L. Palla

Grand unified schemes and spontaneous compactification

Abstract The mass spectrum of spontaneously compactified Einstein-Yang-Mills theories is computed using the Wu-Yang monopole harmonic functions. It is found that spontaneous compactification can be used to provide the correct mass scale generating the superstrong symmetry breaking which, in grand unified theories, separates quarks from leptons.

Exact multimonopole solutions in the Bogomolny-Prasad-Sommerfied limit

Abstract A systematic method for generating axially symmetric multimonopole solutions is presented. The Bogomolny-Prasad-Sommerfield one monopole and a new doubly charged monopole are obtained via Harrisons Backlund transformation.

A new family of SU(2) symmetric integrable sigma models

Abstract Local Lagrangians are derived for a class of SU (2) invariant sigma models admitting two commuting Kac-Moody algebras at the level of Poisson brackets. The one-loop renormalizability of these models is established. Some hueristic arguments are presented in favour of their quantum integrability.

Spontaneous compactification and “monopoles” in higher dimensions

Abstract Using the Wu-Yang global gauge description, the minimal gauge group is found which compactifies the extra even D dimensions into a sphere, namely SO(2N). These gauge theory solutions are associated with non-vanishing topological charges. An SO(2N) gauge theory solutions is obtained in D = 2N + 1 dimensions which describes a generalized singular magnetic monopole which conforms to the Yang definition.

Chiral extensions of the WZNW phase space, Poisson-Lie symmetries and groupoids

The chiral WZNW symplectic form Ωρchir is inverted in the general case. Thereby a precise relationship between the arbitrary monodromy dependent 2-form appearing in Ωρchir and the exchange r-matrix that governs the Poisson brackets of the group valued chiral fields is established. The exchange r-matrices are shown to satisfy a new dynamical generalization of the classical modified Yang–Baxter (YB) equation and Poisson–Lie (PL) groupoids are constructed that encode this equation analogously as PL groups encode the classical YB equation. For an arbitrary simple Lie group G, exchange r-matrices are found that are in one-to-one correspondence with the possible PL structures on G and admit them as PL symmetries.

Non-linear superposition of monopoles

Abstract With the aid of Backlund transformations we construct exact multimonopole solutions of the axially and mirror symmetric Bogomolny equations. The explicit form of the length of the Higgs field is given and is studied both analytically and numerically. The energy density for monopoles with charges 2, 3, 5 is also calculated.

Conformal properties of Chern-Simons vortices in external fields

The construction and the symmetries of Chern-Simons vortices in harmonic and uniform magnetic force backgrounds found by Ezawa, Hotta, and Iwazaki and by Jackiw and Pi are generalized using the nonrelativistic Kaluza-Klein-type framework presented in our previous paper. All Schroedinger-symmetric backgrounds are determined.

Conformal symmetry of the coupled Chern-Simons and gauged nonlinear Schrödinger equations

Abstract The non-relativistic conformal symmetry found by Jackiw and Pi for the coupled Chern-Simons and gauged nonlinear Schrodinger equations in the plane is derived in a non-relativistic Kaluza-Klein framework.

Nonperturbative study of the two-frequency sine-Gordon model

Abstract The two-frequency sine-Gordon model is examined. The focus is mainly on the case when the ratio of the frequencies is 1/2, given the recent interest in the literature. We discuss the model both in a perturbative (form factor perturbation theory) and a nonperturbative (truncated conformal space approach) framework, and give particular attention to a phase transition conjectured earlier by Delfino and Mussardo. We give substantial evidence that the transition is of second order and that it is in the Ising universality class. Furthermore, we check the UV-IR operator correspondence and conjecture the phase diagram of the theory.

The k -folded sine-Gordon model in finite volume

Abstract We consider the k -folded sine-Gordon model, obtained from the usual version by identifying the scalar field after k periods of the cosine potential. We examine (1) the ground state energy split, (2) the lowest lying multi-particle state spectrum and (3) vacuum expectation values of local fields in finite spatial volume, combining the Truncated Conformal Space Approach, the method of the Destri–de Vega nonlinear integral equation (NLIE) and semiclassical instanton calculations. We show that the predictions of all these different methods are consistent with each other and in particular provide further support for the NLIE method in the presence of a twist parameter. It turns out that the model provides an optimal laboratory for examining instanton contributions beyond the dilute instanton gas approximation. We also provide evidence for the exact formula for the vacuum expectation values conjectured by Lukyanov and Zamolodchikov.