a special frame to ones found in earlier work in the light-cone gauge, and then can be interpreted quantum mechanically.     

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.     

Light-cone auxiliary fields for ten-dimensional super Yang-Mills

We consider ten-dimensional super Yang-Mills in the light-cone gauge and define a set of auxiliary fields which close the light-cone super algebra off-shell. As a necessary preliminary we give a systematic discussion of the auxiliary field problem for simple super Yang-Mills in dimensions 3, 4, 6 and 10 both covariantly and in the light-cone framework. The motivation for this work is that it may prove useful in conjunction with the ideas of harmonic superspace. With this in mind we indicate how the light-cone theory in ten dimensions can be formulated in light-cone superspace using unconstrained superfields.     

The triangle anomaly in the light-cone gauge

It is shown that the triangle anomaly can be evaluated in the light-cone gauge and that the result obtained is consistent with the usual covariant one. We use two different procedures: (i) Eliminating the nonphysical fields from the covariant anomalous Ward identity. (ii) Carrying out a chiral transformation on the light-cone Lagrangian. The use of both dimensional and Pauli-Villars regularisations are discussed.     

The Nappi-Witten string in the light-cone gauge

Some of the motivations for as well as the main points of the quantization of the Nappi-Witten string in the light-cone gauge are reviewed.