arXiv subjects

Fabian Hahner

Publications and source records attributed to Fabian Hahner.

10 recordsLinked to original sources

arXiv2026

Moduli spaces of type II twists

We provide a complete classification of twisting supercharges for type IIA supergravity in a flat background by determining the orbits of square-zero elements in the (1,1) super Poincar\'e algebra in ten dimensions under the action of the Spin group. Together with recent results for type IIB, this completes the description of the moduli space of twists for type II supergravities. Further, we discuss the origins of these twists as dimensional reductions from eleven dimensions. Using the pure spinor formulation of the superstring, we relate the target space classification to worldsheet twists and identify supergravity counterparts of mixed A/B models. Finally, we work out the action of T-duality that relates twists of type IIA with those of type IIB.

hep-th↗

arXiv2026

Twisting BFSS & IKKT

In this note we initiate the study of ``twisted holography'' for the dualities involving the BFSS matrix quantum mechanics and the IKKT matrix model in their $N \rightarrow \infty$ limits. We identify the admissible twists of each model, compute their cohomology in the BV-BRST formalism, and identify them -- in the planar limit and in perturbation theory around the trivial background -- with corresponding twists of IIA and IIB string theories, respectively. The twisted gravitational duals make manifest certain infinite dimensional symmetry algebras. In the BFSS example, the dual IIA supergravity twists are also obtained as certain zero mode truncations of the minimal (1/16-BPS) and maximal (1/4-BPS) twists of eleven-dimensional supergravity.

hep-th↗

arXiv2025

On square-zero elements in the IIB supersymmetry algebra

We describe the variety of square-zero elements in the (2,0) super Poincar\'e algebra in ten dimensions, together with its orbit stratification induced by the action of the spin group and R-symmetry. This provides a classification of all possible twisting supercharges of type IIB supergravity in a flat background. Compared to other varieties of square-zero elements in super Poincar\'e algebras, we find that the orbit structure is more involved and exhibits several novel features. Among other things, we show that there are two distinct orbits of holomorphic twisting supercharges and a number of mixed topological-holomorphic twists.

math-ph↗

arXiv2025

Higher Symmetries in Twisted Eleven-Dimensional Supergravity

In supersymmetric theories, protected quantities can be reorganized into holomorphic-topological theories by twisting. Recently, it was observed by Jonsson, Kim and Young that residual super-Poincar\'e symmetries in certain twisted theories can receive higher corrections, turning them into $L_\infty$ algebras with non-strict actions on the twisted fields. In this note, we show that the same phenomenon occurs for the two admissible twists of eleven-dimensional supergravity. Along the way, we discuss in detail the connection between components of physical and twisted fields.

hep-th↗

arXiv2024

Eleven-dimensional supergravity as a Calabi-Yau twofold

We construct a generalization of Poisson-Chern-Simons theory, defined on any supermanifold equipped with an appropriate filtration of the tangent bundle. Our construction recovers interacting eleven-dimensional supergravity in Cederwall's formulation, as well as all possible twists of the theory, and does so in a uniform and geometric fashion. Among other things, this proves that Costello's description of the maximal twist is the twist of eleven-dimensional supergravity in its pure spinor description. It also provides a pure spinor lift of the interactions in the minimally twisted theory. Our techniques enhance the BV formulation of the interactions of each theory to a homotopy Poisson structure by defining a compatible graded-commutative product; this suggests interpretations in terms of deformations of geometric structures on superspace, and provides some concrete evidence for a first-quantized origin of the theories.

