arXiv subjects

Lorenzo Ruggeri

Publications and source records attributed to Lorenzo Ruggeri.

11 recordsLinked to original sources

arXiv2026

Half-Spacetime Gauging of 2-Group Symmetry in 3d

We construct a class of non-invertible duality defects, in (2+1)d quantum field theories, arising from half-spacetime gauging of a 2-group symmetry. Starting from a parent theory with two discrete and Abelian 0-form symmetries and a prescribed mixed anomaly, we show that gauging one factor produces a theory with a 2-group symmetry, while gauging the other yields a theory with a non-invertible 0-form symmetry, whose fusion rules we derive explicitly. When the parent theory possesses three such symmetries with a cyclic anomaly structure, gauging different factors can produce mutually dual theories and the half-spacetime gauging of the 2-group is implemented by a non-invertible duality defect, whose fusion rules we obtain. We illustrate the construction with explicit examples, including a $U(1)\times U(1)\times U(1)$ gauge theory and a general class of product theories. We also include a self-contained pedagogical introduction to the cohomological tools employed throughout the article.

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arXiv2026

Projecting Gravitational Fluctuations onto Near-Horizon Throats

We show that, for stationary geometries whose linearized fluctuation equations separate into radial and angular Heun equations, a pair of diffeomorphisms projects the full problem onto two coupled, isospectral Gauss hypergeometric problems in complementary spacetime regions. This projection requires Robin boundary conditions to be imposed at the intersection between the complementary regions, which are uniquely fixed by requiring the two diffeomorphisms to match there. The method provides an independent derivation of recent results obtained from the correspondence between Heun connection coefficients and instanton partition functions in the Nekrasov-Shatashvili limit. As an application, we identify a subset of modes in Kerr-de Sitter and Kerr-anti-de Sitter black holes that, in the near-extremal limit, continuously reduce to a basis of the Schwarzian/Jackiw-Teitelboim functional space of gravitational fluctuations.

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arXiv2026

Codimension-Two Defects and SYM on Orbifolds

We study $U(N)$ SYM theories on spaces with orbifold singularities via an equivalent description in terms of gauge theories on smooth manifolds with insertions of Gukov-Witten and twist defects. The combined effect of the defects is to render the fields multivalued with respect to rotations around the support of the defects. This motivates a relation with theories on branched covers, for which the multivaluedness has a geometric interpretation. We compute the partition function of the theory with defects on a patch and use it as a building block to compute partition functions on several closed spaces with conical singularities.

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arXiv2026

Contour Integral for the Partition Function of $\mathcal{N}=2$ Topologically Twisted on $\mathbb{CP}^2$ and Physical Fluxes

We compute the contour integral for the partition function of an $\mathcal{N}=2$ $SU(2)$ topologically twisted theory on $\mathbb{CP}^2$, dimensionally reducing from an $\mathcal{N}=1$ theory on $S^5$. Earlier works presented the partition function as a sum over three equivariant fluxes, one for each toric divisor of $\mathbb{CP}^2$. Our result depends only on a single physical flux, assigned to the non-trivial two-cycle of the manifold. The reduced summation over fluxes is compensated by a contour of integration, arising from a different solution of the BPS equations, which captures more poles in each topological sector. As our observable involves a position-dependent Yang-Mills coupling, we compute new equivariant invariants of $\mathbb{CP}^2$, which reduce to Donaldson invariants in the non-equivariant limit. Stability conditions of gauge bundles over $\mathbb{CP}^2$ appear intrinsically via the dimensional reduction.

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arXiv2025

Exact Results for SYM on $Y^{p,q}$ and $S^2\times S^2$ with Conical Singularities

Starting from a theory on $S^3\times S^3$ and dimensionally reducing, we compute the full partition function, including flux and instanton contributions, for an $\mathcal{N}=1$ theory of vector multiplets and hypermultiplets on five-dimensional toric Sasakian manifolds $Y^{p,q}$. Dimensionally reducing, we obtain the partition function for Pestun-like theories on a class of manifolds whose topology is $S^2\times S^2$. Generalizing the procedure starting from branched covers of $S^3\times S^3$, we reduce to a theory on $Y^{p,q}$ with codimension two twist defects. Exploiting a proposed equivalence with partition functions on spaces with orbifold singularities, our results provide the partition function of an $\mathcal{N}=2$ theory on the product of two spindles.

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arXiv2025

From 5d Flat Connections to 4d Fluxes (the Art of Slicing the Cone)

We compute the Coulomb branch partition function of the 4d $\mathcal{N}=2$ vector multiplet on closed simply-connected quasi-toric manifolds $B$. This includes a large class of theories, localising to either instantons or anti-instantons at the torus fixed points (including Donaldson-Witten and Pestun-like theories as examples). The main difficulty is to obtain flux contributions from the localisation procedure. We achieve this by taking a detour via the 5d $\mathcal{N}=1$ vector multiplet on closed simply-connected toric Sasaki-manifolds $M$ which are principal $S^1$-bundles over $B$. The perturbative partition function can be expressed as a product over slices of the toric cone. By taking finite quotients $M/\mathbb{Z}_h$ along the $S^1$, the locus picks up non-trivial flat connections which, in the limit $h\to\infty$, provide the sought-after fluxes on $B$. We compute the one-loop partition functions around each topological sector on $M/\mathbb{Z}_h$ and $B$ explicitly, and then factorise them into contributions from the torus fixed points. This enables us to also write down the conjectured instanton part of the partition function on $B$.

