Research

Beyond providing a consistent unified model of all fundamental interactions, in the last few years string theory has become also a powerful scheme to analyse and study field theories, and in particular gauge theories. In fact the latter can be engineered as the low-energy theories living on the world-volume of stacks of D-branes, which are also non-perturbative extended configurations of string theory with a non-trivial associated geometry. The direct interplay between open strings (i.e. gauge theories) and closed strings (i.e. (super)gravity) offered by the D-brane picture has been thoroughly exploited in recent times: several gauge/gravity dualities have been established, and remarkable results have been obtained both perturbatively and non-perturbatively. However, further progress is still needed. The research activity of this local unit will be devoted to some of the open problems in this field, but will touch also other related aspects of superstring theory, supergravity, branes and the associated geometry. In particular our research program will cover the following main themes:

- Study of the gauge/gravity correspondence for theories with reduced supersymmetry and without conformal invariance (more info)
- Study of the properties of instantons in supersymmetric gauge theories by means of D(-1) branes (more info)
- Study of deformed gauge theories and theories with fluxes (more info)
- Study of systems of branes at angles and of magnetized branes (more info)
- Study of the pure spinor string theory (more info)
- Study of the global structures in gauge theories with higher rank gauge potentials (more info)

- M. Billo, M. Frau, I. Pesando, A. Lerda, N=1/2 GAUGE THEORY AND ITS INSTANTON MODULI SPACE FROM OPEN STRINGS IN RR BACKGROUND JHEP 0405:023,2004;
- E. Imeroni, A. Lerda, NONPERTURBATIVE GAUGE SUPRPOTENTIALS FROM SUPERGRAVITY JHEP 0312:051,2003;
- M. Billo, M. Frau, I. Pesando, F. Fucito, A. Lerda, A. Liccardo, CLASSICAL GAUGE INSTANTONS FROM OPEN STRINGS JHEP 0302:045,2003;
- P. Di Vecchia, A. Lerda, P. Merlatti, N=1 AND N=2 SUPER YANG_MILLS THEORIES FROM WRAPPED BRANES Nucl.Phys.B646:43,2002;
- M. Bertolini, P. Di Vecchia, M. Frau, A. Lerda, R. Marotta, MORE ANOMALIES FROM FRACTIONAL BRANES Phys.Lett.B540:104,2002;
- M. Bertolini, P. Di Vecchia, M. Frau, A. Lerda, R. Marotta, N=2 GAUGE THEORIES ON SYSTEMS OF FRACTIONAL D3/D7 BRANES Nucl.Phys.B621:157,2002;
- M. Bertolini, P. Di Vecchia, M. Frau, A. Lerda, R. Marotta, I. Pesando, FRACTIONAL D-BRANES AND THEIR GAUGE DUALS JHEP 0102:014,2001;
- P. Di Vecchia, M. Frau, A. Lerda, A. Liccardo, (F,D(P))BOUND STATES FROM THE BOUNDARY STATE Nucl.Phys.B565:397,2000;
- M. Billo, P. Di Vecchia, M. Frau, A. Lerda, R. Russo, S. Sciuto, THE LORENTZ FORCE BETWEEN D0 AND D6-BRANES IN STRING AND M(ATRIX) THEORY Mod.Phys.Lett.A13:2977,1998;
- M. Billo, P. Di Vecchia, M. Frau, A. Lerda, I. Pesando, R. Russo, S. Sciuto MICROSCOPIC STRING ANALYSIS OF THE D0-D8 BRANE SYSTEM AND DUAL R-R STATES Nucl.Phys.B526:199,1998;
- P. Di Vecchia, M. Frau, A. Lerda, I. Pesando, R. Russo, S. Sciuto,CLASSICAL P-BRANES FROM BOUNDARY STATE Nucl.Phys.B507:259,1997;
- M. Frau, I. Pesando, S. Sciuto, A. Lerda, R. Russo, SCATTERING OF CLOSED STRINGS FROM MANY D-BRANES Phys.Lett.B400:52,1997;
- L. Castellani, C. Pagani, FINITE GROUP DISCRETIZATION OF YANG-MILLS AND EINSTEIN ACTIONS Annals Phys.297:295,2002;
- L. Castellani, L. Sommovigo, NEW ADS(3) X G/H COMPACTIFICATIONS OF CHIRAL IIB SUPERGRAVITY JHEP 0007:044,2000;
