Gabor Zsolt Toth

The particle spectrum of the three-state Potts field theory: a numerical study

The three-state Potts field theory in two dimensions with thermal and magnetic perturbations provides the simplest model of confinement allowing for both mesons and baryons, as well as for an extended phase with deconfined quarks. We study numerically the evolution of the mass spectrum of this model over its whole parameter range, obtaining a pattern of confinement, particle decay and phase transitions which confirms recent predictions.

Numerical investigation of the late-time Kerr tails

The late-time behavior of a scalar field on fixed Kerr background is examined in a numerical framework incorporating the techniques of conformal compactification and hyperbolic initial value formulation. The applied code is 1+(1+2) as it is based on the use of the spectral method in the angular directions while in the time-radial section fourth order finite differencing, along with the method of lines, is applied. The evolution of various types of stationary and non-stationary pure multipole initial states are investigated. The asymptotic decay rates are determined not only in the domain of outer communication but along the event horizon and at future null infinity as well. The decay rates are found to be different for stationary and non-stationary initial data, and they also depend on the fall off properties of the initial data toward future null infinity. The energy and angular momentum transfers are found to show significantly different behavior in the initial phase of the time evolution. The quasinormal ringing phase and the tail phase are also investigated. In the tail phase, the decay exponents for the energy and angular momentum losses at are found to be smaller than at the horizon which is in accordance with the behavior of the field itself and it means that at late times the energy and angular momentum falling into the black hole become negligible in comparison with the energy and angular momentum radiated toward . The energy and angular momentum balances are used as additional verifications of the reliability of our numerical method.

Weak cosmic censorship, dyonic Kerr–Newman black holes and Dirac fields

It was investigated recently, with the aim of testing the weak cosmic censorship conjecture, whether an extremal Kerr black hole can be converted into a naked singularity by interaction with a massless classical Dirac test field, and it was found that this is possible. We generalize this result to electrically and magnetically charged rotating extremal black holes (i.e. extremal dyonic Kerr– Newman black holes) and massive Dirac test fields, allowing magnetically or electrically uncharged or nonrotating black holes and the massless Dirac field as special cases. We show that the possibility of the conversion is a direct consequence of the fact that the Einstein–Hilbert energy-momentum tensor of the classical Dirac field does not satisfy the null energy condition, and is therefore not in contradiction with the weak cosmic censorship conjecture. We give a derivation of the absence of superradiance of the Dirac field without making use of the complete separability of the Dirac equation in dyonic Kerr–Newman background, and we determine the range of superradiant frequencies of the scalar field. The range of frequencies of the Dirac field that can be used to convert a black hole into a naked singularity partially coincides with the superradiant range of the scalar field. We apply horizon-penetrating coordinates, as our arguments involve calculating quantities at the event horizon. We describe the separation of variables for the Dirac equation in these coordinates, although we mostly avoid using it.

Test of the weak cosmic censorship conjecture with a charged scalar field and dyonic Kerr-Newman black holes

A thought experiment considered recently in the literature, in which it is investigated whether a dyonic Kerr–Newman black hole can be destroyed by overcharging or overspinning it past extremality by a massive complex scalar test field, is revisited. Another derivation of the result that this is not possible, i.e. the weak cosmic censorship is not violated in this thought experiment, is given. The derivation is based on conservation laws, on a null energy condition, and on specific properties of the metric and the electromagnetic field of dyonic Kerr–Newman black holes. The metric is kept fixed, whereas the dynamics of the electromagnetic field is taken into account. A detailed knowledge of the solutions of the equations of motion is not needed. The approximation in which the electromagnetic field is fixed is also considered, and a derivation for this case is also given. In addition, an older version of the thought experiment, in which a pointlike test particle is used, is revisited. The same result, namely the non-violation of the cosmic censorship, is rederived in a way which is simpler than in earlier works.

Reformulating the TBA equations for the quark anti-quark potential and their two loop expansion

A bstractThe boundary thermodynamic Bethe Ansatz (BTBA) equations introduced in [1, 2] to describe the cusp anomalous dimension contain imaginary chemical potentials and singular boundary fugacities, which make its systematic expansion problematic. We propose an alternative formulation based on real chemical potentials and additional source terms. We expand our equations to double wrapping order and find complete agreement with the direct two-loop gauge theory computation of the cusp anomalous dimension.

Exact Mass-Coupling Relation for the Homogeneous Sine-Gordon Model

We derive the exact mass-coupling relation of the simplest multiscale quantum integrable model, i.e., the homogeneous sine-Gordon model with two mass scales. The relation is obtained by comparing the perturbed conformal field theory description of the model valid at short distances to the large distance bootstrap description based on the models integrability. In particular, we find a differential equation for the relation by constructing conserved tensor currents, which satisfy a generalization of the Θ sum rule Ward identity. The mass-coupling relation is written in terms of hypergeometric functions.

Higher spin fields with reversed spin-statistics relation

A construction of massive free fields with arbitrary spin and reversed spin-statistics relation is presented. The main idea of the construction is to consider fields that transform according to representations of the Lorentz group that are doubled in comparison with the representations according to which normal (physical) fields transform. This allows the definition of opposite commutation properties for these fields, while the spin of the particles they describe remains unchanged. The correspondence established by the construction between fields obeying normal and reversed spin-statistics relation makes it possible to express e.g. the polarization states, (anti)commutators, or Feynman propagators of the latter fields in terms of those of the normal fields to which they correspond. The cases of the scalar and Dirac fields are discussed in additional detail.

Proposal to improve the behaviour of self-energy contributions to the S-matrix

A simple modification of the definition of the S-matrix is proposed. It is expected that the divergences related to nonzero self-energies are considerably milder with the modified definition than with the usual one. This conjecture is verified in a few examples using perturbation theory. The proposed formula is written in terms of the total Hamiltonian operator and a free Hamiltonian operator and is therefore applicable in any case when these Hamiltonian operators are known.

On the mass-coupling relation of multi-scale quantum integrable models

A bstractWe determine exactly the mass-coupling relation for the simplest multi-scale quantum integrable model, the homogenous sine-Gordon model with two independent mass-scales. We first reformulate its perturbed coset CFT description in terms of the perturbation of a projected product of minimal models. This representation enables us to identify conserved tensor currents on the UV side. These UV operators are then mapped via form factor perturbation theory to operators on the IR side, which are characterized by their form factors. The relation between the UV and IR operators is given in terms of the sought-for mass-coupling relation. By generalizing the Θ sum rule Ward identity we are able to derive differential equations for the mass-coupling relation, which we solve in terms of hypergeometric functions. We check these results against the data obtained by numerically solving the thermodynamic Bethe Ansatz equations, and find a complete agreement.

Projection operator approach to the quantization of higher spin fields

A general method to construct free quantum fields for massive particles of arbitrary definite spin in a canonical Hamiltonian framework is presented. The main idea of the method is as follows: a multicomponent Klein–Gordon field that satisfies canonical (anti)commutation relations and serves as an auxiliary higher spin field is introduced, and the physical higher spin field is obtained by acting on the auxiliary field by a suitable differential operator. This allows the calculation of the (anti)commutation relations, the Green functions and the Feynman propagators of the higher spin fields. In addition, canonical equations of motions, which are expressed in terms of the auxiliary variables, can be obtained also in the presence of interactions, if the interaction Hamiltonian operator is known. The fields considered transform according to the (n/2,m/2)⊕(m/2,n/2) and (n/2,m/2) representations of the Lorentz group.