Quantum Field Theory, Lattice and Strings
Welcome to the web pages of the section Quantum Field theory, Lattice Field Theory and Strings at the Department of Physics and Earth Sciences.
Our research activities are mainly focused on the investigation of the structural and mathematical properties of Quantum Field Theories and their extension as String Theories and of the lattice formulation of Quantum Chromodynamics (and its accurate study through numerical simulations) . The group consists of members also involved in the local INFN Group (Gruppo Collegato di Parma, Sezione Milano Bicocca LINK INFN PAGE). They belong to INFN projects (iniziative specifiche) GAST and QCDLAT.
Detailed descriptions can be found in the personal web pages linked in the left column.
Quantum Field Theories, Supersymmetry and Cosmology
The development of nonperturbative methods to extract informations from the strong coupling regime of Quantum Field Theories (QFT) still represents a challenging problem. In particular it lacks an analytical description of important aspects of gauge theories, as the confinement of quarks or the phase structure of quantum chromodynamics. At the same time a "natural" formulation of the physics beyond the Standard Model would require a new symmetry, exchanging fermions and bosons, known as Supersymmetry. Supersymmetry provides also a favorable arena in which to study, in a simplified context, the mentioned longstanding problems, due to the severe constraints imposed by its deep mathematical structure. We study non perturbative analytical approaches to QFT, in supersymmetric and nonsupersymmetric models, using methods and advanced mathematical techniques inspired by supersymmetry (as localization of pathintegrals, integrability, matrix models) and also the related perturbative aspects in scattering amplitudes, Wilson loops and correlation functions of composite operators. Furthermore applications of QFT techniques to cosmology are considered and, more generally, the study of CMB spectrum in this context is under examination. 

Lattice Field Theory
The theory of strong interactions, Quantum Chromodynamics (QCD), describes in principle the bound states among quarks as protons, neutrons, mesons and all the interactions of hadronic matter. While its highenergy regime can be analytically explored (and successfully tested in the accelerators) through perturbation theory, its lowenergy predictions (among them the masses and interactions of hadrons), still represent a challenging problem. Lattice Field Theory is the most powerful approach in this context: spacetime is discretized on a lattice and QCD (or any other QFT) is described a statistical system, viable for numerical simulations on supercomputers. While this approach is able to capture many aspects of QCD, ranging from the masses of mesons, interaction potentials, nonperturbative matrix elements, thermodynamical properties, its effective application needs the use of heavy computer simulations, specific numerical codes and dedicated computer architectures. We have a long expertise on these topics, starting from the eighties, and we study, in particular, the phase diagram of QCD, the vacuum structure and renormalization problems. A peculiar product of Parma group is the socalled Stochastic Perturbation Theory on Lattice that provides a powerful tool to explore the large order behavior of observables. More recently we have also developed mathematical and numerical methods to solve a longstanding problems, known a the sign problem, arising in presence of chemical potentials in QCD.


String theory and AdS/CFT correspondence
The quantization of gravity is probably the most elusive problem in modern high energy physics: the usual quantum field theoretical methods seem to fail when energies of the order of Planck scale are approached. A possible solution is represented by String Theory, where point particles appear as the lowenergy limit of fundamental onedimensional objects call "strings", whose excitations describe all the known elementary particles and include graviton. The quantum theory of strings is mathematically difficult and largely unknown but recently it has provided a number of tools to explore aspects of quantum gravity (black hole entropy) and of gauge theories (gauge/gravity duality). The famous AdS/CFT correspondence (and example of such duality) suggests to describe gauge theories in the strong coupling regime as weakly coupled gravitational systems and produced a large number of theoretical results. We study in this context the behavior of computable observables and their strong coupling limit: for example the potentials between particleantiparticle systems, scattering amplitudes, thermodynamical entropies and their gravitational dual description.
