Topology and theta-dependence in QCD and QCD-like theories from the lattice

by Claudio Bonanno (PI)


The study of topology and theta-dependence is of utmost importance for its theoretical and phenomenological implications for the Standard Model and beyond. For instance, axion physics at early times of the Universe evolution is related to the theta-dependence of QCD at high temperatures, while theta-dependence of SU(N) pure-gauge theories is related to the U(1)_A anomaly and to the eta prime meson physics in the large-N limit. In my talk I will present new results obtained about topology and theta-dependence adopting the lattice approach. First, I will discuss the spectral projectors definition of the topological charge on the lattice and will test it in the quenched case. This method allows to obtain a theoretically well-defined lattice fermion definition whose scaling towards the continuum limit can be controlled through the cut-off of the spectral sums. Then, I will present lattice studies, achieved with a newly-proposed algorithm, of the large-N limit of 4d SU(N) gauge theories and of 2d CP(N-1) models, underlining analogies and differences. In particular, I will show that, while the large-N expected scaling of 4d SU(N) gauge theories already holds for N>2, for 2d CP(N-1) models the convergence of the 1/N series is very slow and plagued by large higher-order corrections.  Finally, I will present results about the small-N limit of 2d CP(N-1) models, whose pathological critical behavior around N=2 could be the origin of the slow convergence of the 1/N series at large N.