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arXiv2025

Super Yang-Mills on Branched Covers and Weighted Projective Spaces

In this work we conjecture the Coulomb branch partition function, including flux and instanton contributions, for the $\mathcal{N}=2$ vector multiplet on weighted projective space $\mathbb{CP}^2_{\boldsymbol{N}}$ for equivariant Donaldson-Witten and ``Pestun-like'' theories. We claim that this partition function agrees with the one obtained from dimensional reduction of the 5d $\mathcal{N}=1$ vector multiplet on a certain branched cover of $S^5$. More precisely, the branch locus and indices have to be such that they match the singular locus and deficit angles in $\mathbb{CP}^2_{\boldsymbol{N}}$. Our conjecture is substantiated by checking that partition functions on spindles are similarly obtained from dimensional reduction of the 3d $\mathcal{N}=2$ vector multiplet on branched covers of $S^3$. This work paves the way for obtaining partition functions on more generic symplectic toric orbifolds.

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arXiv2024

Non-Invertible Surface Defects in 2+1d QFTs from Half Spacetime Gauging

We study duality defects in 2+1d theories with $\bZ^{(0)}_N\times\bZ^{(1)}_N$ global symmetry and trivial mixed 't Hooft anomaly. By gauging these symmetries simultaneously in half of the spacetime, we define duality defects for theories that are self-dual under gauging. We calculate the fusion rules involving duality defects and show that they obey a fusion 2-category. We also construct the corresponding symmetry topological field theory, a four-dimensional BF theory on a slab which realizes the duality defects on the boundary upon shrinking the interval. Furthermore, we provide explicit examples of such duality defects in $U(1)\times U(1)$ gauge theories and in more general product theories. Finally, we find duality defects in non-Lagrangian theories obtained by compactification of 6d $\cN=(2,0)$ SCFTs of type $A_{N-1}$ on various three-manifolds.

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arXiv2022

Index of the Transversally Elliptic Complex in Pestunization

In this note we present a formula for the equivariant index of the cohomological complex obtained from localization of $\mathcal{N}=2$ SYM on simply-connected compact four-manifolds with a $T^2$-action. Knowledge of said index is essential to compute the perturbative part of the partition function for the theory. In the topologically twisted case, the complex is elliptic and its index can be computed in a standard way using the Atiyah-Bott localization formula. Recently, a framework for more general types of twisting, so-called cohomological twisting, was introduced for which the complex turns out to be only transversally elliptic. While the index of such a complex has been computed for some cases where the manifold can be lifted to a Sasakian $S^1$-fibration in five dimensions, a general four-dimensional treatment was still lacking. We provide a formal, purely four-dimensional treatment of the cohomological complex, showing that the Laplacian part can be globally split off while the remaining part can be trivialized uniquely in the group-direction. This ultimately produces a simple formula for the index applicable for any compact simply-connected four-manifold. Finally, the index formula is applied to examples on $S^4$, $\mathbb{CP}^2$ and $\mathbb{F}^1$. For the latter, we use the result to compute the perturbative partition function.

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arXiv2022

SYM on Quotients of Spheres and Complex Projective Spaces

We introduce a generic procedure to reduce a supersymmetric Yang-Mills (SYM) theory along the Hopf fiber of squashed $S^{2r-1}$ with $U(1)^r$ isometry, down to the $\mathbb{CP}^{r-1}$ base. This amounts to fixing a Killing vector $v$ generating a $U(1)\subset U(1)^r$ rotation and dimensionally reducing either along $v$ or along another direction contained in $U(1)^r$. To perform such reduction we introduce a $\mathbb{Z}_p$ quotient freely acting along one of the two fibers. For fixed $p$ the resulting manifolds $S^{2r-1}/\mathbb{Z}_p\equiv L^{2r-1}(p,\pm 1)$ are a higher dimensional generalization of lens spaces. In the large $p$ limit the fiber shrinks and effectively we find theories living on the base manifold. Starting from $\mathcal{N}=2$ SYM on $S^3$ and $\mathcal{N}=1$ SYM on $S^5$ we compute the perturbative partition functions on $L^{2r-1}(p,\pm 1)$ and, in the large $p$ limit, on $\mathbb{CP}^{r-1}$, respectively for $r=2$ and $r=3$. We show how the reductions along the two inequivalent fibers give rise to two distinct theories on the base. Reducing along $v$ gives an equivariant version of Donaldson-Witten theory while the other choice leads to a supersymmetric theory closely related to Pestun's theory on $S^4$. We use our technique to reproduce known results for $r=2$ and we provide new results for $r=3$. In particular we show how, at large $p$, the sum over fluxes on $\mathbb{CP}^2$ arises from a sum over flat connections on $L^{5}(p,\pm 1)$. Finally, for $r=3$, we also comment on the factorization of perturbative partition functions on non simply connected manifolds.

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arXiv2020

Cohomological Localization of $\mathcal N = 2$ Gauge Theories with Matter

We construct a large class of gauge theories with extended supersymmetry on four-dimensional manifolds with a Killing vector field and isolated fixed points. We extend previous results limited to super Yang-Mills theory to general $\mathcal{N}=2$ gauge theories including hypermultiplets. We present a general framework encompassing equivariant Donaldson-Witten theory and Pestun's theory on $S^4$ as two particular cases. This is achieved by expressing fields in cohomological variables, whose features are dictated by supersymmetry and require a generalized notion of self-duality for two-forms and of chirality for spinors. Finally, we implement localization techniques to compute the exact partition function of the cohomological theories we built up and write the explicit result for manifolds with diverse topologies.

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