arXiv subjects

Christopher Couzens

Publications and source records attributed to Christopher Couzens.

At least 19 recordsLinked to original sources

arXiv2026

Ten-dimensional localization

We construct equivariantly closed polyforms for the fluxes and the action of (massive) type IIA and type IIB supergravity directly in ten dimensions. We illustrate applications of our formalism to two distinct classes of solutions in massive type IIA. Our analysis straightforwardly reproduces and vastly generalizes all known results for on-shell actions in these classes, with no need for a consistent truncation. Where known, we match the corresponding field theory partition functions at leading order, and our results extend easily to other solutions of type II supergravity.

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arXiv2026

Probing black holes with equivariant localization

We introduce equivariant localization as a method for computing the action of probe branes in supergravity backgrounds. We apply it to supersymmetric probe D3-branes in type IIB supersymmetric spacetimes obtained by uplifting the Kerr-Newman-AdS$_5$ black hole on a toric Sasaki-Einstein space. Depending on the cycles they wrap, such branes represent non-perturbative corrections to or defect operator insertions in the superconformal index of a large family of four-dimensional $\mathcal{N}=1$ quiver superconformal field theories. The resulting action reduces to equivariant integrals and can be evaluated entirely from toric data.

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arXiv2026

IIB an equivariantly localized puncture

We use equivariant localization to compute various observables for $\mathcal{N}=(2,2)$ preserving AdS$_3$ solutions in type IIB supergravity. Our method for localizing the odd-dimensional internal space is to perform a dimensional reduction along a shrinking circle which introduces a boundary in the remaining even-dimensional spacetime. Canonical even-dimensional localization can then be performed on this space after taking into account contributions from the boundary. We illustrate with a number of supersymmetric solutions. One of the novel aspects of this work is applying these techniques to study punctures and defects using localization. We obtain new results for the central charge of 2d SCFTs arising from compactifying $\mathcal{N}=4$ SYM on a punctured Riemann surface.

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arXiv2025

Localizing punctures in M-theory

We use equivariant localization and holography to study four-dimensional $\mathcal{N}=1$ superconformal field theories arising from M5-branes wrapped on a punctured Riemann surface. We explain how, given a Riemann surface with marked points, one can glue in a ``puncture geometry'' locally around each point. Using equivariant localization we show that the central charge consists of a bulk contribution plus localized puncture contributions. We recover and generalize the known results for locally $\mathcal{N}=2$ preserving punctures, and derive new results for genuinely locally $\mathcal{N}=1$ preserving punctures.

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arXiv2025

Localizing Romans supergravity

We derive a general formula for the on-shell action of six-dimensional Euclidean Romans supergravity using equivariant localization. Our results are obtained without the need for solving any of the equations of motion, instead working on the assumption of the existence of a solution. We show that the on-shell action is completely determined in terms of the R-symmetry Killing vector and topological data. We easily recover known results in the literature, make predictions for hitherto unknown solutions, and also match to holographic field theory duals.

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arXiv2024

A geometric dual of F-maximization in massive type IIA

Using equivariant localization we construct a geometric dual of F-maximization in massive type IIA supergravity. Our results use only topological data to quantize the fluxes, compute the free-energy and conformal dimensions of operators in the dual field theory without the need for explicit solutions. We utilize our formalism to study various classes of solutions, including examples where an explicit solution is not known.

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arXiv2024

On the Class $\mathcal{S}$ Origin of Spindle Solutions

We analyse the backreacted geometry corresponding to a stack of M5-branes wrapped on a spindle, with a view towards precision tests of the dual $\mathcal{N} = 1$ superconformal field theory. We carefully study the singular loci of the uplifted geometry and show that these correspond to $\mathbf{C}^3/\mathbf{Z}_n$ conical singularities. Therefore, these solutions present one of the first explicit realisations of honest locally $\mathcal{N} = 1$ preserving punctures in class $\mathcal{S}$. Additionally, we study the symmetries and anomalies of the dual field theory through anomaly inflow and compute a variety of holographic observables including dimensions of BPS operators. This work paves the way for advancements in the study and identification of the precise dual field theories.

