arXiv subjects

Davide Rovere

Publications and source records attributed to Davide Rovere.

11 recordsLinked to original sources

arXiv2026

Teleparallel formulation of $E_{8(8)}$ Exceptional Field Theory

The potential of $E_{8(8)} \times \mathbb{R}^+$ exceptional field theory, suited for studying three-dimensional maximally supersymmetric compactifications of higher-dimensional supergravities, is derived in teleparallel formulation. This means that, starting from an ansatz of the most general combination of the quadratic scalar contractions of the intrinsic torsion, which is manifestly invariant under generalised diffeomorphisms, one selects the potential by imposing the invariance under infinitesimal rotation of the maximal compact subgroup of the duality group. The teleparallel formulation makes manifest at geometric level the preeminent role of the intrinsic torsion in studying compactifications of higher-dimensional supergravities, where the intrinsic torsion is identified with the embedding tensor of the resulting gauged supergravity.

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arXiv2026

Conformal Renormalisation of 8D Einstein Gravity

We show that Holographic Renormalisation (HR) in eight dimensions is encoded in the unique conformal gravity theory that admits an Einstein sector with constant negative curvature. We explicitly relate HR to Topological Regularisation (TR), where the latter prescribes to add the Euler term to the Einstein-Hilbert Lagrangian density, with a precise coefficient so as to ensure that the resulting density is polynomial in the anti de Sitter (AdS) curvature. The polynomial is still asymptotically divergent. We find that the aforementioned, unique conformal gravity action in 8D, reproduces the polynomial, together with extra boundary terms that cancel the divergent terms in the action. We conjecture that, in arbitrary even dimension, HR is equivalent to conformally completing the Einstein-Hilbert action with negative cosmological constant, plus the Euler term with fixed coupling prescribed by TR.

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arXiv2025

The Use of Torsion in Supergravity Uplifts and Covariant Fractons

The aim of this Thesis is twofold. On the one hand, we find the necessary and sufficient conditions for a maximally supersymmetric supergravity theory in 3D to be a solution of 11D supergravity (but the result is general and also holds for 10D supergravities), with 8 dimensions compactified into a coset space. The used method is based on the formalism of generalised geometry, useful for the study of dualities in string theory and supergravity. The analysis extends the known results to the case in which the duality group of the reduced theory is $E_{8(8)}$, whose generalised geometry is still little understood. On the other hand, we study properties of the so-called covariant fracton gauge theory, computing the BRST cohomology and consistent anomalies, and showing that its solutions describe a specific subsector of an extension of General Relativity, called Moller-Hayashi-Shirafuji theory. Covariant fracton theory is the gauge theory of a symmetric rank-2 tensor, invariant under gauge transformations depending on the second derivative of a scalar parameter, and is the Lorentz-covariant extension of the continuous limit of spin-chain theories admitting excitations with reduced mobility (called fractons), due to the conservation of the dipole moment. In both cases, the Weitzenb\"ock torsion plays a crucial r\^ole. The Thesis includes a self-contained review of the main notions needed to understand the original results, comprising, in addition to the already mentioned topics, duality in supergravity theories, the generalised Lie derivative, formulation of eleven-dimensional supergravity suitable to reductions with duality groups given by exceptional Lie groups, salient aspects of three-dimensional gravity, and the BRST formalism for computing anomalies in field theories.

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arXiv2025

8D conformal gravity with Einstein sector, and its relation to the Q-curvature

We first streamline the construction of the unique six-dimensional conformal gravity action found by L\"u, Pang and Pope, that admits Einstein metrics as solutions to the field equations. We then prove that there exists a unique eight-dimensional conformal gravity action that admits Einstein metrics as solutions to the field equations, and explicitly build the corresponding action. Finally, we relate these results to Branson's Q-curvature and the Fefferman-Graham obstruction tensor, to conclude that on every even-dimensional space there exists a unique -- up to boundary terms -- conformally-invariant gravity theory that is extremised by Einstein metrics.

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arXiv2025

How to uplift non-maximal gauged supergravities

In this paper, we provide an algorithm to perform the uplift of non-maximal $G_g$-gauged supergravities to type IIB or 11D supergravities. Using tools of exceptional field theory and generalised geometry, we show that the internal manifold admits a $G_g$-action, and that consistency of the uplift is equivalent to solving a simpler PDE on the quotient $M_{\text{int}}/G_g$. As an application, we classify all possible uplifts of pure half-maximal four-dimensional $\textrm{SO}(4)$-gauged supergravity to type IIB and we recover consistent truncations around any of the D'Hoker-Estes-Gutperle solutions \cite{DHoker:2007hhe}.

