Light-cone Lattice Research Articles

TT¯ Deformation: A Lattice Approach

Integrable quantum field theories can be regularized on the lattice while preserving integrability. The resulting theories on the lattice are integrable lattice models. A prototype of such a regularization is the correspondence between a sine-Gordon model and a six-vertex model on a light-cone lattice. We propose an integrable deformation of the light-cone lattice model such that in the continuum limit we obtain the TT¯-deformed sine-Gordon model. Under this deformation, the cut-off momentum becomes energy dependent and the underlying Yang–Baxter integrability is preserved. Therefore, this deformation is integrable but non-local: similar to the TT¯ deformation of quantum field theory.

Determination of the generalized parton distributions through the analysis of the world electron scattering data considering two-photon exchange corrections

We determine the valence generalized parton distributions (GPDs) $ H_v^q $ and $ E_v^q $ with their uncertainties at zero skewness by performing a $ \chi^2 $ analysis of the world electron scattering data considering two-photon exchange corrections. The data include a wide and updated range of the electric and magnetic form factors (FFs) of the proton and neutron. As a result, we find that there are no enough constraints on GPDs $ E_v^q $ from FFs data solely though $ H_v^q $ are well constrained. By including the new data of the charge and magnetic radius of the nucleon in the analysis, we show that they put new constraints on the final GPDs, especially on $ E_v^q $. Moreover, we calculate the gravitational FF $ M_2 $ and the total angular momentum $ J^q $ using the extracted GPDs and compare them with the FFs obtained from the light-cone QCD sum rules (LCSR) and Lattice QCD. We show that our results are interestingly in a good consistency with the pure theoretical predictions.

Identification of Brillouin Zones by In-Plane Lasing from Light-Cone Surface Lattice Resonances.

Because of translational symmetry, electromagnetic fields confined within 2D periodic optical structures can be represented within the first Brillouin zone (BZ). In contrast, the wavevectors of scattered electromagnetic fields outside the lattice are constrained by the 3D light cone, the free-photon dispersion in the surrounding medium. Here, we report that light-cone surface lattice resonances (SLRs) from plasmonic nanoparticle lattices can be used to observe the radiated electromagnetic fields from extended BZ edges. Our coupled dipole radiation theory reveals how lattice geometry and induced surface plasmon dipole orientation affect angular distributions of the radiated fields. Using dye molecules as local dipole emitters to excite the light-cone SLR modes, we experimentally identified high-order BZ edges by directional, in-plane lasing emission. These results provide insight into nanolaser architectures that can emit at multiple wavelengths and in-plane directions simply by rotating the nanocavity lattice.

Norm of Bethe-wave functions in the continuum limit

The 6-vertex model with appropriately chosen alternating inhomogeneities gives the so-called light-cone lattice regularization of the sine-Gordon (Massive-Thirring) model. In this integrable lattice model we consider pure hole states above the antiferromagnetic vacuum and express the norm of Bethe-wave functions in terms of the hole's positions and the counting-function of the state under consideration. In the light-cone regularized picture pure hole states correspond to pure soliton (fermion) states of the sine-Gordon (massive Thirring) model. Hence, we analyze the continuum limit of our new formula for the norm of the Bethe-wave functions. We show, that the physically most relevant determinant part of our formula can be expanded in the large volume limit and turns out to be proportional to the Gaudin-determinant of pure soliton states in the sine-Gordon model defined in finite volume.

Exact finite volume expectation values of overline{varPsi}varPsi in the massive Thirring model from light-cone lattice correlators

In this paper, using the light-cone lattice regularization, we compute the finite volume expectation values of the composite operator overline{varPsi}varPsi between pure fermion states in the Massive Thirring Model. In the light-cone regularized picture, this expectation value is related to 2-point functions of lattice spin operators being located at neighboring sites of the lattice. The operator overline{varPsi}varPsi is proportional to the trace of the stress-energy tensor. This is why the continuum finite volume expectation values can be computed also from the set of non-linear integral equations (NLIE) governing the finite volume spectrum of the theory. Our results for the expectation values coming from the computation of lattice correlators agree with those of the NLIE computations. Previous conjectures for the LeClair-Mussardo-type series representation of the expectation values are also checked.

Lattice approach to finite volume form-factors of the Massive Thirring (Sine-Gordon) model

In this paper we demonstrate, that the light-cone lattice approach for the Massive-Thirring (sine-Gordon) model, through the quantum inverse scattering method, admits an appropriate framework for computing the finite volume form-factors of local operators of the model. In this work we compute the finite volume diagonal matrix elements of the U(1) conserved current in the pure soliton sector of the theory. Based on the systematic large volume expansion of our results, we conjecture an exact expression for the finite volume expectation values of local operators in pure soliton states. At large volume in leading order these expectation values have the same form as in purely elastic scattering theories, but exponentially small corrections differ from previous Thermodynamic Bethe Ansatz conjectures of purely elastic scattering theories.

