## Scientific activities of the various Research Units

Supersymmetric Quantum Field Theories derived from Strings and other extended
objects proved an extraordinary fertile arena where proposals for the unification of
Gravity with the other Fundamental Interactions have been explored now for several
decades. In particular Supergravity, the gauge theory of supersymmetry extending
Einstein’s theory of General Relativity, discovered 40 years ago and widely developed by
participating members of the proposed network, has played a prominent role as a lowenergy
effective field theory for string and brane models. In special instances, remnants
of Planck-scale Physics can now be probed by explicit computations, and can start to be
confronted with experiments in the sky and at particle accelerators. Moreover, in the
context of the AdS/CFT correspondence, Supergravity has provided unique tools to
investigate perturbative and non-perturbative dynamical aspects of ordinary gauge
theories. Black hole solutions of Supergravity have been extensively studied as
theoretical laboratories to probe unusual regimes of gravity in string theory: the counting
of microstates underlying their entropy proposes extraordinary challenges where one is
just beginning to shed light. Recent ideas have also managed to extract from String
Theory and Supergravity interesting models of the early universe, where inflationary
scenarios are explored from a more constrained perspective.
String models are well known to be interrelated by a complex web of dualities, which
include the renowned AdS/CFT correspondence, which has laid a unified framework
for supergravity and gauge theories via Conformal Invariance, which nowadays made a
come back in a reproposition of the bootstrap program in dimensions larger than 2.
Scattering amplitudes in gauge theories reconsidered under the spell of the AdS/CFT
correspondence have displayed a very high degree of symmetry that hints to the
integrability of broad classes of models. Unexpected relations between gravity and
Yang Mills amplitudes may uncover new ways to explore the ultraviolet behaviour of
gravity theories, which might provide insight on the longstanding issue of finiteness in
N=8 supergravity and in some lower-N cases. Mathematical aspects encoded in
algebraic and geometric structures of spacetime and moduli spaces are a longdeveloped
expertise of GSS members. Today these include investigations of noncommutative
behaviour, geometry of supermanifolds, higher-spin gauge theories,
topological models and supersymmetric localisation techniques and others which may
also bring more clarity on long-standing conundrums of fields, string and branes.
The research network of GSS 2.0 consists of 7 INFN divisions (GE-LE-MI-MIB-PD-PITO)
which host several internationally known experts in the domain of strings, branes,
supergravity, AdS/CFT correspondence and their applications to gauge theories, gravity
and cosmology. They have a long history of mutual collaborations (TO-PD, MI-MIB, PDMIB,
PI-MIB-PD) within Italian projects, strong international relations fostered throughout
various EU networks, and many acknowledged results in the field under study. They plan
to meet once a year during the course of the project in workshops devoted to sharing
information, contributing to the education of young scientists and stimulating joint
scientific research. GSS 2.0 aims to impact the following main
directions:
###

The Genova node contributes a wide expertise in area C, on
###

The Lecce group has a lively young group with a growing expertise both on higher spin theories
and Conformal Field Theories. It proposes an activity related to C, with springoffs also
on E. Building on its previous results, the group will explore the conformal properties
of higher spin gauge theories in curved backgrounds, focussing on the relation with the
tensionless limit of string theory. It will also continue to investigate correlation functions
in Conformal Field Theories, with the aim of extending recent analytical results for the
Virasoro blocks derived in the semi-classical approximations to models with additional
W-symmetry. A concrete goal is to devise new AdS/CFT tests based on Witten’s
geodesic diagram technique. Another planned activity is meant to relate conformal
blocks with instanton partition functions in N=2 gauge theories via the AGT
correspondence.
###

Milano operates traditionally in the areas of Superconformal Field Theories and of
Supergravity black holes, contributing to topics C, D, also in collaboration with MIB, TO,
PD.

###

Milano-Bicocca is a strong and multi-faceted Unit that will pursue several topics in
areas A, C and D, in close connection with GE, PD, PI, TO.

###

Padova has a strong expertise in all areas of the project and will operate in close
connection with MIB, PI, TO. It will cover in particular the following subjects.

