A. New strategies for supersymmetry breaking,using, for example,geometrical techniques such as G-structures, andproperties of compactifications with large hierarchies between the internal and external curvature.This analysis aims to shed light on the existence and stability of string and AdS vacua, also in connections with recent conjectures.

B.  Properties of supersymmetric theories in different dimensions. Some specific directions involve 1) global symmetry and supersymmetry enhancement as well as conformal manifolds in 3d and 4d gauge theories, to understand possible marginal deformations (this can potentially lead to new CFT’s and new dualities). 2) IR dynamics of 4d SCFTs obtained as compactifications of 6d SCFT. These theories are expected to often display enhancement of global symmetries and admit multiple dual geometric realisations. 3) the definition of a cohomology for (super) conformal defect lines and BPS Wilson Loops in ABJM and the computation of correlation functions of local operators in these cohomologies. These results will be checked against predictions from localisation and dual gravity description. The group will also study higher dimensional supersymmetric Wilson-like objects.

C.The participants will continue their successful investigation of the microstate counting for AdS black holes in diverse dimensions, and the study of entropy functions for AdS black objects, with the goal of extending the results beyond the leading order and possibly beyond supersymmetry. A clever combination of holography, dualities and localisation techniques will be crucial to allow for the exact evaluation of Euclidean path integrals. 

PADOVA has a consolidated expertise in all areas of the proposal, and will operate in synergy with all other units. For their research activities, please see  http://active.pd.infn.it/g4/gss/

MILANO operates both on supersymmetric gauge theories and basic properties of black hole solutions from supergravity, contributing mainly to B and C in synergy with MIB, TO, PD.

B: The participants will explore the derivation of new 3d supersymmetric dualities using localization. They will also study the Cardy limit of the superconformal index and its holographic relation with the black hole entropy. Moreover, they plan to analyse conformal Feynman integrals in strongly coupled N=4 SYM theories.                                                        

C: The group will develop techniques which allow a systematic construction and classification of black hole solutions in asymptotically AdS spaces, which play an important role in the gauge/gravity correspondence. In particular, their goal is to examine if and how the integrability properties that are present in ungauged supergravities can be extended to the gauged case.

GENOVA will pursue their strategic expertise in area B, of interest also to MIB, LE, TO, PD, exploring topological quantum field and string theories, boundary field theories in 3 and 4 dimensions, massive quantum gravity, their non-perturbative dynamics and application to supersymmetric theories and also Fractional Quantum Hall effect and Topological Insulators. They will apply their original approach to supersymmetric localisation based on emergent topological structures in supergravity to superconformal 4-dimensional N=2 supergravity, with the goal of classifying the space of supersymmetric vacua of N=2, 4-dimensional gauge theories. They will also attempt to elucidate the long-standing issue of supersymmetry quantum anomalies by putting them in relation with the topological multiplets inside supergravity. Another direction will revolve around  Linearised Massive Gravity in a new approach,  whereby it is treated as a gauge field theory, developed to overcome the difficulties related to the vDVZ discontinuity of the old standard Fierz-Pauli theory.

LECCE has a lively young group with expertise mainly in B, with springoffs also in D.

B: Low dimensional AdS/CFT. In particular, the partially unclear AdS2/CFT1 correspondence will be addressed from a twofold point of view: 1) considering the defect CFT that lives on the path of a (non) supersymmetric Wilson loop in N=4 SYM, and the dual description at strong coupling in terms of a Nambu-like sigma-model in AdS2. 2) exploring the features of rigid (non-gravitational) holography for a Weyl invariant theory in AdS2. This includes Liouville theory and more complicated WZW actions. 

D: Dualities of theories living on the worldvolume of D-(5 − 2m) branes probing toric Calabi Yau (m+2)-folds. These dualities can be motivated in various ways including mirror symmetry, and they lead to Diophantine equations whose solutions can allow to characterise these duality phases. Another theme concerns the localisation analysis of generic N=2 superconformal theories in 4d, both in the large charge and large N limits, where holography requires at strong coupling the study of type IIB orientifolds considered in the past by Ennes, Lozano, Naculich and Schnitzer.

PISA is a strategic part of GSS due to seminal contributions to many of its research lines, and will mainly contribute to A, B and  D in synergy with MIB, PD and TO.