Boundary effects on the supersymmetric sine-Gordon model through light-cone lattice approach

We discussed subspaces of the N=1 supersymmetric sine-Gordon model with Dirichlet boundaries through light-cone lattice regularization. In this paper, we showed, unlike the periodic boundary case, both of Neveu–Schwarz (NS) and Ramond (R) sectors of a superconformal field theory were obtained. Using a method of nonlinear integral equations for auxiliary functions defined by eigenvalues of transfer matrices, we found that an excitation state with an odd number of particles is allowed for a certain value of a boundary parameter even on a system consisting of an even number of sites. In a small-volume limit where conformal invariance shows up in the theory, we derived conformal dimensions of states constructed through the lattice-regularized theory. The result shows existence of the R sector, which cannot be obtained from the periodic system, while a winding number is restricted to an integer or a half-integer depending on boundary parameters.

Worldsheet propagator on the lightcone worldsheet lattice

We develop new more powerful techniques, based on an almost closed form for the lattice worldsheet propagator, for analyzing planar open string worldsheets defined on a lightcone lattice. We show that results obtained in earlier work are easily reproduced with far more precision. In particular, consistency checks that required numerical analysis in the earlier work can now be confirmed exactly.

Digitizing the Neveu-Schwarz model on the lightcone worldsheet

The purpose of this article is to extend the light-cone worldsheet lattice description of string theory to include the Neveu-Schwarz model. We model each component of the fermionic worldsheet field by a critical Ising model. We show that a simple choice of boundary conditions for the Ising variables leads to the half-integer modes required by the model. We identify the $G$-parity operation within the Ising model and formulate the procedure for projecting onto the even $G$-parity sector. We construct the lattice version of the three open string vertex, with the necessary operator insertion at the interaction point. We sketch a formalism for summing planar open string multiloop amplitudes, and we discuss prospects for numerically summing them. If successful, the methods described here could provide an alternative to lattice gauge theory for computations in large $N$ QCD.

The Status of the Wave Function in Dynamical Collapse Models

The idea that in dynamical wave function collapse models the wave function is superfluous is investigated. Evidence is presented for the conjecture that, in a model of a field theory on a 1+1 lightcone lattice, knowing the field configuration on the lattice back to some time in the past, allows the wave function or quantum state at the present moment to be calculated, to arbitrary accuracy so long as enough of the past field configuration is known.

TBA equations for excited states in the sine–Gordon model

We propose thermodynamic Bethe ansatz (TBA) integral equations for multi-particle soliton (fermion) states in the sine–Gordon (massive Thirring) model. This is based on T-system and Y-system equations, which follow from the Bethe ansatz solution in the light-cone lattice formulation of the model. Even and odd charge sectors are treated on an equal footing, corresponding to periodic and twisted boundary conditions, respectively. The analytic properties of the Y-system functions are conjectured on the basis of the large volume solution of the system, which we find explicitly. A simple relation between the TBA Y-functions and the counting function variable of the alternative non-linear integral equation (Destri–deVega equation) description of the model is given. At the special value β2 = 6π of the sine–Gordon coupling, exact expressions for energy and momentum eigenvalues of one-particle states are found.

Finite size effects in the XXZ and sine-Gordon models with two boundaries

We compute the boundary energy and the Casimir energy for both the spin- 1 2 XXZ quantum spin chain and (by means of the light-cone lattice construction) the massive sine-Gordon model with both left and right boundaries. We also derive a nonlinear integral equation for the ground state of the sine-Gordon model on a finite interval. These results, which are based on a recently-proposed Bethe ansatz solution, are for general values of the bulk coupling constant, and for both diagonal and nondiagonal boundary interactions. However, the boundary parameters are restricted to obey one complex (two real) constraints.

Proper time and Minkowski structureon causal graphs

For causal graphs we propose a definition of proper time which for smallscales is based on the concept of volume, while for large scales the usualdefinition of length is applied. The scale where the change from `volume' to`length' occurs is related to the size of a dynamical clock and defines anatural cut-off for this type of clock. By changing the cut-off volume wemay probe the geometry of the causal graph on different scales andthereby define a continuum limit. This provides an alternative to thestandard coarse-graining procedures. For regular causal lattices (such as,for example, the two-dimensional lightcone lattice) this concept can be proven to lead to aMinkowski structure. An illustrative example of this approach is providedby the breather solutions of the sine-Gordon model on a two-dimensionallightcone lattice.