###

Pisa’s Unit is a strategic new entry in GSS, due to seminal contributions to the present
research lines. The group will include members from the INFN Frascati Unit and will
devote itself to study aspects of Spontaneous Supersymmetry Breaking, both in
Cosmology and in Particle Physics, and Higher Spin Fields, also in collaboration with
MIB, PD and TO. In particular, they plan to investigate the Partial breaking of
Supersymmetry and brane dynamics, which motivated the recent wave of activity on
non linear supergravity, from both a string and a field theory perspective. These subjects
include generalisations of the Born-Infeld theory, also involving scalars and form fields,
the study of duality symmetries, and the use of non linear realisations of Supersymmetry
(Nilpotent Superfields) in models of inflationary Cosmology. This is a recent methodology
in rapid evolution, which was originally developed by the group. They will continue their
investigations of new classes of inflaton potentials in diverse limits where the masses of
the sgoldstino, inflatino and/or sinflaton become large. Moreover, they will continue to
pursue their line of expertise on Higher Spin Fields, addressing mass generation
mechanisms and long-standing locality issues, combining BRST techniques with a
detailed analysis of the singular behaviour of string amplitudes for massive states in the
massless limit. Massive gravity will provide an interesting case study of intermediate
difficulty. A long term goal is to clarify the connection between massless dynamics in
AdS and massive dynamics in flat space.
###

Torino is a large and composite Unit (Torino, Polytechnic and Alessandria U.) that will
work in close connection with PI, PD, MIB and MI, contributing to
topics A, B, D and E.

- String Theory, compactifications and string vacua. In a supersymmetric context, this portion of the project will address the geometry of higher dimensional string compactifications, their reduction to an effective supergravity using generalized geometry, F-theory flux compactifications and holographic effective actions for strongly coupled CFT. Moreover, in the presence of broken supersymmetry, where current string techniques become ineffective, the low energy analysis has the potential to provide novel, if partial, informations on string vacua. Research along these lines will be performed by Units MIB, PD, PI, TO, with expected collaborations among all of them.
- Supersymmetry breaking by fields and branes. Branes bring along, in string theory, non-linear realisations of supersymmetry. This phenomenon occurs both in the supersymmetric context, where the mere introduction of a BPS brane in the vacuum halves the number of its supersymmetries, and in more complicated contexts, including brane supersymmetry breaking, where no residual supersymmetry is left. All the lost ones appear to be non-linearly realised and supergravity provides a rich tool to explore their manifestations. In particular, the partial breaking of N=2 supersymmetry, the last case that has been analysed in any detail so far, calls for the elegant Born-Infeld generalisation of electrodynamics, and more is to be expected from higher-N or higher dimensional cases. This is a timely subject, also in view of ongoing searches for supersymmetry at LHC and of the emerging role of broken supersymmetry in cosmology and inflationary models. Research along these lines will be performed by Units MIB, PD, PI, TO, with expected collaborations among all of them.
- Supersymmetric Gauge Theories, holography and dualities. The goal of this endeavour will be a deeper understanding of gauge theories in various dimensions, also relying on branes and on their deeply interconnected web of strongly coupled supersymmetric manifestations. Several groups will focus on superconformal field theories that afford an embedding in string theory and are related to AdS supergravity. Integrability properties and scattering amplitudes in three and four dimensional models will be explored, with the long term goal to disclose model-independent lessons of the AdS/CFT correspondence. Protected quantities in various dimensions, topological theories for gravity and issues concerning mass generation for higher spins will be investigated. Research along these lines will be performed by Units GE, LE, MIB, PD with expected collaborations between GE and MIB, MI and MIB.
- Black Holes in supergravity. This subject has long been pursued by several members of GSS. New interesting directions have recently emerged. These include entropy computations for AdS4 black holes made possible by clever combinations of holographic and localisation techniques, static AdS4 black-hole solutions emerging from M-theory compactifications, supergravity descriptions of microstates, solution-generating methods for black holes in gauged supergravities, and the classification of attractors in gauged supergravities in the presence of hypermultiplets. Another promising direction is the use of CFT techniques to explore the information paradox. Finally, the ``double-copy” relation that connects gravity to Yang-Mills theory scattering amplitudes will be explored in the context of Kerr-Schild black holes, where it recently proved valuable to relate gravitational emission and electromagnetic Bremsstrahlung. Research along these lines will be performed by Units MI, MIB, PD, TO, with expected collaborations among all of them.
- Mathematical methods: This project will also entail the development of some mathematical tools related to Wilson loop operators, non-commutative geometry, superspace methods, non-linear realisations of supersymmetry, aspects of higher spins, of conformal blocks and of localisation techniques for path integrals. Research along these lines will be performed by GE, LE, TO, PI, with expected collaborations mostly between PI and TO. /li>

### __ Genova __

The Genova node contributes a wide expertise in area C, on
*topological gauge theories*and their coupling to topological gravity backgrounds, and on*supersymmetric localization*techniques of interest to MIB, TO, PD. Using their powerful cohomological approach to localization, the group plans to investigate applications of their newly discovered localizing backgrounds to two-dimensional supersymmetric gauge theories and to extend the analysis to higher-dimensional gauge theories and supergravity, with potential applications to black hole entropy computations. In collaboration with MIB, the group will also apply their methods to new topological string models on non-Kahler complex varieties that are relevant for describing four-dimensional compactifications of type II superstrings with reduced supersymmetry.### __ Lecce __

