Light-cone Hamiltonian Research Articles

Anyon scattering from lightcone Hamiltonian: the singlet channel

We study U(N) Chern-Simons theory coupled to massive fundamental fermions in the lightcone Hamiltonian formalism. Focusing on the planar limit, we introduce a consistent regularization scheme, identify the counter terms needed to restore relativistic invariance, and formulate scattering theory in terms of unambiguously defined asymptotic states. We determine the 2 → 2 planar S-matrix element in the singlet channel by solving the Lippmann-Schwinger equation to all orders, establishing a result previously conjectured in the literature.

BMS algebra from residual gauge invariance in light-cone gravity

We analyze the residual gauge freedom in gravity, in four dimensions, in the light-cone gauge, in a formulation where unphysical fields are integrated out. By checking the invariance of the light-cone Hamiltonian, we obtain a set of residual gauge transformations, which satisfy the BMS algebra realized on the two physical fields in the theory. Hence, the BMS algebra appears as a consequence of residual gauge invariance in the bulk and not just at the asymptotic boundary. We highlight the key features of the light-cone BMS algebra and discuss its connection with the quadratic form structure of the Hamiltonian.

Exact symmetries and threshold states in two-dimensional models for QCD

Two-dimensional SU(N) gauge theory coupled to a Majorana fermion in the adjoint representation is a nice toy model for higher-dimensional gauge dynamics. It possesses a multitude of “gluinoball” bound states whose spectrum has been studied using numerical diagonalizations of the light-cone Hamiltonian. We extend this model by coupling it to Nf flavors of fundamental Dirac fermions (quarks). The extended model also contains meson-like bound states, both bosonic and fermionic, which in the large-N limit decouple from the gluinoballs. We study the large-N meson spectrum using the Discretized Light-Cone Quantization (DLCQ). When all the fermions are massless, we exhibit an exact mathfrak{osp} (1|4) symmetry algebra that leads to an infinite number of degeneracies in the DLCQ approach. More generally, we show that many single-trace states in the theory are threshold bound states that are degenerate with multi-trace states. These exact degeneracies can be explained using the Kac-Moody algebra of the SU(N) current. We also present strong numerical evidence that additional threshold states appear in the continuum limit. Finally, we make the quarks massive while keeping the adjoint fermion massless. In this case too, we observe some exact degeneracies that show that the spectrum of mesons becomes continuous above a certain threshold. This demonstrates quantitatively that the fundamental string tension vanishes in the massless adjoint QCD2 without explicit four-fermion operators.

Ehlers symmetry in four dimensions

Starting with the light-cone Hamiltonian for gravity, we perform a field redefinition that reveals a hidden symmetry in four dimensions, namely the Ehlers $SL(2,R)$ symmetry. The field redefinition, which is non-local in space but local in time, acts as a canonical transformation in the Hamiltonian formulation keeping the Poisson bracket relations unaltered. We discuss the electro-magnetic duality symmetry of gravity in the light-cone formalism, which forms the $SO(2)$ subgroup of the Ehlers symmetry. The helicity states in the original Hamiltonian are not in a representation of the enhanced symmetry group. In order to make the symmetry manifest, we make a change of variables in the path integral from the helicity states to new fields that transform linearly under the $SO(2)$ duality symmetry.

Conformal truncation of chern-simons theory at large Nf

We set up and analyze the lightcone Hamiltonian for an abelian Chern-Simons field coupled to Nf fermions in the limit of large Nf using conformal truncation, i.e. with a truncated space of states corresponding to primary operators with dimension below a maximum cutoff Δmax. In both the Chern-Simons theory, and in the O(N) model at infinite N, we compute the current spectral functions analytically as a function of Δmax and reproduce previous results in the limit that the truncation Δmax is taken to ∞. Along the way, we determine how to preserve gauge invariance and how to choose an optimal discrete basis for the momenta of states in the truncation space.

Lightcone effective Hamiltonians and RG flows

We present a prescription for an effective lightcone (LC) Hamiltonian that includes the effects of zero modes, focusing on the case of Conformal Field Theories (CFTs) deformed by relevant operators. We show how the prescription resolves a number of issues with LC quantization, including i) the apparent non-renormalization of the vacuum, ii) discrepancies in critical values of bare parameters in equal-time vs LC quantization, and iii) an inconsistency at large N in CFTs with simple AdS duals. We describe how LC quantization can drastically simplify Hamiltonian truncation methods applied to some large N CFTs, and discuss how the prescription identifies theories where these simplifications occur. We demonstrate and check our prescription in a number of examples.

