arXiv subjects

Carolina Matté Gregory

Publications and source records attributed to Carolina Matté Gregory.

5 recordsLinked to original sources

arXiv2026

Beyond the polynomial ansatz: regular $AdS_3\times M_8$ solutions of M-theory

We study regular compact solutions of the cohomogeneity-one $AdS_3\times M_8$ system of Gauntlett, Mac Conamhna, Mateos and Waldram, where $M_8$ is an $S^2$ bundle over three constant-curvature Riemann surfaces. We find that an endpoint argument rules out every non-flat curvature-sign sector without a positive-curvature factor, while an analytic deformation gives regular families with four radial shape parameters in all remaining sectors, with the base geometry held fixed. The known polynomial solutions form a proper analytic locus in these families. Non-polynomiality is therefore generic in parameter space, although the deviation from an endpoint-matching polynomial can be very small. Apart from the completely flat exception, the curvature-sign criterion is necessary and sufficient within this ansatz. Four magnetic flux ratios give local coordinates near the reference solution and its small-curvature deformations, and a rational inverse reconstructs candidate endpoint data directly from finite flux ratios. In the fully positive sector we prove that one explicit four-dimensional finite-ratio neighbourhood lies inside the physical flux image. The magnetic periods and leading holographic central charge reduce to endpoint data, and, once the common Brown--Henneaux normalization is fixed, the nontrivial flux dependence of the equivariant localization formula agrees with the endpoint result as an exact algebraic identity. We also quantify the non-polynomial corrections and analyse finite degenerations under explicit convergence hypotheses.

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arXiv2026

Localizing $\mathcal{N}=(2,0)$ $AdS_3$ solutions of M-theory

We apply equivariant localization to supersymmetric $AdS_3\times M_8$ solutions of eleven-dimensional supergravity, dual to two-dimensional $\mathcal N=(2,0)$ SCFTs. We construct equivariantly closed polyforms encoding the magnetic flux and its dual, calibrated M2-branes and the warped volume, reducing protected observables to fixed point data of the $U(1)$ R-symmetry action. We apply the framework to $S^4$ bundles over coassociative four-cycles and $S^2$ bundles over compact six-manifolds, obtaining topological formulae for leading central charges and gravitational anomalies in terms of quantized fluxes and topological data. We recover the known results for $T^2\times KE_4$ solutions and construct a compact numerical solution with quantized flux that lies outside the known polynomial branch.

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arXiv2026

Geodesic equation in noncommutative space: a field theory perspective

We derive the geodesic equation for point particles propagating in Moyal-type noncommutative spacetimes using a field-theoretic approach based on the quasi-classical limit of the noncommutative Klein-Gordon equation. Starting from a twisted-geometric construction of the covariant Laplace-Beltrami operator, we obtain the noncommutative Hamilton-Jacobi equation and show that all noncommutative effects are absorbed into an effective, position-dependent mass function $M(x)$ appearing in an otherwise standard relativistic dispersion relation. The corresponding particle dynamics then acquires an additional term in the geodesic equation that takes the form of a fixed external force $F_{\text{NC}}^μ= -\frac{1}{2} g^{μν}\partial_νM^2(x)$, sourced entirely by the quantum nature of spacetime. We compute this effective mass perturbatively up to fourth order in the noncommutativity parameter for a general metric, proving that all odd-order corrections vanish identically. For the specific case of an $(r-θ)$ twist applied to spherically symmetric backgrounds, we obtain explicit expressions demonstrating that the leading correction to geodesic motion appears at $Θ^2$ order and is proportional to the probe particle's mass, while massless particles remain unaffected.

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arXiv2026

Current Reconstruction and Higher Interactions in Gauge Theory

We revisit Deser's current reconstruction in first-order Yang--Mills theory with an independent two-form. We fix the quadratic auxiliary sector and the first gauge correction, and ask whether a prescribed curvature interaction can be added without higher-order action terms. For a compact semisimple gauge algebra, requiring the mixed Noether identity to close without a $gh$ action term fixes the algebraic auxiliary representative to the tangent representative, up to linear curvature and dual-curvature terms on each simple ideal. For the analytic radial class $U=Φ(f\cdot f)$, with first nonlinear term $c_p(f\cdot f)^p$, no allowed representative avoids a third-order action correction when all second-order action coefficients vanish. A free-field scaling argument inside a root $\mathfrak{su}(2)$ subalgebra establishes this result for every compact semisimple gauge algebra. Ordinary covariantization and an auxiliary-field shift give an explicit completion. For $p=2$, its seven-gluon contact term cancels a nonzero tree-level Ward contraction at real nonsingular kinematics. We also study an affine star-gauge sector motivated by Seiberg--Witten maps, where strict current feedback and second-order action truncation select different representatives. Together these results show how the prescribed auxiliary data determine which interactions are required by current reconstruction.

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arXiv2019

Classifying solutions to Romans supergravity with a zero B-field

Expanding on previous papers, we continue studying Euclidean Romans supergravity in six dimensions with a non-trivial Abelian R-symmetry gauge field. Using a set of differential constraints on a $SU(2)$ structure, we look for further geometric solutions to such equations when we turn off the two-form potential B. We find that the six-dimensional space is described by a two-dimensional fibration over a four-dimensional manifold with a Kähler metric. We then classify these types of solutions.

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