Discrete Light-cone Quantization Research Articles

Study ofqq¯states in transverse lattice QCD using alternative fermion formulations

In this work we investigate $q\overline{q}$ spectra and wave functions of light front transverse lattice Hamiltonians that result from different methods of formulating fermions on the transverse lattice. We adopt the one link approximation for the transverse lattice and discrete light cone quantization (DLCQ) to handle longitudinal dynamics. We perform a detailed study of the continuum limit of DLCQ and associated techniques to manage severe light front infrared divergences. We explore the effects of various parameters of the theory, especially the strength of the helicity-flip interaction and the link mass on spectra and wave functions.

Kinks in discrete light cone quantization

We investigate non-trivial topological structures in discrete light cone quantization (DLCQ) through the example of the broken symmetry phase of the two-dimensional φ4 theory using antiperiodic boundary condition (APBC). We present evidence for degenerate ground states which is both a signature of spontaneous symmetry breaking and mandatory for the existence of kinks. Guided by a constrained variational calculation with a coherent state ansatz, we then extract the vacuum energy and kink mass and compare with classical and semi-classical results. We compare the DLCQ results for the number density of bosons in the kink state and the Fourier transform of the form factor of the kink with corresponding observables in the coherent variational kink state.

Penrose limit and discrete light cone quantization of string theory

We argue that the Penrose limit of a general string background is a generalization of the Seiberg-Sen limit describing M(atrix) theory as the DLCQ of M theory in flat space. The BMN theory of type IIB strings on the maximally supersymmetric pp-wave background is understood as the exact analogue of the BFSS M(atrix) theory, namely, a DLCQ of IIB string theory on $AdS_5 \times S^5$ in the limit of infinite longitudinal momentum. This point of view is used to explain some features of the BMN duality.

SYM correlators and the maldacena conjecture

We report on progress in evaluating quantum filed theories with supersymmetric discrete light-cone quantization (SDLCQ). We compare the method to lattice gauge theory and point out its relevance for lattice calculations. As an exciting application we present a test of the Maldacena conjecture. We test the conjecture by evaluating the correlator of the stress-energy tensor in the strong coupling field theory and comparing to the string theory prediction of its behavior as a function of the distance. Our numerical results support the Maldacena conjecture and are within 10–15% of the predicted results.

Anomalously light bound-states in SYM Cherns-Simons theory

We apply supersymmetric discrete light-cone quantization (SDLCQ) to the study of supersymmetric YangMills-Chern-Simons (SYM-CS) theory on R × S 1 × S 1 . One of the compact directions is chosen to be light-like and the other to be space-like. Since the SDLCQ regularization explicitly preserves supersymmetry, this theory is totally finite, and thus we can solve for bound-state wave functions and masses numerically without renormalizing. The Chern-Simons term is introduced here to provide masses for the particles while remaining totally within a supersymmetric context. We discuss a set of anomalously light states which are a reflection of the exact BPS state of the underlying of supersymmetric SYM theory.

Discrete light-cone quantization on a twisted torus

Recently it has been demonstrated by Dienes and Mafi that the physics of toroidal compactified models of extra dimensions can depend on the shape angle of the torus. Toroidal compactification has also recently been used as a regulator for numerical solutions of supersymmetric field theories in 2+1 dimensions. The question is: does the shape angle of the torus also affect the physics in this situation? Clearly a numerical solution should be independent of the shape of the space on which we compactify, at least when the regulator is removed. We show that, for standard discrete light-cone quantization with transverse parity invariance, toroidal compactification is only allowed for a specific set of shape angles and for that set of shape angles the numerical solutions are unchanged.

Properties of the bound states of super Yang-Mills–Chern-Simons theory

We apply supersymmetric discrete light-cone quantization (SDLCQ) to the study of supersymmetric Yang-Mills-Chern-Simons (SYM-CS) theory on R x S^1 x S^1. One of the compact directions is chosen to be light-like and the other to be space-like. Since the SDLCQ regularization explicitly preserves supersymmetry, this theory is totally finite, and thus we can solve for bound-state wave functions and masses numerically without renormalizing. The Chern-Simons term is introduced here to provide masses for the particles while remaining totally within a supersymmetric context. We examine the free, weak and strong-coupling spectrum. The transverse direction is discussed as a model for universal extra dimensions in the gauge sector. The wave functions are used to calculate the structure functions of the lowest mass states. We discuss the properties of Kaluza-Klein states and focus on how they appear at strong coupling. We also discuss a set of anomalously light states which are reflections of the exact Bogomol'nyi-Prasad-Sommerfield states of the underlying SYM theory.

