Chiral symmetry of the 2-dimensional chiral Gross-Neveu model is broken explicitly by a bare mass term as well as a splitting of scalar and pseudo-scalar coupling constants. The vacuum and light hadrons - mesons and baryons which become massless in the chiral limit - are explored analytically in leading order of the derivative expansion by means of a double sine-Gordon equation. Depending on the parameters, this model features new phenomena as compared to previously investigated 4-fermion models: spontaneous breaking of parity, a non-trivial chiral vacuum angle, twisted kink-like baryons whose baryon number reflects the vacuum angle, crystals with alternating baryons, and appearance of a false vacuum.
The Gross-Neveu model in 1+1 dimensions is generalized to the case of different scalar and pseudoscalar coupling constants. This enables us to interpolate smoothly between the standard massless Gross-Neveu models with either discrete or continuous chiral symmetry. We present the solution of the generalized model in the large N limit including the vacuum, fermion-antifermion scattering and bound states, solitonic baryons with fractional baryon number and the full phase diagram at finite temperature and chemical potential.
We study the phase diagram of the 1+1 dimensional Gross-Neveu model at finite number of fermion flavors using lattice field theory. Numerical results are presented, which indicate the existence of an inhomogeneous phase, where the chiral condensate is a spatially oscillating function.
Guided by a study of kink-antikink scattering in the Gross-Neveu model and other known solutions of the Hartree-Fock approach of a particularly simple type, we demonstrate a quantitative relationship between three different problems: Quantized 1+1-dimensional fermions in the large N limit, solitons of the classical sinh-Gordon equation and classical strings moving in 3-dimensional anti de Sitter space. Aside from throwing light on the relationship between quantum field theory and classical physics, this points to the full solvability of the dynamical N-kink-antikink problem in the Gross-Neveu …
Baryons in the large N limit of two-dimensional Gross-Neveu models are reconsidered. The time-dependent Dirac-Hartree-Fock approach is used to boost a baryon to any inertial frame and shown to yield the covariant energy-momentum relation. Momentum distributions are computed exactly in arbitrary frames and used to interpolate between the rest frame and the infinite momentum frame, where they are related to structure functions. Effects from the Dirac sea depend sensitively on the occupation fraction of the valence level and the bare fermion mass and do not vanish at infinite momentum. In the cas…
We study a special classical current in the O(3) Gross-Neveu model that becomes supersymmetric when quantum anomalies are included. Following its definition, we generalize the current for the general case, the O(N) Gross-Neveu models. We compute its algebra and discuss the possibility of supersymmetry can be established for these models.
We investigate the Gross-Neveu model in $2+1$ dimensions in a constant and homogeneous magnetic field using one reducible flavor of overlap fermions. Our lattice simulations suggest that the magnetic catalysis phenomenon, i.e., an increase of the chiral condensate with the magnetic field, is present for all temperatures below the chiral phase transition, in accordance with predictions from mean-field and beyond-mean-field calculations.
The free field representation of the Zamolodchikov-Faddeev algebra for the chiral Gross-Neveu model is analysed in detail, and used to construct an integral representation for form factors of the model.
A class of 1+1 dimensional supersymmetric theories with four-fermionic interaction will be built from scratch. The vacua of selected examples will be examined in the 't Hooft limit and compared to the Gross-Neveu model.
In this letter we study some relevant physical parameters of the massless Gross-Neveu model in a finite spatial dimension for different boundary conditions. It is considered the standard homogeneous Hartree Fock solution using zeta function regularization for the study the mass dynamically generated and its respective beta function. It is found that the beta function does not depend on the Boundary conditions. On the other hand, it was considered the Casimir effect of the resulting effective theory. There appears a complex picture where the sign of the generated forces depends on the parameter…
We study the $(1+1)$-dimensional chiral Gross-Neveu model on the lattice. At finite density, analytic mean-field results predict the existence of inhomogeneous condensates breaking both chiral symmetry and spacetime symmetries spontaneously. We investigate the fate of these inhomogeneities for two flavors and find remnant structural order, albeit with a decaying amplitude. We also map out phase diagrams in the plane spanned by the chemical potential and temperature for different lattice spacings and physical volumes. Finally, we comment on the interpretation of our results in the light of vari…
We investigate the discrete chiral transformation of a Majorana fermion on a torus. Depending on the boundary conditions the integration measure can change sign. Taking this anomalous behavior into account we define a chiral order parameter as a ratio of partition functions with differing boundary conditions. Then the lattice realization of the Gross-Neveu model with Wilson fermions is simulated using the recent `worm' technique on the loop gas or all-order hopping representation of the fermions. An algorithm is formulated that includes the Gross-Neveu interaction for N fermion species. The cr…
There is substantial evidence that the ground state of the 2d chiral Gross-Neveu model, in the presence of a $U(1)$ fermion number chemical potential $μ$ and in the large $N$ limit, is given by a {\it chiral spiral} phase, namely an inhomogeneous phase with a chiral condensate having a spatially periodic phase. We show that the chiral spiral configuration persists at finite $N$ and $T=0$ for any $μ>0$. Our analysis is based on non-abelian bosonization, that relates the model to a $U(N)_1$ WZW model deformed by current-current interactions. In this description the appearance of the inhomogeneou…
The critcal exponent $ω$ is evaluated at $O(1/N)$ in $d$-dimensions in the Gross-Neveu model using the large $N$ critical point formalism. It is shown to be in agreement with the recently determined three loop $β$-functions of the Gross-Neveu-Yukawa model in four dimensions. The same exponent is computed for the chiral Gross-Neveu and non-abelian Nambu-Jona-Lasinio universality classes.