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arXiv2025

Worldline Formulations of Covariant Fracton Theories

We develop worldline formulations of covariant fracton gauge theories. These are a one-parameter family of gauge theories of a rank-two symmetric tensor field, invariant under a scalar gauge transformation involving a double derivative. These theories, which can be interpreted as linearized gravity theories invariant under longitudinal diffeomorphisms, provide a covariant framework for studying Lorentz-breaking fracton quasiparticles, which are excitations with restricted mobility due to dipole-moment conservation. We construct three worldline models. The first two are obtained by deducing their constraint structure directly from the spacetime gauge transformations. By applying BRST quantization, we show that these models reproduce the BV spectrum and the associated BRST transformations of two specific fracton theories. The third model is defined as a deformation of the second one: although free, it is analyzed by drawing inspiration from the standard treatment of interacting worldline systems, and is shown to capture almost the entire family of covariant fracton theories. Finally, we discuss the gauge-fixing, comparing the BV-BRST spacetime perspective with the worldline analogue of the ``Siegel gauge" employed in string field theory.

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arXiv2025

Covariant Fractons and Weitzenb\"ock Torsion

The relation between covariant fracton gauge theory and Moller-Hayashi-Shirafuji theory of gravity is investigated. The former is the gauge theory of a rank-two symmetric tensor with gauge symmetry given by the double derivative of a scalar parameter; the latter is the most general theory, whose action is quadratic in the Weitzenb\"ock torsion. We show that the solutions of covariant fracton gauge theory describe a subsector of the space of solutions of Moller-Hayashi-Shirafuji theory, providing a new insight in the relation between covariant fractons and gravity, and elucidating the meaning of covariant fracton theory as a new type of gauge theory.

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arXiv2024

How to uplift D=3 maximal supergravities

We prove necessary and sufficient algebraic conditions to determine whether a D=3 gauged maximal supergravity can be obtained from consistent Kaluza-Klein truncation of ten- or eleven-dimensional supergravity. We describe the procedure to identify the internal geometry and explicitly construct the frame encoding the reduction ansatz. As byproducts, we derive several results on twistings, deformations and global aspects of E$_8$ exceptional geometry and define E$_8$ generalised diffeomorphism for massive IIA supergravity. We devise simple algebraic conditions for imposing compactness of the internal space and derive no-go results for the uplift of compact gaugings and of a large class of gauged maximal supergravities with N=(8,0) AdS$_3$ solutions.

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arXiv2024

Anomalies in Covariant Fracton Theories

Covariant (Lorentz invariant) fracton matter, minimally coupled and charged under a symmetric rank two gauge tensor, is considered. The gauge transformations correspond to linearized longitudinal diffeomorphisms. Consistent possible anomalies are computed using the BRST cohomology method. They depend only on the gauge field, treated as a background field, and on the gauge parameter, promoted to an anticommuting scalar ghost field. The problem is phrased in terms of polyforms, whose total degree is the sum of the form degree and of the ghost number. The most general anomaly in two dimensions and in four dimensions is computed and an anomaly in arbitrary dimensions is individuated. In conclusion, it is shown that a simple higher-derivative scalar field theory is an example of covariant fracton matter.

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arXiv2024

Kodaira-Spencer Anomalies with Stora-Zumino Method

Holomorphic diffeomorphism anomalies of $2\,n$-dimensional gravitational theories in Beltrami parametrisation (Kodaira-Spencer anomalies) are computed in the BRST framework, using an extension of the Stora-Zumino method. This method, which allows to compute anomalies in a very concise way, makes manifest the topological origin of anomalies. They have a clear geometric interpretation, since they are expressed in terms of Chern polynomials and Pontryagin invariants. The key ingredient is the formulation of the BRST transformations in terms of polyforms, whose total degree is the sum of the form degree and of the ghost number. This approach simplifies significantly the analysis available in literature and it allows to compute many other solutions. Namely, an anomaly, which was computed using different methods, is proved to be a consistent BRST anomaly, thereby supplementing a conclusion in a previous analysis.

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arXiv2023

Superconformal anomalies from superconformal Chern-Simons polynomials

We consider the 4-dimensional $\mathcal{N}=1$ Lie superconformal algebra and search for completely "symmetric" (in the graded sense) 3-index invariant tensors. The solution we find is unique and we show that the corresponding invariant polynomial cubic in the generalized curvatures of superconformal gravity vanishes. Consequently, the associated Chern-Simons polynomial is a non-trivial anomaly cocycle. We explicitly compute this cocycle to all orders in the independent fields of superconformal gravity and establish that it is BRST equivalent to the so-called superconformal $a$-anomaly. We briefly discuss the possibility that the superconformal $c$-anomaly also admits a similar Chern-Simons formulation and the potential holographic, 5-dimensional, interpretation of our results.

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