Nonlinear Supersymmetry as a Hidden Symmetry

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Rotating Higher Spin Partition Functions and Extended BMS Symmetries

We evaluate one-loop partition functions of higher-spin fields in thermal flat space with angular potentials; this computation is performed in arbitrary space-time dimension, and the result is a simple combination of Poincar\'e characters. We then focus on dimension three, showing that suitable products of one-loop partition functions coincide with vacuum characters of higher-spin asymptotic symmetry algebras at null infinity. These are extensions of the bms_3 algebra that emerges in pure gravity, and we propose a way to build their unitary representations and to compute the associated characters. We also extend our investigations to supergravity and to a class of gauge theories involving higher-spin fermionic fields.Comment: 58 pages; clarifications and references added; version to be published in JHE

Resolutions of discriminants and topology of their complements

Abstract. We study topological invariants of spaces of nonsingular geometrical objects (such as knots, operators, functions, varieties) defined by the linking num-bers with appropriate cycles in the complementary discriminant sets of degenerate objects. We describe the main construction of such classes (based on the conical resolutions of discriminants) and list the results for a number of examples. The discriminant subsets of spaces of geometric objects are the sets of all objects with singularities of some chosen type. The important examples are: spaces of poly-nomials with multiple roots, resultant sets of polynomial systems having common roots, spaces of functions with degenerate singular points, of non-smooth algebraic varieties, of linear operators with zero or multiple eigenvalues, of smooth maps S1 → Mn (n ≥ 3) having singular or self-intersection points, of non-generic plane curves, and many others. The discriminants are usually singular varieties, whose stratifications correspond to the classification of degenerations of the corresponding objects. E.g., the discrim-inant subset in the space of polynomials x3 + ax + b is the semicubical parabol