A:The group will devote itself to study aspects of Spontaneous Supersymmetry Breaking, both in Cosmology and in Particle Physics. In particular, they plan to continue recent investigations on the partial breaking of Supersymmetry and brane dynamics, from both a string and a field theory perspective, with particular focus on the issue of vacuum stability in absence of supersymmetry. This top down approach is complementary to swampland criteria. It is aimed at elucidating consistency conditions from the UV side, exploring perturbative and non-perturbative instabilities of vacuum solutions of supergravity that are well motivated by microscopic settings. This allows to go beyond the EFT regime, to some extent, and important inputs from holography provide additional tools in some cases. They will also explore solutions in the presence of boundaries in internal space,non-perturbative aspects of compactifications, aimed at extending the usual duality links among supersymmetric strings,self-duality in field theory, and string perturbation theory in the presence of vacuum redefinitions.

B/D:The team will further pursue their signature line of expertise on Higher Spin Fields, with focus on the Lagrangian construction for the three dimensional higher spins theories and colored gravities, exploring locality of the interactions and the structure of higher-point vertices. 

TORINO is a large and composite Unit, with members in the Physics Department and now also in the Math Department (D. Martelli) of the University, Polytechnic University and University of Eastern Piedmont in Alessandria. They will work in connection with PI, PD, MIB and MI, contributing to topics A, C and D.

A. Analysis of the structure, properties and applications of conformal supergravities, highlighting the role of “hidden symmetries” in supergravities in various dimensions. This is done using their geometric formulation, with particularly emphasis towards its use for path integral quantisation. Further work focusses on possible Lagrangian descriptions for the dynamics of self-dual forms in supergravity, seeking a link between the solutions so far proposed and the integral-form formalism. Another angle deepens the structure of string compactifications, exploiting various approaches such as G-structures, generalised geometry and consistent truncations of higher-dimensional supergravities. Members of the group work to build new classes of so far unexplored orientifold vacua involving magnetic fields on orbifolds,then scan for phenomenologically appealing solutions of tadpole conditions and study their low-energy limit. Notice that these vacua are not T-dual to intersecting branes on geometrical orbifolds.The unit also works to extend the swampland conjecture to vacua with broken supersymmetry, and to uncover the stringy origin of some supergravity couplings and non-linear formulations with the aim of achieving a better understanding of Brane Supersymmetry Breaking. Swampland constraints are also  explored by the methods previously developed for extremal black holes and techniques of special geometry, building on interesting recent literature.

B.  A variety of different topics is pursued: 1) 3d unconventional supersymmetries in connection with their holographic description of graphene, in the presence of curvature and torsion. 2)  the holographic map between gravitational and gauge instantons, and investigations of the dual CFT description of S-fold solutions in maximal gauge supergravity. 2) elucidation on the string realization of the Omega background, constructing the associated refined topological amplitude in heterotic string, and investigations on the role of D-instantons in a full-fledged string perturbative approach to derive the instanton contribution to the Nekrasov free energy. 3)  Push forward the program on integral forms, exploring their role in determining the structure and the dynamics of Chern-Simons theories, BF and Higher Chern-Simons theories on supermanifolds. 4) continue the timely analysis on CFT in the limit of large charge, to study correlation functions and the role and fate of dualities. 

B/C/D:Members of the unit work to improve our understanding of the quantum statistical interpretation of the black hole entropy, by combining holography with modern QFT approaches. These studies are expected to have connections with various areas of mathematical physics, from differential geometry to number theory. New examples of black holes will be constructed by combining solution generating techniques and string/M-theory dualities, together with geometric methods such as G-structure. Moreover, the unit will develop holographic and geometrical approaches for computing the Bekenstin-Hawking entropy, deepening our insight on the microscopic structure of black holes.

D. The group studies  supergeometry to describe Wilson loops and surface operators in gauge theories and, from a more formal viewpoint, to analyse Chevalley-Eilenberg Cohomology for integral forms and pseudo forms for super-Lie algebras. Various studies will explore T-duality of open string effective actions in the presence of fluxes, twisted non-commutative tori and more general non geometric backgrounds. Another line investigates nonabelian T-duality (Poisson-Lie T-duality) for string effective action