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Julian Kupka

Publications and source records attributed to Julian Kupka.

8 recordsLinked to original sources
arXiv2026

Kodaira-Spencer theory for flux backgrounds

We give an explicit description (in component fields) of a holomorphic theory associated to a general supersymmetric background of $\mathcal N=1$ supergravity in ten dimensions. Conjecturally, this provides a sought-for holomorphic realisation of the supergravity twist in such backgrounds, generalising the minimal type I BCOV theory for Calabi-Yau manifolds. Our theory unpacks the recently introduced Courant contact model associated to a holomorphic Courant algebroid. We also show that a coisotropic reduction of this model reproduces the recent model of ref [1], which is formulated in terms of constrained fields.

hep-th↗
arXiv2026

Kodaira-Spencer theory for Courant algebroids

Studying Courant algebroids on dg ringed manifolds, we observe that the associated Roytenberg-Weinstein $L_\infty$ algebra admits a local structure reminiscent of a shifted contact structure. On a dg ringed manifold with an $n$-orientation, its symplectification produces a sheaf of $(2-n)$-shifted symplectic formal moduli problems, which we call the Courant contact model. This construction can be interpreted as a ($\mathbb{Z}/2\mathbb{Z}$-graded) theory in the Batalin-Vilkovisky formalism whenever $n$ is odd. After developing the procedure of reduction and extension of scalars, we show how twisted backgrounds in type I supergravity naturally lead to Courant algebroids over the Dolbeault complex. Specialising to the case of a Calabi-Yau fivefold, we show that the Courant contact model for that Courant algebroid is equivalent to a central extension of minimal type I BCOV theory. Inspired by this, we extend the conjecture of Costello and Li and place it within the setting of generalized geometry, conjecturing a description of the BV formulation of type I supergravity in general twisted backgrounds.

math-ph↗
arXiv2025

Geometry of supergravity and the Batalin--Vilkovisky formulation of the $\mathcal N=1$ theory in ten dimensions

We provide full details of a BV formulation of $\mathcal N=1$ supergravity in ten dimensions, to all orders in fermions, built from the generalised geometry description of the theory. In contrast to standard treatments, we introduce neither the degrees of freedom corresponding to orthonormal frames for the metric nor the local Lorentz symmetries that remove them again. Instead, we observe that the field space has a fibred structure, with the fermionic degrees of freedom spanning the fibres. We explain in detail how this geometric picture allows one to understand simultaneous variations of spinorial quantities and the metric with respect to which the spinor bundles are defined. This leads to additional terms in certain commutators on field space which account for the Lorentz transformation terms appearing in the calculation of the supersymmetry algebra. Unencumbered by the Lorentz degrees of freedom, we provide an efficient and full demonstration that our action satisfies the classical master equation.

hep-th↗
arXiv2025

Higher fermions in supergravity

We show that the generalised geometry formalism provides a new approach to the description of higher-fermion terms in $\mathcal N=1$ supergravity in ten dimensions, which does not appeal to supercovariantisation or superspace. We find expressions containing only five higher-fermion terms across the action and supersymmetry transformations, working in the second-order formalism.

hep-th↗
arXiv2025

Direct derivation of $\mathcal N=1$ supergravity in ten dimensions to all orders in fermions

It has been known for some time that generalised geometry provides a particularly elegant rewriting of the action and symmetries of 10-dimensional supergravity theories, up to the lowest nontrivial order in fermions. By exhibiting the full symmetry calculations in the second-order formalism, we show in the $\mathcal N=1$ case that this analysis can be upgraded to all orders in fermions and we obtain a strikingly simple form of the action as well as of the supersymmetry transformations, featuring overall only five higher-fermionic terms. Surprisingly, even after expressing the action in terms of classical (non-generalised geometric) variables one obtains a simplification of the usual formulae. This in particular confirms that generalised geometry provides the natural set of variables for studying (the massless level of) string theory. We also show how this new reformulation implies the compatibility of the Poisson-Lie T-duality with the equations of motion of the full supergravity theory.

hep-th↗
arXiv2024

Supergravity without gravity and its BV formulation

The generalised-geometric formulation of 10-dimensional supergravity suggests a particular simple "limit", which results in a theory whose only dynamical degrees of freedom are the dilaton and the dilatino. The theory is still invariant both under generalised diffeomorphisms and a local supersymmetry and in many aspects is structurally similar to the original supergravity, which makes it a convenient playground for understanding more subtle aspects of the full physical setup. In particular, the simplicity and the geometric nature of the dilatonic theory allow us to build a full BV extension to all orders in the fermionic variables.

hep-th↗
arXiv2024

BPS complexes and Chern--Simons theories from $G$-structures in gauge theory and gravity

We consider a variety of physical systems in which one has states that can be thought of as generalised instantons. These include Yang--Mills theories on manifolds with a torsion-free $G$-structure, analogous gravitational instantons and certain supersymmetric solutions of ten-dimensional supergravity, using their formulation as generalised $G$-structures on Courant algebroids. We provide a universal algebraic construction of a complex, which we call the BPS complex, that computes the infinitesimal moduli space of the instanton as one of its cohomologies. We call a class of these spinor type complexes, which are closely connected to supersymmetric systems, and show how their Laplacians have nice properties. In the supergravity context, the BPS complex becomes a double complex, in a way that corresponds to the left- and right-moving sectors of the string, and becomes much like the double complex of $(p,q)$-forms on a Kähler manifold. If the BPS complex has a symplectic inner product, one can write down an associated linearised BV Chern--Simons theory, which reproduces several classic examples in gauge theory. We discuss applications to (quasi-)topological string theories and heterotic superpotential functionals, whose quadratic parts can also be constructed naturally from the BPS complex.

hep-th↗