Numerical simulations ofN=(1,1)1+1-dimensional super Yang-Mills theory with large supersymmetry breaking

We consider the $N=(1,1)$ super Yang-Mills (SYM) theory that is obtained by dimensionally reducing SYM theory in 2+1 dimensions to 1+1 dimensions and discuss soft supersymmetry breaking. We discuss the numerical simulation of this theory using supersymmetric discrete light-cone quantization when either the boson or the fermion has a large mass. We compare our result to the pure adjoint fermion theory and pure adjoint boson discrete light-cone quantization calculations of Klebanov, Demeterfi, Bhanot and Kutasov. With a large boson mass we find that it is necessary to add additional operators to the theory to obtain sensible results. When a large fermion mass is added to the theory we find that it is not necessary to add operators to obtain a sensible theory. The theory of the adjoint boson is a theory that has stringy bound states similar to the full SYM theory. We also discuss another theory of adjoint bosons with a spectrum similar to that obtained by Klebanov, Demeterfi, and Bhanot.

Anomalously light states in super-Yang–Mills–Chern–Simons theory

Inspired by our previous finding that supersymmetric Yang–Mills–Chern–Simons (SYM–CS) theory dimensionally reduced to 1+1 dimensions possesses approximate Bogomol'nyi–Prasad–Sommerfield (BPS) states, we study the analogous phenomenon in the three-dimensional theory. Approximate BPS states in two dimensions have masses which are nearly independent of the Yang–Mills coupling and proportional to their average number of partons. These states are a reflection of the exactly massless BPS states of the underlying pure SYM theory. In three dimensions we find that this mechanism leads to anomalously light bound states. While the mass scale is still proportional to the average number of partons times the square of the CS coupling, the average number of partons in these bound states changes with the Yang–Mills coupling. Therefore, the masses of these states are not independent of the coupling. Our numerical calculations are done using supersymmetric discrete light-cone quantization (SDLCQ).

Strings from Quivers, Membranes from Moose

We consider N=2 moose/quiver gauge theories corresponding to N_1 D3-branes at a C^2/Z_{N_2} singularity in the ``large moose'' limit where N_1 and N_2 are scaled to infinity together. In the dual holographic description, this scaling gives rise to a maximally supersymmetric pp-wave background with a compact light-cone direction. We identify the gauge theory operators that describe the Discrete Light-Cone Quantization (DLCQ) of the string in this background. For each discrete light-cone momentum and winding sector there is a separate ground state and Fock space. The large moose/quiver diagram provides a useful graphical representation of the string and its excitations. This representation has a natural explanation in a T-dual language. The dual theory is a non-relativistic type IIA string wound around the T-dual direction, and bound by a quadratic Newtonian potential. We end with some comments on D-string/D-particle states, a possible lift to M-theory and the relation to deconstruction.

Perturbative S-matrix in discretized light cone quantization of two-dimensional φ4 theory

We study the S-matrix of two-dimensional λφ 4 theory in Discretized Light Cone Quantization and show how the correct continuum limit is reached for various processes in lowest order perturbation theory.

The Heisenberg Matrix Formulation of Quantum Field Theory

Heisenberg's matrix formulation of quantum mechanics can be generalized to relativistic systems by evolving in light-front time τ = t + z/c. The spectrum and wavefunctions of bound states, such as hadrons in quantum chromodynamics, can be obtained from matrix diagonalization of the light-front Hamiltonian on a finite dimensional light-front Fock basis defined using periodic boundary conditions in x— and x⊥. This method, discretized light-cone quantization (DLCQ), preserves the frame-independence of the front form even at finite resolution and particle number. Light-front quantization can also be used in the Hamiltonian form to construct an event generator for high energy physics reactions at the amplitude level. The light-front partition function, summed over exponentially-weighted light-front energies, has simple boost properties which may be useful for studies in heavy ion collisions. I also review recent work which shows that the structure functions measured in deep inelastic lepton scattering are affected by final-state rescattering, thus modifying their connection to light-front probability distributions. In particular, the shadowing of nuclear structure functions is due to destructive interference effects from leading-twist diffraction of the virtual photon, physics not included in the nuclear light-front wavefunctions.

Simulation of dimensionally reduced super Yang-Mills-Chern-Simons theory

A supersymmetric formulation of a three-dimensional SYM-Chern-Simons theory using light-cone quantization is presented, and the supercharges are calculated in light-cone gauge. The theory is dimensionally reduced by requiring all fields to be independent of the transverse dimension. The result is a non-trivial two-dimensional supersymmetric theory with an adjoint scalar and an adjoint fermion. We perform a numerical simulation of this SYM-Chern-Simons theory in 1+1 dimensions using SDLCQ (Supersymmetric Discrete Light-Cone Quantization). We find that the character of the bound states of this theory is very different from previously considered two-dimensional supersymmetric gauge theories. The low-energy bound states of this theory are very ``QCD-like.'' The wave functions of some of the low mass states have a striking valence structure. We present the valence and sea parton structure functions of these states. In addition, we identify BPS-like states which are almost independent of the coupling. Their masses are proportional to their parton number in the large-coupling limit.

