Research Project PI14

Title: Nonperturbative Dynamics in Gauge Theories and in String Theory


The research group PI14 aims to contribute with original scientific work
to the understanding of some of the key dynamical issues occurring in
the field-theoretic and string-theoretic models of fundamental
interactions. We address ourselves mainly to those areas of theoretical
physics, whose importance grew considerably recently, where string,
gravity and gauge-field theories make contact, inspiring each other,
providing surprising and exact solutions of one or another, and giving
important hints about the nonperturbative properties of each of these.

Indeed, within the recent developments in string theory, there are
the gauge-gravity correspondences (such as AdS/CFT) that allow one
to derive exact results in strongly interacting gauge theories by looking at
string theories in the perturbative regime. On the other side, computations
in gauge or in topological theories are instrumental in verifying conjectures
about string dynamics and the string dualities.

The understanding of the nonperturbative, dynamical properties is
mandatory for Quantum Chromodynamics, the theory of the strong
interactions, and for the composite models of "elementary particles";
for describing black holes in quantum gravity and for finding the correct
vacuum state of string theory. There are common key concepts and
ingredients, which appear in many different guises in the diverse set
of problems covered by our research group, but which truly unify and
characterize our project. Namely, there are the concept of solitons and
their quantum behaviors, of instantons and moduli space; the topics of
sigma models, topological field theories and matrix models; the chiral
(holomorphic) properties of supersymmetric gauge theories and
conformal field theories.

More concretely, the research themes proposed will include the
following problems:


- Study of quantum behavior of solitons in gauge theories; confinement
and dynamical symmetry breaking;
- Conformal and superconformal field theories, Liouville theory;
- Instanton calculus in N=2, N=4 supersymmetric gauge theories;
- AdS-CFT correspondence and gauge-string (or supergravity) duality;
- Topological strings and topological sigma models;
- Gauge theories and matrix models at Large N;
- Exact renormalization group;
- Open string field theory at the tachyonic vacuum.

We intend to promote a synergy of researchers expert in different fields,
exchange of information, promote interactions among experts, young
researchers and graduate students. As a part of our general strategy of
collaborations, we plan to organize a Workshop in Pisa, in June 2007.

We intend to continue to organize further exchange of visits, seminars,
and small workshops. In particular, we wish to create occasions of
discussions and for effective collaborations among the members of the
collaboration.

The research projects for different groups are:

(i) Study of nonabelian monopoles, vortices and their roles in
confinement and/or dynamical symmetry breaking; Study of mixed
monopole- vortex, vortex-wall configurations. Semilocal vortices,
Localization on the moduli space of vortices, Confinement mechanism
in QCD. (PI, PD, PR, RM2, TS groups);

(ii) Study of nonabelian Argyres-Douglas vacua (SCFT) and confinement (PI);

(iii) Study of multi-instanton effects in string theories and in 4D
supersymmetric gauge theories, Instanton effects in N=1 supersymmetric
gauge theories (RM2, PD, PI, TS groups);

(iv) Analysis of gauge theories in noncommutative / non-anticommutative
spacetimes, Use of noncommutative localization techniques to compute
Donaldson invariants (PR, FI, PD, TS groups);

(v) Use of large N_c techniques; exploration of the idea of planar
equivalence between N=0 and N=1 super Yang-Mills theories (FI, PR, MI groups);

Besides these main themes of research, our activities will be further
complemented and enriched by the work covering the following research f
fields:

(vi) Study of tachyon condensation in string theory (TN group),
Unitarity in string theory (PD, TS group);

(vii) Topological field theories and strings (PD,TS groups);

(viii) Low-dimensional gravity, CFT, Relation to BFKL equations (FI,PD groups)

(ix) Random matrices, Matrix quantum mechanics (MI, PR groups)

-----

For more details about the scientific activities, results obtained and
future projects of each subgroups, see Rapporto Attività .