Non-linear integral equation and finite volume spectrum of sine-Gordon theory

We examine the connection between the non-linear integral equation (NLIE) derived from light-cone lattice and sine-Gordon quantum field theory, considered as a perturbed c = 1 conformal field theory. After clarifying some delicate points of the NLIE deduction from the lattice, we compare both analytic and numerical predictions of the NLIE to previously known results in sine-Gordon theory. To provide the basis for the numerical comparison we use data from Truncated Conformal Space method. Together with results from analysis of infrared and ultraviolet asymptotics, we find evidence that it is necessary to change the rule of quantization proposed by Destri and de Vega to a new one which includes as a special case that of Fioravanti et al. This way we find strong evidence for the validity of the NLIE as a description of the finite size effects of sine-Gordon theory.

Scaling functions in the odd charge sector of sine-Gordon/massive Thirring theory

A non-linear integral equation (NLIE) governing the finite size effects of excited states of even topological charge in the sine-Gordon (sG) / massive Thirring (mTh) field theory, deducible from a light-cone lattice formulation of the model, has been known for some time. In this letter we conjecture an extension of this NLIE to states with odd topological charge, thus completing the spectrum of the theory. The scaling functions obtained as solutions to our conjectured NLIE are compared successfully with Truncated Conformal Space data and the construction is shown to be compatible with all other facts known about the local Hilbert spaces of sG and mTh models. With the present results we have achieved a full control over the finite size behaviour of energy levels of sG/mTh theory.

Truncated conformal space at c=1, nonlinear integral equation and quantization rules for multi-soliton states

We develop truncated conformal space (TCS) technique for perturbations of c=1 conformal field theories. We use it to give the first numerical evidence of the validity of the non-linear integral equation (NLIE) derived from light-cone lattice regularization at intermediate scales. A controversy on the quantization of Bethe states is solved by this numerical comparison and by using the locality principle at the ultraviolet fixed point. It turns out that the correct quantization for pure hole states is the one with half-integer quantum numbers originally proposed by Fioravanti et al. [Phys. Lett. B 390 (1997) 243]. Once the correct rule is imposed, the agreement between TCS and NLIE for pure hole states turns out to be impressive.

A local and integrable lattice regularization of the massive Thirring model

The light-cone lattice approach to the massive Thirring model is reformulated using a local and integrable lattice hamiltonian written in terms of discrete Fermi fields. Several subtle points concerning boundary conditions, normal ordering, continuum limit, finite renormalizations and decoupling of fermion doublers are elucidated. The relations connecting the six-vertex anisotropy and the various coupling constants of the continuum are analyzed in detail.

Bethe ansatz and quantum groups: The light-cone approach (II). From RSOS( p + 1) models to p-restricted sine-Gordon field theories

We solve the RSOS( p) models on the light-cone lattice with fixed boundary conditions by disentangling the type-II representations of SU(2) q , at q = e iπ/ p , from the full SOS spectrum obtain through algebraic Bethe ansatz. The rule which realizes the quantum group reduction to the RSOS states is that there must no be singular roots in the solutions of the Bethe ansatz equations describing the states with quantum spin J < ( p − 1)/2. By studying how this rule is active on the particle states, we are able to give a microscopic derivation of the lattice S-matrix of the massive kinks. The correspondence between the light-cone six-vertex model and the sine-Gordon field theory implies that the continuum limit of the RSOS( p + 1) model is to be identified with the p-restricted sine-Gordon field theory.

Bethe ansatz and quantum groups: the light-cone lattice approach (I). Six vertex and SOS models

The six-vertex model is solved with fixed boundary conditions (FBC) that guarantee exact SU(2) q invariance on the lattice. The algebra of the Yang-Baxter (YB) and SU(2) q generators turns to close and the transfer matrix is SU(2) q -invariant for FBC. In addition, the infinite spectral parameter limit of the YB generators yields cleanly the SU(2) q generators. The Bethe ansatz states constructed for FBC are shown to be the highest weights of SU(2) q . The light-cone evolution operator for FBC is introduced and shown to follow from the row-to-row FBC transfer matrix with alternating inhomogeneities. This operator is shown to describe the SOS model after an appropriate gauge choice. Using this FBC light-cone approach, the scaling limit of both six-vertex and SOS models easily follows. Finally, the higher level Bethe ansatz equations (describing the physical excitations) are explicitly derived for FBC.

ON THE CONTINUOUS LIMIT OF THE EIGHT-VERTEX MODEL

The continuous limit of the eight-vertex model is shown to give solely the Massive Thirring Model (MTM). More precisely, using the light-cone lattice approach we find a whole class of lattice spacing (a) dependences in the eight vertex parameters (θ, γ, k) yielding a relative field theory in the a=0 limit. This turns out to be the MTM with no dependence on k. The exact excitation spectrum calculation presented here lead to these conclusions. Analogous results are reached from a perturbative renormalization group study of the anisotropic current-current continuum fermion field theory.