In the limit of a large number of flavors, the ground state of the chiral Gross-Neveu model at finite fermion density exhibits a spatially periodic mean field in the form of the chiral spiral, thereby breaking translational invariance. Here we show that the ground state of the same model at finite fermion current density gives rise to a mean field which is periodic in time, a temporal chiral spiral. Since the current density is the same as axial charge density in two dimensions and axial charge is conserved, this may serve as an example of a time crystal. More specifically, as mean field theor…
Magnetic catalysis of the chiral symmetry breaking and other magnetic properties of the (2+1)-dimensional Gross--Neveu model are studied taking into account the Zeeman interaction of spin-1/2 quasi-particles (electrons) with tilted (with respect to a system plane) external magnetic field. The Zeeman interaction is proportional to magnetic moment $μ_B$ of electrons. It is shown that at $μ_B\ne 0$ the magnetic catalysis effect is drastically changed in comparison with the $μ_B= 0$ case.
We find the general solution to the time-dependent Hartree-Fock problem for the Gross-Neveu models, with both discrete (GN2) and continuous (NJL2) chiral symmetry. We find new multi-baryon, multi-breather and twisted breather solutions, and show that all GN2 baryons and breathers are composed of constituent twisted kinks of the NJL2 model.
We compute the anomalous dimensions of a class of operators of the form $(\barψψ)^p$ and $(\barψψ)^pψ$ to leading order in $ε$ in the Gross-Neveu model in $2+ε$ dimensions. We use the techniques developed in arXiv: 1505.00963.
Due to integrability, baryon-baryon scattering in the massless Gross-Neveu model at large N features only forward elastic scattering. A bare mass term breaks integrability and is therefore expected to induce backward elastic scattering as well as inelastic reactions. We confirm these expectations by a study of baryon-baryon scattering in the massive Gross-Neveu model near the non-relativistic limit. This restriction enables us to solve the time-dependent Hartree-Fock equations with controlled approximations, using a combination of analytical methods from an effective field theory and the numer…
The isomorphism $SU(4) \simeq O(6)$ is used to construct the form factors of the O(6) Gross-Neveu model as bound state form factors of the SU(4) chiral Gross-Neveu model. This technique is generalized and is then applied to use the O(6) as the starting point of the nesting procedure to obtain the O(N) form factors for general even N.
We calculate the critical exponents $ω_\pm$ in the $d$-dimensional Gross-Neveu model in $1/N$ expansion with $1/N^2$ accuracy. These exponents are related to the slopes of the $β$-functions at the critical point in the Gross - Neveu - Yukawa model. They have been computed recently to four loops accuracy. We checked that our results are in complete agreement with the results of the perturbative calculations.
We use the recently developed CFT techniques of Rychkov and Tan to compute anomalous dimensions in the $O(N)$ Gross-Neveu model in $d=2+ε$ dimensions. To do this, we extend the "cowpie contraction" algorithm of arXiv:1506.06616 to theories with fermions. Our results match perfectly with Feynman diagram computations.
The breather is a vibrating multifermion bound state of the massless Gross-Neveu model, originally found by Dashen, Hasslacher and Neveu in the large N limit. We exhibit the salient features of this state and confirm that it solves the relativistic time-dependent Hartree-Fock equations. We then solve the scattering problem of two breathers with arbitrary internal parameters and velocities, generalizing an ansatz recently developed for the baryon-baryon scattering problem in the same model. The exact analytical solution is given and illustrated with a few examples.
We use the large $N$ critical point formalism to compute $d$-dimensional critical exponents at several orders in $1/N$ in an Ising Gross-Neveu universality class where the core interaction includes a Lie group generator. Specifying a particular symmetry group or taking the abelian limit of the final exponents recovers known results but also provides expressions for any Lie group or fermion representation.
Recently it was shown that kink baryons and kink-antikink scattering in the massless Gross-Neveu model are closely related to one- and two-soliton solutions of the sinh-Gordon equation. Here we generalize these findings to the case of n kinks and antikinks. Using the known n soliton solution of the sinh-Gordon equation, we solve the general n kink-antikink scattering problem in the large N Gross-Neveu model analytically, mapping the time-dependent Hartree-Fock approach onto inverse scattering theory.
We consider a version of the Gross-Neveu model in 1+1 dimensions with discrete chiral and continuous flavor symmetry (isospin). In 2+1 dimensions, this model is known as chiral Heisenberg Gross-Neveu model. Spontaneous symmetry breaking and the emergence of two massless and one massive scalar bosons are shown. A duality to the Nambu--Jona-Lasinio model with isospin is exhibited, provided that the isovector pseudoscalar mean field is constrained to a plane in isospin space. This enables us to find the phase diagram as a function of temperature, chemical potential and isospin chemical potential …
We calculate the anomalous dimensions of higher-spin currents, both singlet and non-singlet, in the Gross-Neveu model at the $1/n^2$ order. It was conjectured that in the critical regime this model is dual to a higher-spin gauge theory on $AdS_4$. The $AdS/CFT$ correspondence predicts that the masses of higher-spin fields correspond to the scaling dimensions of the singlet currents in the Gross-Neveu model.
We reconsider the two-flavor version of the massive, chiral Gross-Neveu model in 1+1 dimensions. Its phase diagram as a function of baryon chemical potential, isospin chemical potential and temperature has previously been explored. We recapitulate the results, adding the missing tricritical curves. They can be determined exactly by extending the standard stability analysis, using fourth order almost degenerate perturbation theory. Results for three different bare masses are presented and discussed.
