Two-dimensional Wess-Zumino Model Research Articles

N=(0,2)deformation of theN=(2,2)Wess-Zumino model in two dimensions

We construct a simple $\mathcal{N}=(0,2)$ deformation of the two-dimensional Wess-Zumino model. In addition to superpotential, it includes a ``twisted'' superpotential. Supersymmetry may or may not be spontaneously broken at the classical level. In the latter case an extra right-handed fermion field ${\ensuremath{\zeta}}_{R}$ involved in the $\mathcal{N}=(0,2)$ deformation plays the role of Goldstino.

Two-dimensional Wess-Zumino models at intermediate couplings

We consider the two-dimensional $\mathcal{N}=(2,2)$ Wess-Zumino model with a cubic superpotential at weak and intermediate couplings. Refined algorithms allow for the extraction of reliable masses in a region where perturbation theory no longer applies. We scrutinize the Nicolai improvement program, which guarantees lattice supersymmetry, and compare the results for ordinary and nonstandard Wilson fermions with those for SLAC derivatives. It turns out that this improvement leads to better results for SLAC fermions but not for Wilson fermions. Furthermore, even without improvement terms the models with all three fermion species reproduce the correct values for the fermion masses in the continuum limit.

From the Dirac operator to Wess–Zumino models on spatial lattices

We investigate two-dimensional Wess–Zumino models in the continuum and on spatial lattices in detail. We show that a non-antisymmetric lattice derivative not only excludes chiral fermions but in addition introduces supersymmetry breaking lattice artifacts. We study the non-local and antisymmetric SLAC derivative which allows for chiral fermions without doublers and minimizes those artifacts. The supercharges of the lattice Wess–Zumino models are obtained by dimensional reduction of Dirac operators in high-dimensional spaces. The normalizable zero modes of the models with N=1 and N=2 supersymmetry are counted and constructed in the weak- and strong-coupling limits. Together with known methods from operator theory this gives us complete control of the zero mode sector of these theories for arbitrary coupling.

The two-dimensional Wess-Zumino model in the Hamiltonian lattice formulation

We investigate a Hamiltonian lattice version of the two-dimensional Wess-Zumino model, with special emphasis to the pattern of supersymmetry breaking. Results are obtained by Quantum Monte Carlo simulations and Density Matrix Renormalization group techniques.

Lattice study of the two-dimensional Wess-Zumino model

We present results from a numerical simulation of the two-dimensional Euclidean Wess-Zumino model. In the continuum the theory possesses N=1 supersymmetry. The lattice model we employ was analyzed by Golterman and Petcher in \cite{susy} where a perturbative proof was given that the continuum supersymmetric Ward identities are recovered without finite tuning in the limit of vanishing lattice spacing. Our simulations demonstrate the existence of important non-perturbative effects in finite volumes which modify these conclusions. It appears that in certain regions of parameter space the vacuum state can contain solitons corresponding to field configurations which interpolate between different classical vacua. In the background of these solitons supersymmetry is partially broken and a light fermion mode is observed. At fixed coupling the critical mass separating phases of broken and unbroken supersymmetry appears to be volume dependent. We discuss the implications of our results for continuum supersymmetry breaking.

A hamiltonian lattice study of the two-dimensional Wess-Zumino model

We investigate a Hamiltonian lattice version of the two-dimensional Wess-Zumino model by Quantum Monte Carlo simulations. In order to study the pattern of supersymmetry breaking, we measure the ground state energy and the correlation length along a trajectory approaching the continuum limit. The algorithm is very effective in measuring the ground state energy, and adequate for the correlation length.

