Massive QFT Research Articles

Induced actions for higher spin fields

We have calculated two-point correlators of higher spin currents, with spins up to six, in free massive QFT’s with scalar and Dirac fields in D = 3,4,5,6 spacetime dimensions. The infrared and ultraviolet limits are analysed, with the motivation for improving our understanding of the interacting higher spin theories.

The S-matrix bootstrap II: two dimensional amplitudes

We consider constraints on the S-matrix of any gapped, Lorentz invariant quantum field theory in 1 + 1 dimensions due to crossing symmetry and unitarity. In this way we establish rigorous bounds on the cubic couplings of a given theory with a fixed mass spectrum. In special cases we identify interesting integrable theories saturating these bounds. Our analytic bounds match precisely with numerical bounds obtained in a companion paper where we consider massive QFT in an AdS box and study boundary correlators using the technology of the conformal bootstrap.

Equilibration and GGE in interacting-to-free quantum quenches in dimensions

Ground states ofinteracting QFTs are non-Gaussian states, i.e. their connected n-point correlation functions do not vanish for , in contrast to the free QFT case. We show that, when the ground state of an interacting QFT evolves under a free massive QFT for a long time (a scenario that can be realised by a quantum quench), the connected correlation functions decay and all local physical observables equilibrate to values that are given by a Gaussian density matrix that retains memory only of the two-point initial correlation function. The argument hinges upon the fundamental physical principle of cluster decomposition, which is valid for the ground state of a general QFT. An analogous result was already known to be valid in the case of d = 1 spatial dimensions, where it is a special case of the so-called generalised Gibbs ensemble (GGE) hypothesis, and we now generalise it to higher dimensions. Moreover, in the case of massless free evolution, despite the fact that the evolution may lead not to equilibration but instead to unbounded increase of correlations with time, the GGE gives correctly the leading-order asymptotic behaviour of correlation functions in the thermodynamic and large time limit. The demonstration is performed in the context of a bosonic relativistic QFT, but the arguments apply more generally.

Integrable structure of Quantum Field Theory: classical flat connections versus quantum stationary states

We establish a correspondence between an infinite set of special solutions of the (classical) modified sinh-Gordon equation and a set of stationary states in the finite-volume Hilbert space of the integrable 2D QFT invented by V.A. Fateev. The modified sinh-Gordon equation arise in this case as a zero-curvature condition for a class of multivalued connections of the punctured Riemann sphere, similarly to Hitchin's self-duality equations. The proposed correspondence between the classical and quantum integrable systems provides a powerful tool for deriving functional and integral equations which determine the full spectrum of local integrals of motion for massive QFT in a finite volume. Potential applications of our results to the problem of non-perturbative quantization of classically integrable non-linear sigma models are briefly discussed.

Bi-partite Entanglement Entropy in Massive QFT with a Boundary: the Ising Model

In this paper we give an exact infinite-series expression for the bi-partite entanglement entropy of the quantum Ising model both with a boundary magnetic field and in infinite volume. This generalizes and extends previous results involving the present authors for the bi-partite entanglement entropy of integrable quantum field theories, which exploited the generalization of the form factor program to branch-point twist fields. In the boundary case, we isolate in a universal way the part of the entanglement entropy which is related to the boundary entropy introduced by Affleck and Ludwig, and explain how this relation should hold in more general QFT models. We provide several consistency checks for the validity of our form factor results, notably, the identification of the leading ultraviolet behaviour both of the entanglement entropy and of the two-point function of twist fields in the bulk theory, to a great degree of precision by including up to 500 form factor contributions.