The Lecce group has a lively young group with a growing expertise both on higher spin theories
and Conformal Field Theories. It proposes an activity related to C, with springoffs also
on E. Building on its previous results, the group will explore the conformal properties
of higher spin gauge theories in curved backgrounds, focussing on the relation with the
tensionless limit of string theory. It will also continue to investigate correlation functions
in Conformal Field Theories, with the aim of extending recent analytical results for the
Virasoro blocks derived in the semi-classical approximations to models with additional
W-symmetry. A concrete goal is to devise new AdS/CFT tests based on Witten’s
geodesic diagram technique. Another planned activity is meant to relate conformal
blocks with instanton partition functions in N=2 gauge theories via the AGT
correspondence.
### __ Milano __

Milano operates traditionally in the areas of Superconformal Field Theories and of
Supergravity black holes, contributing to topics C, D, also in collaboration with MIB, TO,
PD.**C.**The participants are investigating various properties of Scattering Amplitudes (like Wilson-loop/Scattering Amplitudes duality and dual conformal invariance) and integrability in N=4 SYM Theories, in N=2 Superconformal-QCD and in threedimensional Chern-Simons ABJM theories. They plan to extend their recent calculation of the four-point amplitude at two loops in N=2 superconformal-QCD to five- and sixpoint functions, in order to gain information on whether the result is Regge exact. This is relevant in comparison with QCD and N=4 SYM. They also plan to perform a perturbative analysis of the form factors of some gauge-invariant operators, in order to test a recent proposal on the role of form factors as a link between on-shell amplitudebased methods and the integrability of composite operators.**D.**The group will study the residual symmetries in gauged supergravity that leave the equations of motion invariant, in order to generate new solutions from a given seed, by generalizing their own method. Such solution-generating techniques are expected to have a wide range of applications in holography, for instance to construct hairy black holes, which are instrumental e.g. in the holographic modeling of strongly coupled condensed matter systems. They will also continue their recent work on the classification of attractor points for extremal black holes in gauged supergravity, both in the case of Fayet-Iliopoulos gauging and in presence of hypermultiplets. This can be done by using the effective black hole potential found by members of PI, with whom a collaboration is envisaged. TO and PD are also expected to collaborate and contribute via their experience with hypermultiplets.### __ Milano Bicocca __

Milano-Bicocca is a strong and multi-faceted Unit that will pursue several topics in
areas A, C and D, in close connection with GE, PD, PI, TO.**A.**The participants will aim at extending their previous results on higher-dimensional AdS solutions to the case of four and five dimensions with extended supersymmetry. They will also continue to explore the physics of conformal field theories in six dimensions, focussing on their properties under RG flows, on the operator spectrum (via Kaluza-Klein compactifications) and on their moduli spaces, making connection with topic C. They will also investigate the string-theoretic phenomena suggested by these theories, in M- and F-theory.**C.**Wilson loops and integrability. The group will perform a detailed analysis of the spectrum of BPS operators in three-dimensional CFT with various degrees of supersymmetry, using both localization and perturbative techniques. They will derive non-trivial connections with the Bremsstrahlung function and the cusp anomaly. They will also face the long-standing problem of proving the self T-duality of string theory in AdS4xCP3, which lies at the heart of integrability of the ABJM model, and of Wilson loop/scattering amplitudes duality. The general goal will be to explore the regimes of validity of the new structures discovered within explicit examples.**C, D.**Gauge theories, holography and dualities. The participants will pursue their general investigation of the properties of supersymmetric theories in curved space. On the one hand, the aim is to understand higher dimensional theories and the still elusive (2,0) conformal theory in 6d and the connected web of supersymmetric theories and dualities. On the other hand, the aim is to understand the properties low dimensional superconformal Field Theories and Quantum Mechanics, and their relation to the microscopic counting of degrees of freedom for AdS black holes and black strings, generalizing the recent and successful entropy counting for AdS4 BH performed by the participants. A clever combination of holography, dualities and localization techniques that allow for the exact evaluation of Euclidean path integrals are crucial ingredients of all these investigations.### __ Padova __