Exact lattice supersymmetry: The two-dimensionalN=2Wess-Zumino model

We study the two-dimensional Wess-Zumino model with extended N=2 supersymmetry on the lattice. The lattice prescription we choose has the merit of preserving {\it exactly} a single supersymmetric invariance at finite lattice spacing $a$. Furthermore, we construct three other transformations of the lattice fields under which the variation of the lattice action vanishes to $O(ga^2)$ where $g$ is a typical interaction coupling. These four transformations correspond to the two Majorana supercharges of the continuum theory. We also derive lattice Ward identities corresponding to these exact and approximate symmetries. We use dynamical fermion simulations to check the equality of the massgaps in the boson and fermion sectors and to check the lattice Ward identities. At least for weak coupling we see no problems associated with a lack of reflection positivity in the lattice action and find good agreement with theory. At strong coupling we provide evidence that problems associated with a lack of reflection positivity are evaded for small enough lattice spacing.

Hamiltonian Monte Carlo simulation of the two-dimensional Wess-Zumino model

We study a Hamiltonian lattice version of the two-dimensional Wess-Zumino model. Preliminary results obtained by Quantum Monte Carlo with a many-parameter guiding wave function are presented. We analyze the pattern of supersymmetry breaking by measuring the ground state energy and a set of supersymmetric Ward identities. The algorithm is quite effective and allows very precise measurements.

Quantum corrections to the supersymmetry algebra

The Bjorken–Johnson–Low technique is used to compute the equal time anticommutator of the spinor currents associated with the supersymmetry of a two-dimensional Wess–Zumino model containing a Majorana spinor, a scalar, and an auxiliary field. Operator regularization is used to compute radiative effects as this does not explicitly break the supersymmetry present in the classical Lagrangian. We find that the spinor current is not conserved, and that the algebra of the generators of the supersymmetry transformation is altered. This is analogous to what has been found in theories with a classical axial gauge symmetry.

Canonical quantisation of the gauged Wess-Zumino model

The canonical formalism is developed for the two-dimensional Wess-Zumino model on a group manifold G with a subgroup H⊂G gauged, using time as the evolution parameter. The system is a constrained hamiltonian system which is dealt with using Dirac's procedure. The theory is gauge fixed and quantised, and is found to be equivalent to the theory associated with the GKO coset construction for the coset G/H.

A priori estimates forN=2 Wess-Zumino models on a cylinder

We establish bounds uniform in the ultraviolet cutoff (i.e., in the number of degrees of freedom) for a family of two-dimensional Wess-Zumino models. These estimates are useful in proving existence of the models, as well as in investigating their properties. For example, we require these estimates for the analysis of the supercharge and of the Hamiltonian. These are the fundamental a priori estimates for elliptic regularity in infinite dimensions.

Exactly solvable models of conformal-invariant quantum field theory in D-dimensional space

The method for exact solution of a certain class of models of conformal quantum field theory in D-dimensional Euclidean space is proposed. The method allows one to derive closed differential equations for all the Green functions and also algebraic equations to scale dimensions of all field. A scalar field P of a scale dimension d p = D − 2 is needed for nontrivial solutions to exist. At D ≠ 2 this field is converted to a constant that coincides with the central charge of two-dimensional theories. A new class of D = 2 models has been obtained, where the infinite-parametric symmetry is not manifest. The two-dimensional Wess-Zumino model is used to illustrate the method of solution.

Patterns of two-dimensional supersymmetry breaking: A Monte Carlo study

Patterns of spontaneous supersymmetry breaking in the two-dimensional Wess-Zumino model are studied by hamiltonian Monte Carlo methods.

N = 2 two-dimensional Wess-Zumino model on the lattice

A lattice version of the N = 2 SUSY two-dimensional Wess-Zumino model was constructed and studied. The correct continuum limit is checked in perturbation theory. The strong-coupling limit is defined and investigated. We find that the ground state of the model has zero energy and infinite degeneracy. The connection between this degeneracy and the properties of the Nicolai-Parisi-Sourlas transformation is discussed.

Высщие порядки теории воэмушений для супер-(ф3)2-модели

We use the Lipatov method to estimate large orders of perturbation theory for the Euclidean version of the two-dimensional Wess-Zumino model. As a main result, we find that the growth ofZ k is not as fast as expected, if one puts together naively a theory containing fermions and a theory with bosons.