Perturbative analysis of general renorm-group solutions in a massive case

General solutions of the renormalization group (RG) functional equations for a massive QFT as formulated by N. Bogoliubov and the present author in terms of a pole mass are considered. We represent them as a power expansion in the coupling constant and study the structure of the expansion coefficients. Explicit results for the effective coupling and one-argument functions in a massive one-coupling case are presented up to four- and three-loop order. Comparing them with an approximate solution of the massive RG differential equations obtained earlier allows us to get an explicit estimate of the accuracy of these solutions. An important consequence is the improvement of a two-loop RG massive solution for one-argument functions, e.g. the propagator amplitude or the moment of the structure functions. We discuss also the threshold behavior of this solution and the correspondence between the ultraviolet and threshold properties of perturbation coefficients. Our investigation was prompted by the problem of explicitly taking into account heavy quark masses in QCD. However the results obtained are important from a more general point of view for a discussion of the scheme dependence problem in QFT. The method used could also be of interest for RG applications in other fields within the situation with disturbed homogeneity, such as e.g. intermediate asymptotics in hydrodynamics, finite-size scaling in critical phenomena and the excluded volume problem in polymer theory.

Exact solution of the [formula omitted] lattice models

The exact solutions of the integrable lattice vertex models associated to the B n (1), D n (1), A 2n (2), A 2n−1 (2), D n (2) and E 6 (2) are presented. The free energies and excitation energies of these two-dimensional models are found as functions of the spectral and anisotropy parameters as well as the finite-size corrections yielding the central charges and conformal dimensions. These lattice models yield new massive QFT whose mass spectrum and S- matrix are obtained through the light-cone approach.

Yang-Baxter algebras, integrable theories and quantum groups

• The Yang-Baxter algebras (YBA) are introduced in a general framework stressing their power to exactly solve the lattice models associated to them. The algebraic Bethe Ansatz is developed as an eigenvector construction based on the YBA. The six-vertex model solution is given explicitely. • It is explained how these lattice models yield both solvable massive QFT and conformal models in appropriated scaling (continuous) limits within the lattice light-cone approach. This approach permit to define and solve rigorously massive QFT as an appropriate continuum limit of gapless vertex models. • The deep links between the YBA and Lie algebras are analyzed including the quantum groups that underly the trigonometric/hyperbolic YBA. Braid and quantum groups are derived from trigonometric/hyperbolic YBA in the limit of infinite spectral parameter. • To conclude, some recent developments in the domain of integrable theories are summarized.

Exact solution of the A(2)nlattice models

The exact solution of the A(2)n integrable lattice models is presented. The free energy and excitation energies of the vertex models are found as functions of the spectral and anisotropy parameters as well as the finite-size corrections yielding the central charges and conformal dimensions. These lattice models yield a new massive QFT where the mass spectrum and the S-matrix are obtained through the light-cone approach. The ground state and excitation energies of a new anisotropic spin-one integrable chain associated to the A(2)2 model are computed.

Yang-Baxter algebras and quantum groups

Integrable massive QFT and conformal invariant models follow from lattice integrable models in suitable scaling limits. There are Yang-Baxter algebras (YBA) associated with all these two-dimensional models. These YBA allow one to construct the exact solution (spectrum, S-matrix, form-factors,…) for this class of theories. Braid groups and quantum groups are derived as limiting cases of YBA when θ (spectral parameter) goes to ±∞.

YANG-BAXTER ALGEBRAS, INTEGRABLE THEORIES AND BETHE ANSATZ

The Yang-Baxter algebras (YBA) are introduced in a general framework stressing their power to exactly solve the lattice models associated to them. The algebraic Bethe Ansatz is developed as an eigenvector construction based on the YBA. The six-vertex model solution is given explicitly. The generalization of YB algebras to face language is considered. The algebraic BA for the SOS model of Andrews, Baxter and Forrester is described using these face YB algebras. It is explained how these lattice models yield both solvable massive QFT and conformal models in appropiated scaling (continuous) limits within the lattice light-cone approach. This approach permit to define and solve rigorously massive QFT as an appropiate continuum limit of gapless vertex models. The deep links between the YBA and Lie algebras are analyzed including the quantum groups that underly the trigonometric/hyperbolic YBA. Braid and quantum groups are derived from trigonometric/hyperbolic YBA in the limit of infinite spectral parameter. To conclude, some recent developments in the domain of integrable theories are summarized.