Nonperturbative results for two-index conformal windows

Via large and small N c relations we derive nonperturbative results about the conformal window of two-index theories. Using Schwinger-Dyson methods as well as four-loops results we estimate subleading corrections and show that naive large number of colors extrapolations are unreliable when N c is less than about six. Nevertheless useful nonper-turbative inequalities for the size of the conformal windows, for any number of colors, can be derived. By further observing that the adjoint conformal window is independent of the number of colors we argue, among other things, that: the large N c two-index conformal window is twice the conformal window of the adjoint representation (which can be determined at small N c) expressed in terms of Dirac fermions; lattice results for adjoint matter can be used to provide independent information on the conformal dynamics of two-index theories such as SU(N c) with two and four symmetric Dirac flavors.

Casimir effect with quantized charged spinor matter in background magnetic field

We study the influence of a background uniform magnetic field and boundary conditions on the vacuum of a quantized charged spinor matter field confined between two parallel neutral plates; the magnetic field is directed orthogonally to the plates. The admissible set of boundary conditions at the plates is determined by the requirement that the Dirac Hamiltonian operator be self-adjoint. It is shown that, in the case of a sufficiently strong magnetic field and a sufficiently large separation of the plates, the generalized Casimir force is repulsive, being independent of the choice of a boundary condition, as well as of the distance between the plates. The detection of this effect seems to be feasible in the foreseeable future.

Comparison of different lattice definitions of the topological charge

We present a comparison of different definitions of the topological charge on the lattice, using a small-volume ensemble with 2 flavours of dynamical twisted mass fermions. The investigated definitions are: index of the overlap Dirac operator, spectral projectors, spectral flow of the HermitianWilson- Dirac operator and field theoretic with different kinds of smoothing of gauge fields (HYP and APE smearings, gradient flow, cooling). We also show some results on the topological susceptibility.