Padova has a strong expertise in all areas of the project and will operate in close
connection with MIB, PI, TO. It will cover in particular the following subjects.**B.**They will explore non-linear realisations of supersymmetry as a tool to describe effective theories of strings and to construct models for inflation and for the phenomenology of fundamental interactions. The focus will be on the ultraviolet origin of the constraints that appear when the non-linear realisations are expressed in terms of superfields, on the equivalence between general supergravity actions with constrained superfields and effective theories of branes, and on the extension of the existing phenomenological models based on previous results by the group.**A,C.**Flux Compactifications and Holography. In the framework of minimally supersymmetric flux compactifications, the group will further develop the program of including backreaction and non-perturbative effects in the four-dimensional effective theory. The same techniques will also be applied to local models, in which fourdimensional gravity is decoupled. Many of these are dual to strongly coupled CFTs with minimal supersymmetry, and the group aims to derive their holographic effective theories using the supergravity description. This will offer a powerful holographic framework for studying the vacuum structure of such SCFTs in phases in which the conformal symmetry is spontaneously broken. The underlying SCFT structure will be used to investigate the properties of (local) models of flux compactifications beyond the lowest supergravity approximation.**D.**Efforts to clarify the microscopic origin of the thermodynamic properties of black holes will be pushed forward in several directions. The group will broaden the family of supergravity solutions representing microstates of supersymmetric black holes and apply holographic methods to analyse existing solutions that still lack a microscopic understanding. They will also develop CFT techniques to tackle the information paradox when black microstates do not admit a description in supergravity, by identifying a class of CFT observables capable to distinguish the microstates among themselves and from the thermal ensemble dual to the black hole.### __ Pisa __

Pisa’s Unit is a strategic new entry in GSS, due to seminal contributions to the present
research lines. The group will include members from the INFN Frascati Unit and will
devote itself to study aspects of Spontaneous Supersymmetry Breaking, both in
Cosmology and in Particle Physics, and Higher Spin Fields, also in collaboration with
MIB, PD and TO. In particular, they plan to investigate the Partial breaking of
Supersymmetry and brane dynamics, which motivated the recent wave of activity on
non linear supergravity, from both a string and a field theory perspective. These subjects
include generalisations of the Born-Infeld theory, also involving scalars and form fields,
the study of duality symmetries, and the use of non linear realisations of Supersymmetry
(Nilpotent Superfields) in models of inflationary Cosmology. This is a recent methodology
in rapid evolution, which was originally developed by the group. They will continue their
investigations of new classes of inflaton potentials in diverse limits where the masses of
the sgoldstino, inflatino and/or sinflaton become large. Moreover, they will continue to
pursue their line of expertise on Higher Spin Fields, addressing mass generation
mechanisms and long-standing locality issues, combining BRST techniques with a
detailed analysis of the singular behaviour of string amplitudes for massive states in the
massless limit. Massive gravity will provide an interesting case study of intermediate
difficulty. A long term goal is to clarify the connection between massless dynamics in
AdS and massive dynamics in flat space.
### __ Torino __

Torino is a large and composite Unit (Torino, Polytechnic and Alessandria U.) that will
work in close connection with PI, PD, MIB and MI, contributing to
topics A, B, D and E.**A.**The group will investigate quantum properties (in particular the stability issue) of fullfledged string configurations with spontaneously broken supersymmetry, and their connection with suitable supergravity low-energy effective actions, and the stringy realisation of N=2* gauge theories in the Omega background, via the computation of suitable topological amplitudes. The group will also study heterotic string compactifications in the presence of non-trivial fluxes, addressing in particular the elliptic genus and radiative corrections to gauge and gravitational couplings via localization techniques. Hidden symmetries of higher dimensional supergravities in relation with free differential algebras, and several issues in exceptional/double field theories will also be examined.**B.**Building on their recent general two-derivative description of multi-field Born-Infeld actions involving vector, scalar and tensor fields, the group will explore relations with partially broken supergravity, non-abelian BI-models, their relationship with SYM, and extensions to N=4 supersymmetry and supergravity. Some members will also investigate new D-branes descriptions based on Arnold-Beltrami fluxes, and related D=7 supergravity solutions.**D.**The group will study new characterizations of regularity for multi-center black hole solutions in terms of real nilpotent orbits, and AdS black holes in gauged supergravity with non trivial hypermultiplets (joining efforts with MI and MIB). Some members will also address the “double copy” issue for radiation by accelerating black holes.**E.**As springoff of the preceding activities, members of the Unit are expected to improve the method of integral forms in supergravity in several dimensions and for different supersymmetry extensions, to explore non-commutative (super)-gravity theories and their cosmological implications, also allowing for a dynamical field giving rise to noncommutativity. Possible generalizations, also suggested by string theory in the presence of background fluxes, include a non-associative and NC gravity theory. Other topics will include a general formulation of massive supergravity without introducing nonphysical propagating degrees of freedom, and 2+1 dimensional quantum gravity with Goldman brackets that respects the area phases, possibly extending the construction to other surfaces, and connecting it to other approaches.^ Back to Top