Off-shell spinor-helicity amplitudes from light-cone deformation procedure

We study the consistency conditions for interactions of massless fields of any spin in four-dimensional flat space using the light-cone approach. We show that they can be equivalently rewritten as the Ward identities for the off-shell light-cone amplitudes built from the light-cone Hamiltonian in the standard way. Then we find a general solution of these Ward identities. The solution admits a compact representation when written in the spinor-helicity form and is given by an arbitrary function of spinor products, satisfying well-known homogeneity constraints. Thus, we show that the light-cone consistent deformation procedure inevitably leads to a certain off-shell version of the spinor-helicity approach. We discuss how the relation between the two approaches can be employed to facilitate the search of consistent interaction of massless higher-spin fields.

Maximally supersymmetric Yang-Mills in five dimensions in light-cone superspace

We formulate maximally supersymmetric Yang-Mills theory in five dimensions in light-cone superspace. The light-cone Hamiltonian is of the quadratic form and the theory can be understood as an oxidation of the $ \mathcal{N} = 4 $ Super Yang-Mills Theory in four dimensions. We specifically study three-point counterterms and show how these counterterms vanish on-shell. This study is a preliminary to set up the technique in order to study possible four-point counterterms.

D2-brane in the Penrose limits ofAdS4×CP3

We consider a D2-brane in the pp-wave backgrounds obtained from AdS$_4\times$CP$^3$ when electric and magnetic fields have been turned on. Upon fixing the light-cone gauge, light-cone Hamiltonian and BPS configurations are obtained. In particular we study BPS configurations with electric dipole on the two sphere giant and a giant graviton rotating in transverse directions. Moreover we show that the gauge field living on the D2-brane is replaced by a scalar field in the light-cone Hamiltonian. We also present a matrix model by regularizing (quantizing) 2-brane theory.

On the worldsheet theory of the type IIA $ {\text{Ad}}{{\text{S}}_4} \times \mathbb{C}{\mathbb{P}_3} $ superstring

We perform a detailed study of the type IIA superstring in AdS(4) x CP(3). After introducing suitable bosonic light-cone and fermionic kappa worldsheet gauges we derive the pure boson and fermion SU(2|2) x U(1) covariant light-cone Hamiltonian up to quartic order in fields. As a first application of our derivation we calculate energy shifts for string configurations in a closed fermionic subsector and successfully match these with a set of light-cone Bethe equations. We then turn to investigate the mismatch between the degrees of freedom of scattering states and oscillatory string modes. Since only light string modes appear as fundamental Bethe roots in the scattering theory, the physical role of the remaining $4_F+4_B$ massive oscillators is rather unclear. By continuing a line of research initiated by Zarembo, we shed light on this question by calculating quantum corrections for the propagators of the bosonic massive fields. We show that, once loop corrections are incorporated, the massive coordinates dissolve in a continuum state of two light particles.

Classification of IIB backgrounds with 28 supersymmetries

We show that all IIB backgrounds with strictly 28 supersymmetries are locally isometric to the plane wave solution of arXiv:hep-th/0206195. Moreover, we demonstrate that all solutions with more than 26 supersymmetries and only 5-form flux are maximally supersymmetric. The N=28 plane wave solution is a superposition of the maximally supersymmetric IIB plane wave with a heterotic string solution. We investigate the propagation of strings in this background, find the spectrum and give the string light-cone Hamiltonian.

A Light-Cone QCD Inspired Effective Hamiltonian Model with SU(3) Flavor Mixing

The effective light-cone Hamiltonian is extended to include the SU(3) flavor mixing interaction besides the confining potential. Solving the coupled J = 0 mass eigen equations for the up, down, and strange quark components numerically, the masses of π° and π, their radial wave functions, and rms radii are obtained in agreement with the experimental data.

An approach towards a constituent quark model on the light cone

We use the vacuum expectation value of a Wegner–Wilson loop representing a fast moving quark–antiquark pair to derive the light cone Hamiltonian for a q q ¯ meson. We solve the corresponding Schrödinger equation for various trial wave functions. The result shows how confinement determines the meson mass and wave function for valence quarks on the light cone. We also parametrize the effect of the spin-dependent splitting for a light meson and charmonium. The correct chiral-symmetry breaking pattern for the pion mass is obtained due to the self-energy of the quark.

