arXiv research

Lagrangian contact supersymmetries (depending on derivatives of arbitrary order) are treated in very general setting. The cohomology of the variational bicomplex on an arbitrary graded manifold and the iterated cohomology of a generic nilpotent contact supersymmetry are computed. In particular, the first variational fo…

Explains basics of supersymmetry and supergeometry.

We construct a two parameter family of eleven-dimensional indecomposable Cahen-Wallach spaces with irreducible, non-flat, non-restricted geometric supersymmetry of fraction $ν=\tfrac{3}{4}$. Its compactified moduli space can be parametrized by a compact interval with two points corresponding to two non-isometric, decom…

Introduces supermanifolds and supersymmetry for mathematicians.

Extends Tanaka theory to supergeometry for upper bounds on supersymmetry.

Extended supersymmetry leads to Yano F structures on a manifold.

We discuss additional supersymmetries for N = (2, 2) supersymmetric non-linear sigma models described by left and right semichiral superfields.

The cohomology of a compact Kaehler (resp. hyperKaehler) manifold admits the action of the Lie algebra so(2,1) (resp. so(4,1)). In this paper we show, following an idea of Witten, how this action follows from supersymmetry, in particular from the symmetries of certain supersymmetric sigma models. In addition, many of t…

We discuss the conditions for additional supersymmetry and twisted supersymmetry in N = (2, 2) supersymmetric non-linear sigma models described by one left and one right semi-chiral superfield and carrying a pair of non-commuting complex structures. Focus is on linear non-manifest transformations of these fields that h…

Reconstructs supersymmetry and supergravity in complexified Z/2-graded Algebraic Geometry.

The Carrollian superplane is constructed as a supermanifold generalization of the Carrollian plane.

Semichiral sigma models with a four-dimensional target space do not support extended N=(4,4) supersymmetries off-shell arXiv:0903.2376, arXiv:0912.4724. We contribute towards the understanding of the non-manifest on-shell transformations in (2,2) superspace by analyzing the extended on-shell supersymmetry of such model…

Introduces a new phase space for 2D supersymmetric sigma models.

Study the connection between supersymmetry and geometric flows in supergravity.

We study the equations governing rigid N=1 supersymmetry in five dimensions. If the supersymmetry spinor satisfies a reality condition, these are foliations admitting families of almost complex structures on the leaves. In other words, all these manifolds have families of almost Cauchy-Riemann (CR) structures. After de…

Semichiral $(2,2)$ sigma models with $4d$ target space are discussed. A novel description in $(1,1)$ superspace allows an analysis of possible extended supersymmetries. It is argued that a manifest semichiral realization of an extra supersymmetry is only possible for hyperkähler target geometry. A semichiral formulatio…

It is of interest to study supergravity solutions preserving a non-minimal fraction of supersymmetries. A necessary condition for supersymmetry to be preserved is that the spacetime admits a Killing spinor and hence a null or timelike Killing vector field. Any spacetime admitting a covariantly constant null vector fiel…

We study the extent to which the gauge symmetry of abelian Yang-Mills can be deformed under two conditions: first, that the deformation depend on a two-form scale. Second, that the deformation preserve supersymmetry. We show that (up to a single parameter) the only allowed deformation is the one determined by the star …

Supersymmetry is deeply related to division algebras. Nonabelian Yang-Mills fields minimally coupled to massless spinors are supersymmetric if and only if the dimension of spacetime is 3, 4, 6 or 10. The same is true for the Green-Schwarz superstring. In both cases, supersymmetry relies on the vanishing of a certain tr…

We construct examples of isometric M-theory backgrounds which preserve a different amount of supersymmetry depending on the choice of spin structure. These examples are of the form AdS_4 x L, where L is a seven-dimensional lens space whose fundamental group is cyclic of order 4k.

We review coupled ${\rm SU}(3)$-structures, also known in the literature as restricted half-flat structures, in relation to supersymmetry. In particular, we study special classes of examples admitting such structures and the behaviour of flows of ${\rm SU}(3)$-structures with respect to the coupled condition.

We prove that supersymmetry backgrounds of (1,0) and (2,0) six-dimensional supergravity theories preserving more than one half of the supersymmetry are locally homogeneous. As a byproduct we also establish that the Killing spinors of such a background generate a Lie superalgebra.

We describe the construction of a Lie superalgebra associated to an arbitrary supersymmetric M-theory background, and discuss some examples. We prove that for backgrounds with more than 24 supercharges, the bosonic subalgebra acts locally transitively. In particular, we prove that backgrounds with more than 24 supersym…

We classify non-nilpotent complex structures on 6-nilmanifolds and their associated invariant balanced metrics. As an application we find a large family of solutions of the heterotic supersymmetry equations with non-zero flux, non-flat instanton and constant dilaton satisfying the anomaly cancellation condition with re…

Two geometric realizations of $F(4)$ Lie superalgebra found.

We consider IIA compactifications on solvmanifolds with O6/D6 branes and study the conditions for obtaining de Sitter vacua in ten dimensions. While this is a popular set-up for searching de Sitter vacua, we propose a new method to include supersymmetry breaking sources. For space-time filling branes preserving bulk su…

Study S-duality and supersymmetry on curved manifolds using localization.

