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Abstract We investigate Q-balls in a 1+1 dimensional complex scalar field theory. We find that the relaxation of a squashed Q-ball is dominated by the decay of a normal mode through nonlinear coupling to scattering modes and a long-lasting quasi-normal mode. We also study how these Q-balls behave when exposed to scalar radiation, finding that for certain conditions they can experience negative radiation pressure.

Abstract Recently we showed how, in two-dimensional scalar theories, one-loop threshold diagrams can be cut into the product of one or more tree-level diagrams [1]. Using this method on the ADE series of Toda models, we computed the double- and single-pole coefficients of the Laurent expansion of the S-matrix around a pole of arbitrary even order, finding agreement with the bootstrapped results. Here we generalise the cut method explained in [1] to multiple loops and use it to simplify large networks of singular diagrams. We observe that only a small number of cut diagrams survive and contribute to the expected bootstrapped result, while most of them cancel each other out through a mechanism inherited from the tree-level integrability of these models. The simplification mechanism between cut diagrams inside networks is reminiscent of Gauss’s theorem in the space of Feynman diagrams.

Abstract We investigate soliton collisions in a one-parameter family of scalar field theories in 1+1 dimensions which was first discussed by Christ and Lee [1]. The models have a sextic potential with three local minima, and for suitably small values of the parameter their kinks have an internal structure in the form of two weakly-bound subkinks. We show that for these values of the parameter kink collisions are best understood as an independent sequence of collisions of these subkinks, and that a static mode analysis is not enough to explain resonant structures emerging in this model. We also emphasise the role of radiation and oscillon formation in the collision process.

Abstract Various features of the even order poles appearing in the S-matrices of simply-laced affine Toda field theories are analysed in some detail. In particular, the coefficients of first- and second-order singularities appearing in the Laurent expansion of the S-matrix around a general 2N th order pole are derived in a universal way using perturbation theory at one loop. We show how to cut loop diagrams contributing to the pole into particular products of tree-level graphs that depend on the on-shell geometry of the loop; in this way, we recover the coefficients of the Laurent expansion around the pole exploiting tree-level integrability properties of the theory. The analysis is independent of the particular simply-laced theory considered, and all the results agree with those obtained in the conjectured bootstrapped S-matrices of the ADE series of theories.

Abstract We investigate the perturbative integrability of massive (1+1)-dimensional bosonic quantum field theories, focusing on the conditions for them to have a purely elastic S-matrix, with no particle production and diagonal scattering, at tree level. For theories satisfying what we call ‘simply-laced scattering conditions’, by which we mean that poles in inelastic 2 to 2 processes cancel in pairs, and poles in allowed processes are only due to one on-shell propagating particle at a time, the requirement that all inelastic amplitudes must vanish is shown to imply the so-called area rule, connecting the 3-point couplings C abc 3 $$ {C}_{abc}^{(3)} $$ to the masses m a , m b , m c of the coupled particles in a universal way. We prove that the constraints we find are universally satisfied by all affine Toda theories, connecting pole cancellations in amplitudes to properties of the underlying root systems, and develop a number of tools that we expect will be relevant for the study of loop amplitudes.

Abstract We study kink-antikink collisions in a model which interpolates smoothly between the completely integrable sine-Gordon theory, the ϕ 4 model, and a ϕ 6-like model with three degenerate vacua. We find a rich variety of behaviours, including integrability breaking, resonance windows with increasingly irregular patterns, and new types of windows near the ϕ 6-like regime. False vacua, extra kink modes and kink fragmentation play important roles in the explanations of these phenomena. Our numerical studies are backed up by detailed analytical considerations.

We study the decay of large amplitude, almost periodic breather-like states in a deformed sine-Gordon model in one spatial dimension. We discover that these objects decay in a staggered fashion via a series of transitions, during which higher harmonics are released as short, staccato bursts of radiation. Further, we argue that this phenomenon is not restricted to one particular model, and that similar mechanisms of radiative decay of long-lived oscillating states can be observed for a wide class of physical systems, including the ϕ6 model.

We investigate the role that quasinormal modes can play in kink–antikink collisions, via an example based on a deformation of the ϕ4 model. We find that narrow quasinormal modes can store energy during collision processes and later return it to the translational degrees of freedom. Quasinormal modes also decay, which leads to energy leakage, causing a closing of resonance windows and an increase of the critical velocity. We observe similar phenomena in an effective model, a small modification of the collective-coordinate approach to the ϕ4 model. Keywords: Kink collisions, Fractals, Quasinormal modes

Abstract We study boundary scattering in the ϕ 4 model on a half-line with a oneparameter family of Neumann-type boundary conditions. A rich variety of phenomena is observed, which extends previously-studied behaviour on the full line to include regimes of near-elastic scattering, the restoration of a missing scattering window, and the creation of a kink or oscillon through the collision-induced decay of a metastable boundary state. We also study the decay of the vibrational boundary mode, and explore different scenarios for its relaxation and for the creation of kinks.

This paper reviews a recently discovered link between integrable quantum field theories and certain ordinary differential equations in the complex domain. Along the way, aspects of -symmetric quantum mechanics are discussed, and some elementary features of the six-vertex model and the Bethe ansatz are explained. [ABSTRACT FROM AUTHOR]

We explore boundary scattering in the sine-Gordon model with a non-integrable family of Robin boundary conditions. The soliton content of the field after collision is analysed using a numerical implementation of the direct scattering problem associated with the inverse scattering method. We find that an antikink may be reflected into various combinations of an antikink, a kink, and one or more breathers, depending on the values of the initial antikink velocity and a parameter associated with the boundary condition. In addition we observe regions with an intricate resonance structure arising from the creation of an intermediate breather whose recollision with the boundary is highly dependent on the breather phase. [ABSTRACT FROM AUTHOR]

We study a three-parameter family of \mathcal {PT} -symmetric Hamiltonians, related via the ODE/IM correspondence to the Perk-Schultz models. We show that real eigenvalues merge and become complex at quadratic and cubic exceptional points, and explore the corresponding Jordan block structures by exploiting the quasi-exact solvability of a subset of the models. The mapping of the phase diagram is completed using a combination of numerical, analytical and perturbative approaches. Among other things this reveals some novel properties of the Bender-Dunne polynomials, and gives new insight into a phase transition to infinitely many complex eigenvalues that was first observed by Bender and Boettcher. A new exactly solvable limit, the inhomogeneous complex square well, is also identified. [ABSTRACT FROM AUTHOR]

Within the framework of the ODE/IM correspondence, we show that the minimal conformal field theories with c < 1 emerge naturally from the monodromy properties of certain families of ordinary differential equations. [ABSTRACT FROM AUTHOR]