Perturbative expansion in DLCQ of field and string theories

We explore the perturbative aspects in discrete light-cone quantization (DLCQ) of field and string theories. In field theory, we develop a systematic DLCQ perturbation and establish the Feynman rules. From the Feynman rules, we show that DLCQ S-matrix does not have a covariant continuum limit for processes with p+ = 0 exchange. Furthermore, we study the relationship between Feynman rules in (conventional) DLCQ and those in DLCQ as a light-like limit (L3) and show that the difference between DLCQ and L3 is only the existence of the divergences by the zero-mode loop diagrams in L3, which are absent in DLCQ. In string theory, we study the scattering amplitudes in L3 and discuss that at any order in perturbation, the zero-mode loop divergences are absent even in L3. This result suggests that the scattering amplitudes in L3 string theory are well-defined and coincides with those in DLCQ string theory.

Wave functions and spectra from (S)DLCQ

Applications of discretized light-cone quantization (DLCQ) to (3+1)-dimensional Yukawa theory with Pauli-Villars regulators and of supersymmetric DLCQ (SDLCQ) to (2+1)-dimensional super Yang-Mills theory are discussed. The ability of these methods to provide wave functions as well as spectra is emphasized.

DLCQ strings and branched covers of torii

In this talk I will review some results about the discrete light-cone quantization (DLCQ) of strings and some connections of the results with matrix string theory.

The spectrum of SY M2+1

Abstract We apply supersymmetric discrete light-cone quantization (SDLCQ) to the study of supersymmetric Yang-Mills theory on R × S 1 × S 1 . One of the compact directions is chosen to be light-like and the other to be space-like. Since the SDLCQ regularization explicitly preserves supersymmetry, this theory is totally finite, and thus we can solve for bound-state wave functions and masses numerically without renormalizing. We present an overview of all the massive states of this theory, and we see that the spectrum divides into two distinct and disjoint sectors. In one sector the SDLCQ approximation is only valid up to intermediate coupling. There we find a well defined and well behaved set of states, and we present a detailed analysis of these states and their properties. In the other sector, which contains a completely different set of states, we find that while these state have a well defined spectrum their masses grow with the transverse momentum cutoff.

Exploring N = 1 SYM (2+1): the stress-tensor correlator

The evaluation of field theoretic correlators at strong couplings is especially interesting in the light of recently discovered string/field theory correspondences. We present a calculation of the stress-tensor correlator in N = 1 SYM theory in 2+1 dimensions. We calculate this object numerically with the method of supersymmetric discrete light-cone quantization (SDLCQ) at large N c . For small distances we reproduce the conformal field theory result with the correlator behaving like 1/ r 6 . In the large r limit the correlator is determined by the (massless) BPS states of the theory. We find a critical value of the coupling where the correlator goes to zero in this limit. This critical coupling is shown to grow linearly with the square root of the transverse momentum resolution.

Exact Solutions to Pauli–Villars-Regulated Field Theories

We present a new class of quantum field theories which are exactly solvable. The theories are generated by introducing Pauli–Villars (PV) fermionic and bosonic fields with masses degenerate with the physical positive metric fields. An algorithm is given to compute the spectrum and corresponding eigensolutions. We also give the operator solution for a particular case and use it to illustrate some of the tenets of light-cone quantization. Since the solutions of the solvable theory contain ghost quanta, these theories are unphysical. However, the existence of an exact solution provides an important check on the implementation of PV-regulated discretized light-cone quantization (DLCQ). In the limit of exact mass degeneracy of the ghost and physical fields, the numerical DLCQ solutions are constrained to reduce to the explicit forms we give here. We also discuss how perturbation theory in the difference between the masses of the physical and PV particles could be developed, thus generating physical theories. The existence of explicit solutions of the solvable theory also allows one to study the relationship between the equal-time and light-cone vacua and eigensolutions.

Manifestation of a nontrivial vacuum in discrete light-cone quantization.

We study a (1+1)-dimensional lambda phi(4) model with a light-cone zero mode and constant external source to describe spontaneous symmetry breaking. In the broken phase, we find degenerate vacua and discuss their stability based on effective-potential analysis. The vacuum triviality is spurious in the broken phase because these states have lower energy than Fock vacuum. Our results are based on the variational principle.