- L. Castellani, ON G/H GEOMETRY AND ITS USE IN M-THEORY COMPACTIFICATIONS Ann. of Phys. 287:1,2001;
- L. Castellani, GRAVITY ON FINITE GROUPS Commun. Math. Phys. 218:609, 2001;
- L. Castellani, A. Ceresole, R. D'Auria, S. Ferrara, P.Fre, M. Trigiante G/H M-BRANES AND ADS(P+2) GEOMETRIES Nucl.Phys. B527:142,1998;
- P. Aschieri, B. Jurco, GERBES, M5-BRANE ANOMALIES AND E_8 GAUGE THEORY JHEP 0410:068,2004;
- P. Aschieri, L. Cantini, B. Jurco, NONABELIAN BUNDLE GERBES, THEIR DIFFERENTIAL GEOMETRY AND GAUGE THEORY Commun. Math. Phys. 254:367, 2005;
- P. Aschieri, J. Madore, P. Manousselis, G. Zoupanos, DIMENSIONAL REDUCTION OVER FUZZY COSET SPACES JHEP 0404:034,2004;
- P. Aschieri, B. Jurco, P. Schupp, J. Wess, NONCOMMUTATIVE GUTS, STANDARD MODEL AND CPT Nucl.Phys. B651:45,2003;
- P. Aschieri, L. Castellani, A. Isaev, DISCRETIZED YANG-MILLS AND BORN-INFELD ACTIONS ON FINITE GROUP GEOMETRIES Int.J.Mod.Phys.A18:3555,2003;
- P. Aschieri, DUALITY ROTATIONS AND BPS MONOPOLES WITH SPACE AND TIME NONCOMMUTATIVITY. Nucl.Phys. B617:321-347,2001;
- P. Aschieri, D.Brace, B. Morariu, B. Zumino, PROOF OF A SYMMETRIZED TRACE CONJECTURE FOR THE ABELIAN BORN-INFELD LAGRANGIAN Nucl.Phys. B588:521-527,2000;
- P. Aschieri, D. Brace, B. Morariu, B. Zumino, NONLINEAR SELFDUALITY IN EVEN DIMENSIONS Nucl.Phys. B574:551-570,2000;
- L. Anguelova, P.A. Grassi, P. Vanhove, COVARIANT ONE-LOOP AMPLITUDES IN D=11 Nucl.Phys.B702:269,2004;
- P.A. Grassi, P. van Nieuwenhuizen, N=4 SUPERCONFORMAL SYMMETRY FOR THE COVARIANT QUANTUM SUPERSTRING. Phys.Lett.B610:129,2005;
- P.A. Grassi, L. Tamassia,VERTEX OPERATORS FOR CLOSED SUPERSTRINGS JHEP 0407:071,2004;
- P.A. Grassi, P. van Nieuwenhuizen, HARMONIC SUPERSPACES FROM SUPERSTRINGS Phys.Lett.B593:271,2004;
- P.A. Grassi, R. Ricci, D. Robles-Llana INSTANTON CALCULATIONS FOR N = 1/2 SUPERYANG-MILLS THEORY JHEP 0407:065,2004;
- L. Anguelova, P.A. Grassi, SUPER D-BRANES FROM BRST SYMMETRY. JHEP 0311:010,2003;
- P.A. Grassi, G. Policastro, P. van Nieuwenhuizen, THE QUANTUM SUPERSTRING AS A WZNW MODEL. Nucl.Phys.B676:43,2004;
- J. de Boer, P.A. Grassi, P. van Nieuwenhuizen, NONCOMMUTATIVE SUPERSPACE FROM STRING THEORY Phys.Lett.B574:98-104,2003;
- P.A. Grassi, G. Policastro, P. van Nieuwenhuizen, THE COVARIANT QUANTUM SUPERSTRING AND SUPERPARTICLE FROM THEIR CLASSICAL ACTIONS Phys.Lett.B553:96,2003;
- P.A. Grassi, G. Policastro, P. van Nieuwenhuizen, THE MASSLESS SPECTRUM OF COVARIANT SUPERSTRINGS JHEP 0211:001,2002;
- P.A. Grassi, G. Policastro, P. van Nieuwenhuizen, ON THE BRST COHOMOLOGY OF SUPERSTRINGS WITH/WITHOUT PURE SPINORS. Adv.Theor.Math.Phys.7:499,2003;
- P.A. Grassi, G. Policastro, M. Porrati, P. van Nieuwenhuizen, COVARIANT QUANTIZATION OF SUPERSTRINGS WITHOUT PURE SPINOR CONSTRAINTS. JHEP 0210:054,2002;

1) Study of the gauge/gravity correspondence for theories with reduced supersymmetry and without conformal invariance. The main goal is to obtain further insight on the perturbative and non-perturbative structure of supersymmetric gauge theories in four dimensions using the dual geometry produced by suitable configurations of D-branes. In this context, it would be particularly interesting to obtain information on the infrared confining behaviour of gauge theories with N=1 supersymmetry, on their non-perturbatively generated superpotential, on the vacuum structure and on the tension of domain walls and confining strings, starting from dual supergravity solutions.

