Fabio Zwirner

A bstract: We consider compactifications of higher-dimensional supergravities on Riemann-flat manifolds of dimension d ( d ≤ 7) that fully break supersymmetry at the classical level on a resulting D -dimensional Minkowski space. We systematically discuss consistency conditions, the Kaluza-Klein (KK) spectrum and harmonics, and the resulting one-loop effective potential V ₁ , focusing for illustration on maximal supergravity and d = 3, in particular on the 𝕋 ³ /ℤ ₃ and on the Hantzsche-Wendt manifolds. We show how the KK spectrum can be re-organized in multiplets of the broken D -dimensional supersymmetry, derive new universal supertrace mass relations valid at each redefined KK level and obtain an analytic finite expression for V ₁ after resumming the contributions of all KK levels. In all examples V ₁ is negative definite and scales with inverse powers of some internal radii. We extensively comment, when applicable, on the relation with the Scherk-Schwarz mechanism and with supersymmetry-breaking string compactifications on freely acting symmetric orbifolds. We also finally clarify the assumptions and constraints under which Scherk-Schwarz reductions correspond to twisted tori compactifications.

To connect supergravity with the real world, a highly non-trivial requirement is complete spontaneous supersymmetry breaking in an approximately flat four-dimensional space-time. In no-scale supergravity models, this naturally happens at the classical level: the gravitino mass, setting the scale of supersymmetry breaking, slides along a flat direction of the potential with vanishing energy. This contribution briefly describes, with a personal selection of simple illustrative examples, some qualitative features of no-scale models that relate them to a possible dynamical generation of the hierarchies between the vacuum energy scale, the weak scale and the Planck scale. It includes comments on their versions with extended supersymmetry, on their higher-dimensional origin and on how their still unsolved problems of quantum stability can already be addressed, with some results, at the level of supergravity compactifications, although their solution (if any) will eventually require a better understanding of superstring theories.

We perform a systematic analysis of the one‐loop effective potential of pure supergravities, with supersymmetry fully broken by a Scherk–Schwarz compactification on the circle, as a function of the radial modulus. We discuss the precise correspondence between the effective potential in the full compactified theory and its counterpart in the reduced theory. We confirm that is finite for any , in contrast to . We find that for broken supergravity is negative definite even after accounting for the Kaluza–Klein states. We outline a program for future work where the study of a different kind of Scherk‐Schwarz compactifications, still at the field theory level but with at least three extra dimensions, could lead to qualitatively new results.

We discuss how to consistently use Effective Field Theories (EFTs) to set universal bounds on heavy-mediator Dark Matter at colliders, without prejudice on the model underlying a given effective interaction. We illustrate the method for a Majorana fermion, universally coupled to the Standard Model quarks via a dimension-6 axial-axial four-fermion operator. We recast the ATLAS mono-jet analysis and show that a considerable fraction of the parameter space, seemingly excluded by a na\"ive EFT interpretation, is actually still unexplored. Consistently set EFT limits can be reinterpreted in any specific underlying model. We provide two explicit examples for the chosen operator and compare the reach of our model-independent method with that obtainable by dedicated analyses.

We go a step further in the search for a consistent and realistic supergravity model of large-field inflation by building a class of models with the following features: during slow-roll, all the scalar fields other than the inflaton are frozen by large inflaton-dependent masses or removed from the spectrum; at the end of inflation, supersymmetry is spontaneously broken with naturally vanishing classical vacuum energy. We achieve this by combining some geometrical properties of the Kaehler potential with the consistent use of a single nilpotent chiral superfield, in one-to-one correspondence with the supersymmetry-breaking direction in field space at the vacuum.