On Form Factors in nested Bethe Ansatz systems

We investigate form factors of local operators in the multi-component Quantum Non-linear Schr\"odinger model, a prototype theory solvable by the so-called nested Bethe Ansatz. We determine the analytic properties of the infinite volume form factors using the coordinate Bethe Ansatz solution and we establish a connection with the finite volume matrix elements. In the two-component models we derive a set of recursion relations for the "magnonic form factors", which are the matrix elements on the nested Bethe Ansatz states. In certain simple cases (involving states with only one spin-impurity) we obtain explicit solutions for the recursion relations.Comment: 34 pages, v2 (minor modifications

Form factor expansion for thermal correlators

We consider finite temperature correlation functions in massive integrable Quantum Field Theory. Using a regularization by putting the system in finite volume, we develop a novel approach (based on multi-dimensional residues) to the form factor expansion for thermal correlators. The first few terms are obtained explicitly in theories with diagonal scattering. We also discuss the validity of the LeClair-Mussardo proposal.Comment: 41 pages; v2: minor corrections, v3: minor correction

Determining matrix elements and resonance widths from finite volume: the dangerous mu-terms

The standard numerical approach to determining matrix elements of local operators and width of resonances uses the finite volume dependence of energy levels and matrix elements. Finite size corrections that decay exponentially in the volume are usually neglected or taken into account using perturbation expansion in effective field theory. Using two-dimensional sine-Gordon field theory as "toy model" it is shown that some exponential finite size effects could be much larger than previously thought, potentially spoiling the determination of matrix elements in frameworks such as lattice QCD. The particular class of finite size corrections considered here are mu-terms arising from bound state poles in the scattering amplitudes. In sine-Gordon model, these can be explicitly evaluated and shown to explain the observed discrepancies to high precision. It is argued that the effects observed are not special to the two-dimensional setting, but rather depend on general field theoretic features that are common with models relevant for particle physics. It is important to understand these finite size corrections as they present a potentially dangerous source of systematic errors for the determination of matrix elements and resonance widths.Comment: 26 pages, 13 eps figures, LaTeX2e fil

One-point functions in massive integrable QFT with boundaries

We consider the expectation value of a local operator on a strip with non-trivial boundaries in 1+1 dimensional massive integrable QFT. Using finite volume regularisation in the crossed channel and extending the boundary state formalism to the finite volume case we give a series expansion for the one-point function in terms of the exact form factors of the theory. The truncated series is compared with the numerical results of the truncated conformal space approach in the scaling Lee-Yang model. We discuss the relevance of our results to quantum quench problems.Comment: 43 pages, 20 figures, v2: typos correcte

Causal effective field theories

Physical principles such as unitarity, causality, and locality can constrain the space of consistent effective field theories (EFTs) by imposing two-sided bounds on the allowed values of Wilson coefficients. In this paper, we consider the bounds that arise from the requirement of low energy causality alone, without appealing to any assumptions about UV physics. We focus on shift-symmetric theories, and consider bounds that arise from the propagation around both a homogeneous and a spherically symmetric scalar field background. We find that low energy causality, namely the requirement that there are no resolvable time advances within the regime of validity of the EFT, produces two-sided bounds in agreement with compact positivity constraints previously obtained from 2 → 2 scattering amplitude dispersion relations using full crossing symmetry

Cosmology of extended proca-nuevo

Proca-Nuevo is a non-linear theory of a massive spin-1 field which enjoys a non-linearly realized constraint that distinguishes it among other generalized vector models. We show that the theory may be extended by the addition of operators of the Generalized Proca class without spoiling the primary constraint that is necessary for consistency, allowing to interpolate between Generalized Proca operators and Proca-Nuevo ones. The constraint is maintained on flat spacetime and on any fixed curved background. Upon mixing extended Proca-Nuevo dynamically with gravity, we show that the constraint gets broken in a Planck scale suppressed way. We further prove that the theory may be covariantized in models that allow for consistent and ghost-free cosmological solutions. We study the models in the presence of perfect fluid matter, and show that they describe the correct number of dynamical variables and derive their dispersion relations and stability criteria. We also exhibit, in a specific set-up, explicit hot Big Bang solutions featuring a late-time self-accelerating epoch, and which are such that all the stability and subluminality conditions are satisfied and where gravitational waves behave precisely as in General Relativity

Highest coefficient of scalar products in SU(3)-invariant integrable models

We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. Scalar products of Bethe vectors in such models can be expressed in terms of a bilinear combination of their highest coefficients. We obtain various different representations for the highest coefficient in terms of sums over partitions. We also obtain multiple integral representations for the highest coefficient.Comment: 17 page

To half-be or not to be?

It has recently been argued that half degrees of freedom could emerge in Lorentz and parity invariant field theories, using a non-linear Proca field theory dubbed Proca-Nuevo as a specific example. We provide two proofs, using the Lagrangian and Hamiltonian pictures, that the theory possesses a pair of second class constraints, leaving D − 1 degrees of freedom in D spacetime dimensions, as befits a consistent Proca model. Our proofs are explicit and straightforward in two dimensions and we discuss how they generalize to an arbitrary number of dimensions. We also clarify why local Lorentz and parity invariant field theories cannot hold half degrees of freedom

R\ue9nyi entropies of generic thermodynamic macrostates in integrable systems

We study the behaviour of R\ue9nyi entropies in a generic thermodynamic macrostate of an integrable model. In the standard quench action approach to quench dynamics, the R\ue9nyi entropies may be derived from the overlaps of the initial state with Bethe eigenstates. These overlaps fix the driving term in the thermodynamic Bethe ansatz (TBA) formalism. We show that this driving term can be also reconstructed starting from the macrostate's particle densities. We then compute explicitly the stationary R\ue9nyi entropies after the quench from the dimer and the tilted N\ue9el state in XXZ spin chains. For the former state we employ the overlap TBA approach, while for the latter we reconstruct the driving terms from the macrostate. We discuss in full detail the limits that can be analytically handled and we use numerical simulations to check our results against the large time limit of the entanglement entropies

Entanglement Dynamics after a Quench in Ising Field Theory: A Branch Point Twist Field Approach

We extend the branch point twist field approach for the calculation of entanglement entropies to time-dependent problems in 1+1-dimensional massive quantum field theories. We focus on the simplest example: a mass quench in the Ising field theory from initial mass m0 to final mass m. The main analytical results are obtained from a perturbative expansion of the twist field one-point function in the post-quench quasi-particle basis. The expected linear growth of the Rényi entropies at large times mt ≫ 1 emerges from a perturbative calculation at second order. We also show that the Rényi and von Neumann entropies, in infinite volume, contain subleading oscillatory contributions of frequency 2m and amplitude proportional to (mt)−3/2. The oscillatory terms are correctly predicted by an alternative perturbation series, in the pre-quench quasi-particle basis, which we also discuss. A comparison to lattice numerical calculations carried out on an Ising chain in the scaling limit shows very good agreement with the quantum field theory predictions. We also find evidence of clustering of twist field correlators which implies that the entanglement entropies are proportional to the number of subsystem boundary points