Electrified BPS giants: BPS configurations on giant gravitons with static electric field

We consider D3-brane action in the maximally supersymmetric type IIB plane-wave background. Upon fixing the light-cone gauge, we obtain the light-cone Hamiltonian which is manifestly supersymmetric. The 1/2 BPS solutions of this theory (solutions which preserve 16 supercharges) are either of the form of spherical three branes, the giant gravitons, or zero size point like branes. We then construct specific classes of 1/4 BPS solutions of this theory in which static electric field on the brane is turned on. These solutions are deformations about either of the two 1/2 BPS solutions. In particular, we study in some detail 1/4 BPS configurations with electric dipole on the three sphere giant, i.e. BIons on the giant gravitons, which we hence call BIGGons. We also study BPS configurations corresponding to turning on a background uniform constant electric field. As a result of this background electric field the three sphere giant is deformed to squashed sphere, while the zero size point like branes turn into circular or straight fundamental strings in the plane-wave background, with their tension equal to the background electric field.

From bubbles to foam: dilute to dense evolution of hadronic wave function at high energy

We derive the evolution of a hadronic light cone wave function with energy at weak coupling. Our derivation is valid both in the high and the low partonic density limit, and thus encompasses both the JIMWLK and the KLWMIJ evolution. The hadronic wave function is shown to evolve by the action of the Bogoliubov-type operator, which diagonalizes on the soft gluon sector the light-cone hamiltonian in the presence of an arbitrary valence charge density. We find explicitly the action of this operator on the soft as well as the valence degrees of freedom of the theory.

A Light-Cone QCD Inspired Meson Model with a RelativisticConfining Potential in Momentum Space

For describing the radial excited states a relativistic confiningpotential in momentum space is included in the meson effectivelight-cone Hamiltonian. The meson eigen equations are transformedfrom the front form to the instant form and formulated in totalangular representation. Details about numerically solving theseequations are discussed, mainly focusing on treating singularitiesarising from one-gluon exchange interactions and confinement. Theresults of pseudo-scalar mesons indicate that the improved mesoneffective light-cone Hamiltonian can describe the ground states andradial excited states well. Some radial excited states are alsopredicted and waiting for experimental test.

The AdS5× S5superstring in light-cone gauge and its Bethe equations

We use the uniform light-cone gauge to derive an exact gauge-fixed Lagrangian and light-cone Hamiltonian for the Green-Schwarz superstring in AdS5xS5. We then quantize the theory perturbatively in the near plane-wave limit, and compute the leading 1/J correction to a generic string state from the rank-1 subsectors. These investigations enable us to propose a new set of light-cone Bethe equations for the quantum string. The equations have a simple form and yield the correct spinning string and flat space limits. Finally, we clarify the notion of closed sectors in string theory by proving the existence of perturbative effective string Hamiltonians which are direct analogues of (all loop) dilatation operators in the dual N=4 gauge theory.

The [formula omitted] supergravity Hamiltonian as a quadratic form

We conjecture that the light-cone Hamiltonian of N = 8 supergravity can be expressed as a quadratic form. We explain why this rewriting is unique to maximally supersymmetric theories. The N = 8 quartic interaction vertex is constructed and used to verify that this conjecture holds to order κ 2 .

Discrete light-cone quantization in pp-wave background

We discuss the discrete light-cone quantization (DLCQ) of a scalar field theory on the maximally supersymmetric pp-wave background in ten dimensions. It has been shown that the DLCQ can be carried out in the same way as in the two-dimensional Minkowski spacetime. Then, the vacuum energy is computed by evaluating the vacuum expectation value of the light-cone Hamiltonian. The results are consistent with the effective potential obtained in our previous work [hep-th/0402028].

A nonperturbative calculation of the electron's magnetic moment

In principle, the complete spectrum and bound-state wave functions of a quantum field theory can be determined by finding the eigenvalues and eigensolutions of its light-cone Hamiltonian. One of the challenges in obtaining nonperturbative solutions for gauge theories such as QCD using light-cone Hamiltonian methods is to renormalize the theory while preserving Lorentz symmetries and gauge invariance. For example, the truncation of the light-cone Fock space leads to uncompensated ultraviolet divergences. We present two methods for consistently regularizing light-cone-quantized gauge theories in Feynman and light-cone gauges: (1) the introduction of a spectrum of Pauli–Villars fields which produces a finite theory while preserving Lorentz invariance; (2) the augmentation of the gauge-theory Lagrangian with higher derivatives. In the latter case, which is applicable to light-cone gauge ( A + = 0 ), the A − component of the gauge field is maintained as an independent degree of freedom rather than a constraint. Finite-mass Pauli–Villars regulators can also be used to compensate for neglected higher Fock states. As a test case, we apply these regularization procedures to an approximate nonperturbative computation of the anomalous magnetic moment of the electron in QED as a first attempt to meet Feynman's famous challenge.