We show that the supersymmetric near horizon black hole geometries of 6-dimensional supergravity coupled to any number of scalar and tensor multiplets are either locally $AdS_3\times Σ^3$, where Σ^3 is a homology 3-sphere, or $\bR^{1,1}\times {\cal S}^4$, where ${\cal S}^4$ is a 4-manifold whose geometry depends on the…

Universal geometry organizes heterotic moduli spaces.

We study the supersymmetric Wilson loop as introduced by Caron-Huot, which attaches to lightlike polygons certain edge and vertex operators, whose shape is determined by supersymmetry constraints. We state explicit formulas for the vertex operators to all orders in the Graßmann expansion, thus filling a gap in the lite…

In this expository article we discuss the relations between Sasakian geometry, reduced holonomy and supersymmetry. It is well known that the Riemannian manifolds other than the round spheres that admit real Killing spinors are precisely Sasaki-Einstein manifolds, 7-manifolds with a nearly parallel G2 structure, and nea…

We explore all warped $AdS_4\times_w M^{D-4}$ backgrounds with the most general allowed fluxes that preserve more than 16 supersymmetries in $D=10$- and $11$-dimensional supergravities. After imposing the assumption that either the internal space $M^{D-4}$ is compact without boundary or the isometry algebra of the back…

We classify non-dilatonic NS-NS type II supergravity backgrounds admitting a consistent absolute parallelism. They are all given by parallelised Lie groups admitting scalar flat bi-invariant lorentzian metrics. There are seven different classes, some of them containing moduli. For each class we determine the amount of …

Sasakian manifolds are odd-dimensional counterpart to Kahler manifolds. They can be defined as contact manifolds equipped with an invariant Kahler structure on their symplectic cone. The quotient of this cone by the homothety action is a complex manifold called Vaisman. We study harmonic forms and Hodge decomposition o…

We construct the general action for Abelian vector multiplets in rigid 4-dimensional Euclidean (instead of Minkowskian) N=2 supersymmetry, i.e., over space-times with a positive definite instead of a Lorentzian metric. The target manifolds for the scalar fields turn out to be para-complex manifolds endowed with a parti…

We present a comprehensive classification of supersymmetric vacua of M-theory compactification on seven-dimensional manifolds with general four-form fluxes. We analyze the cases where the resulting four-dimensional vacua have N = 1,2,3,4 supersymmetry and the internal space allows for SU(2), SU(3) or G_2 structures. In…

Off-shell $(4,0)$ supermultiplets in 2-dimensions are formulated. These are used to construct sigma models whose target spaces are vector bundles over manifolds that are hyperkähler with torsion. The off-shell supersymmetry implies that the complex structures are simultaneously integrable and allows us to write actions…

This study explores Kaluza-Klein reductions of new maximally supersymmetric backgrounds.

We show that the heterotic supersymmetry (Killing spinor equations) and the anomaly cancellation imply the heterotic equations of motion in dimensions five, six, seven, eight if and only if the connection on the tangent bundle is an instanton. For heterotic compactifications in dimension six this reduces the choice of …

We give an intrinsic definition of the special geometry which arises in global N=2 supersymmetry in four dimensions. The base of an algebraic integrable system exhibits this geometry, and with an integrality hypothesis any special Kahler manifold is so related to an integrable system. The cotangent bundle of a special …

Introduces basics of supergeometry for PhD students.

New gauge condition fixes $L^2$ metric divergence in hyperbolic monopole spaces.

In this paper, we derive from the supersymmetry of the Witten Laplacian Brascamp-Lieb's type inequalities for general differential forms on compact Riemannian manifolds with boundary. In addition to the supersymmetry, our results essentially follow from suitable decompositions of the quadratic forms associated with the…

In M-theory vacua with vanishing 4-form F, one can invoke the ordinary Riemannian holonomy H \subset SO(1,10) to account for unbroken supersymmetries n=1, 2, 3, 4, 6, 8, 16, 32. However, the generalized holonomy conjecture, valid for non-zero F, can account for more exotic fractions of supersymmetry, in particular 16<n…

These are the lecture notes from the 26th Winter School "Geometry and Physics", Czech Republic, Srni, January 14 - 21, 2006. These lectures are an introduction into the realm of generalized geometry based on the tangent plus the cotangent bundle. In particular we discuss the relation of this geometry to physics, namely…

We explore two-dimensional sigma models with (0,2) supersymmetry through their chiral algebras. Perturbatively, the chiral algebras of (0,2) models have a rich infinite-dimensional structure described by the cohomology of a sheaf of chiral differential operators. Nonperturbatively, instantons can deform this structure …

We discuss the mathematical properties of six--dimensional non--Kähler manifolds which occur in the context of ${\cal N}=1$ supersymmetric heterotic and type IIA string compactifications with non--vanishing background H--field. The intrinsic torsion of the associated SU(3) structures falls into five different classes. …

In this paper we analyze supergeometric locally covariant quantum field theories. We develop suitable categories SLoc of super-Cartan supermanifolds, which generalize Lorentz manifolds in ordinary quantum field theory, and show that, starting from a few representation theoretic and geometric data, one can construct a f…