2) Study of the properties of instantons in supersymmetric gauge theories by means of D(-1) branes. We intend to continue our analysis (in collaboration with the Turin group) of systems of D3/D(-1) branes that recently have been shown to provide an efficient string theory realization of the instanton calculus for gauge theories with N=4 supersymmetry. We plan to extend our previous analysis to theories with N=2 or N=1 supersymmetry and to the constrained instantons. Furthermore, we plan to develop the formalism to compute string scattering amplitudes on mixed disks in the D3/D(-1) systems that reproduce the instanton contributions in the gauge theory correlation functions. This is part of a more general program for the development of conformal techniques to calculate scattering amplitudes for strings with mixed boundary conditions and twist fields, that we intend to pursue also in connection with the points 3) and 4) of the program in collaboration with the units of Turin and SISSA.

3) Study of deformed gauge theories and theories with fluxes. Deformed gauge theories, which can be engineered using systems of D-branes embedded in supergravity backgrounds with non-trivial fluxes, have recently attracted a lot of attention. In this project (in collaboration with the Turin group) we intend to continue our investigations on deformed gauge theories and develop further the techniques for the calculation of mixed open/closed string amplitudes even in the presence of twist fields. In particular we plan to study non-anticommutative gauge theories with N=2 supersymmetry realized with D3-branes in a RR background, and analyse which closed string fluxes lead to localization in the integration on the instanton moduli space in order to establish a relation with the recently developed equivariant instanton calculus and derive the Seiberg-Witten prepotential and its gravitational corrections using instanton methods.

4) Study of systems of branes at angles and of magnetized branes. Systems of intersecting D-branes at angles are an efficient way of building (semi) realistic models for particle physics, in which gauge symmetries, chiral fermions and family replications emerge in a natural and simple manner. Many relevant quantities of these models, like for example the Kahler potential and Yakawa couplings, can be derived from scattering amplitudes among open strings (describing gauge or matter fields) and closed strings (describing geometric moduli). In this context, in collaboration with researchers from the Turin and SISSA groups, we plan to develop conformal world-sheet techniques to explicitly compute such mixed amplitudes, even in the presence of twisted states, and explore configurations of D-branes at angle or of magnetized D-branes which possess N=1 supersymmetry in four dimensions and for which the closed string background is chosen in such a way that (most of) the Kahler class and complex structure moduli get fixed. The idea is to find how the Kahler potential, Yukawa couplings and other relevant quantities of these gauge theories depend on the geometric moduli of the background, an information which is currently available only for the vacuum energy.

5) Study of the pure spinor string theory. The pure spinor string theory is a quantum formulation of critical superstring theory with manifest target space supersymmetry that overcomes some of the problems of the more traditional Ramond-Neveu-Schwarz and Green-Schwarz formulations. Despite many recent advances in the pure spinor formalism, only a limited amount of information is available. In fact, the computation of scattering amplitudes, the analysis of conformal invariance in generic backgrounds, the structure of the superconformal field theory associated with the BRST symmetry, and the computation of radiative corrections are only partially developed. Thus further work is needed in all these subjects. Among the most relevant topics that we plan to study using the pure spinor formulation of string theory, there are the analysis of D-branes, supermembranes and M-branes in various backgrounds, the computation of the superpotential in the effective low energy limit of string theory, the study of compactifications to lower dimensions, the analysis of orbifolds and orientifolds, and the study of compactifications with fluxes. It would be interesting also to investigate harmonic superspace for N=4 Yang-Mills theory and supergravity starting from the pure spinor string theory, analyse superstring theories in non-critical dimensions, explore the open/closed string duality, and study further the relation between topological M theory and pure spinor string theory.

6) Study of the global structures in gauge theories with higher rank gauge potentials. We plan to continue our analysis on the non-abelian gerbes (a generalization of the notion of vector bundles to the case of connections that are forms of higher rank), study their holonomy properties and, in the case of 2-forms, explore their possible applications to the low energy physics of the Neveu-Schwarz 5-branes. The gauge transformations for grebes have been recently understood also in the non-abelian case; however a Yang-Mills like action is still missing. Furthermore, at present non-abelian Wilson surfaces (holonomies) can be defined only in particular cases, and thus it would be interesting to generalize these constructions. A related issue is that of D-branes classification. It is known that twisted K-theory (that can be seen as the K-theory of bundle gerbes) replaces ordinary K-theory when there is a nontrivial Neveu-Schwarz-Neveu-Schwarz B-field. However, in type IIB string theory defined on compact space-times, some considerations based on S-duality suggest that a more general classification scheme and new structures have to be considered. It would be rather interesting to investigate also this topic.

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Università del Piemonte Orientale - Facoltà di scienze MFN - Alessandria -

Università del Piemonte Orientale - Facoltà di scienze MFN - Alessandria -