math-ph↗

arXiv2024

Local superconformal algebras

Given a supermanifold equipped with an odd distribution of maximal dimension and constant symbol, we construct the formal moduli problem of deformations of the distribution. This moduli problem is described by a local super dg Lie algebra that provides both a resolution of the structure-preserving vector fields on superspace and a derived enhancement of superconformal symmetry. Applying our construction in standard physical examples returns the conformal supergravity multiplet in every known example, in any dimension and with any amount of supersymmetry$\unicode{x2014}$whether or not a superconformal algebra exists. We discuss new examples related to twisted supergravity, higher Virasoro algebras, and exceptional super Lie algebras. The compatibility of our techniques with twisting also leads to a computation of every twist of the stress tensor multiplet of a superconformal theory, including universal operator product expansions. Our approach uses a derived model for the space of functions constant along the distribution, which is applicable even when the distribution is non-involutive; we construct other natural multiplets, such as Kähler differentials, that appear naturally through this lens on superspace geometry.

math-ph↗

arXiv2023

The Derived Pure Spinor Formalism as an Equivalence of Categories

We construct a derived generalization of the pure spinor superfield formalism and prove that it exhibits an equivalence of dg-categories between multiplets for a supertranslation algebra and equivariant modules over its Chevalley-Eilenberg cochains. This equivalence is closely linked to Koszul duality for the supertranslation algebra. After introducing and describing the category of supermultiplets, we define the derived pure spinor construction explicitly as a dg-functor. We then show that the functor that takes the derived supertranslation invariants of any supermultiplet is a quasi-inverse to the pure spinor construction, using an explicit calculation. Finally, we illustrate our findings with examples and use insights from the derived formalism to answer some questions regarding the ordinary (underived) pure spinor superfield formalism.

math-ph↗

arXiv2022

Six-dimensional supermultiplets from bundles on projective spaces

The projective variety of square-zero elements in the six-dimensional minimal supersymmetry algebra is isomorphic to $\mathbb{P}^1 \times \mathbb{P}^3$. We use this fact, together with the pure spinor superfield formalism, to study supermultiplets in six dimensions, starting from vector bundles on projective spaces. We classify all multiplets whose derived invariants for the supertranslation algebra form a line bundle over the nilpotence variety; one can think of such multiplets as being those whose holomorphic twists have rank one over Dolbeault forms on spacetime. In addition, we explicitly construct multiplets associated to natural higher-rank equivariant vector bundles, including the tangent and normal bundles as well as their duals. Among the multiplets constructed are the vector multiplet and hypermultiplet, the family of $\mathcal{O}(n)$-multiplets, and the supergravity and gravitino multiplets. Along the way, we tackle various theoretical problems within the pure spinor superfield formalism. In particular, we give some general discussion about the relation of the projective nilpotence variety to multiplets and prove general results on short exact sequences and dualities of sheaves in the context of the pure spinor superfield formalism.

math-ph↗

arXiv2022

Perspectives on the pure spinor superfield formalism

In this note, we study, formalize, and generalize the pure spinor superfield formalism from a rather nontraditional perspective. To set the stage, we review the notion of a multiplet for a general super Lie algebra, working in the context of the BV and BRST formalisms. Building on this, we explain how the pure spinor superfield formalism can be viewed as constructing a supermultiplet out of the input datum of an equivariant graded module over the ring of functions on the nilpotence variety. We use the homotopy transfer theorem and other computational techniques from homological algebra to relate these multiplets to more standard component-field formulations. Physical properties of the resulting multiplets can then be understood in terms of algebrogeometric properties of the nilpotence variety. We illustrate our discussion with many examples in various dimensions.

hep-th↗

arXiv2021

Maximally twisted eleven-dimensional supergravity

We perform the maximal twist of eleven-dimensional supergravity. This twist is partially topological and exists on manifolds of $G_2 \times SU(2)$ holonomy. Our derivation starts with an explicit description of the Batalin-Vilkovisky complex associated to the three-form multiplet in the pure spinor superfield formalism. We then determine the $L_\infty$ module structure of the supersymmetry algebra on the component fields. We twist the theory by modifying the differential of the Batalin-Vilkovisky complex to incorporate the action of a scalar supercharge. We find that the resulting free twisted theory is given by the tensor product of the de Rham and Dolbeault complexes of the respective $G_2$ and $SU(2)$ holonomy manifolds as conjectured by Costello.

hep-th↗