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arXiv2023

Holographic duals of Higgsed $\mathcal{D}_p^b(BCD)$

We construct the AdS$_5$ holographic duals to all non-Lagrangian 4d $\mathcal{N}=2$ superconformal field theories of Argyres--Douglas type, namely, $\mathcal{D}_p^{\,b}(G)$, arising from class $\mathcal{S}$ of classical type involving irregular punctures of regular semi-simple type. The 11d supergravity duals contain an internal space of the form of a fibered product of a disc with a squashed and fibered four-sphere and includes orbifold projections which depend on the type of twist lines/outer-automorphism twists in the class $\mathcal{S}$ theory. We verify the holographic duality by determining and matching the anomalies (including the central charges $a$ and $c$ and the flavor central charges) at leading and subleading orders. The Higgs branch of the conformal field theory is described via Higgsing by a nilpotent orbit of a classical Lie algebra; we find the exact closed form formulae for the central charges for every Higgsing. We prove that in the supergravity duals, constraints on the type of partitions associated to allowable Higgsings are enforced by the consistency condition known as the t-rule.

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arXiv2023

Symmetry Breaking and Consistent Truncations from M5-branes Wrapping a Disc

We construct new supersymmetric solutions corresponding to M5-branes wrapped on a topological disc by turning on additional scalars in the background. The presence of such scalar fields breaks one of the U(1) isometries of the internal space, explicitly realising the breaking by the Stuckelberg mechanism observed previously. In addition, we construct a consistent truncation of maximal seven-dimensional gauged supergravity on the disc to five-dimensional Romans' SU (2) x U(1) gauged supergravity, allowing us to construct a plethora of new supergravity solutions corresponding to more general states in the dual SCFTs as well as solutions corresponding to M5-branes wrapping four-dimensional orbifolds.

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arXiv2023

A plethora of Type IIA embeddings for $d=5$ minimal supergravity

We construct multiple embeddings of all solutions of $d=5$ minimal (un)gauged supergravity into massive Type IIA supergravity. The internal spaces and warpings of such embeddings are the same as those of the $\mathcal{N}=1$ supersymmetric (Mink$_5$) AdS$_5$ vacua, with the slight modification that the U(1) R-symmetry direction becomes fibered over the external space by the $d=5$ gauge field. In addition the fluxes are appropriately modified. There are many distinct types of the aforementioned internal spaces and as such many different embeddings of the $d=5$ supergravity. As examples of our setup we provide new solutions dual to six-dimensional, $\mathcal{N}=(1,0)$ SCFTs compactified on the product of a constant curvature Riemann surface and a spindle. We also provide a multitude of massive Type IIA embeddings for rotating, asymptotically AdS$_5$ black hole solutions.

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arXiv2022

Holographic duals of M5-branes on an irregularly punctured sphere

We provide explicit holographic duals of M5-branes wrapped on a sphere with one irregular puncture and one regular puncture of arbitrary type. The solutions generalise the solutions corresponding to M5-branes wrapped on a disc recently constructed by Bah-Bonetti-Minasian-Nardoni by allowing for a general choice of regular puncture. We show that the central charges, flavour central charges and conformal dimensions of BPS operators match with a class of Argyres-Douglas theory.

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arXiv2022

D4-branes wrapped on four-dimensional orbifolds through consistent truncation

We construct a consistent truncation of six-dimensional matter coupled $F(4)$ gauged supergravity on a cornucopia of two-dimensional surfaces including a spindle, disc, domain wall and other novel backgrounds to four-dimensional minimal gauged supergravity. Using our consistent truncation we uplift known AdS$_2\times {\Sigma}_1$ solutions giving rise to four-dimensional orbifold solutions, AdS$_2\times{\Sigma}_1\ltimes{\Sigma}_2$. We further uplift our solutions to massive type IIA supergravity by constructing the full uplift formulae for six-dimensional U$(1)^2$-gauged supergravity including all fields and arbitrary Romans mass and gauge coupling. The solutions we construct are naturally interpreted as the near-horizon geometries of asymptotically AdS$_6$ black holes with a four-dimensional orbifold horizon. Alternatively, one may view them as the holographic duals of superconformal quantum mechanical theories constructed by compactifying five-dimensional USp$(2N)$ theory living on a stack of D4-D8 branes on the four-dimensional orbifolds. As a first step to identifying these quantum mechanical theories we compute the Bekenstein--Hawking entropy holographically.

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arXiv2022

Universal spindles: D2's on $Σ$ and M5's on $Σ\times \mathbb{H}^3$

We study the uplift of a 4d black hole in 4d Einstein--Maxwell supergravity with a spindle horizon to massive type IIA and 11d supergravity on $S^4\times \mathbb{H}^3$. The solutions exhibit features distinct to the uplift of the same 4d solution to 11d supergravity on an $S^7$. In particular, whereas the orbifold singularities may be removed in the 11d uplift on an $S^7$, they are always present in both of the classes considered here. We compute the free energy of the solutions giving predictions for the free energy of a class of 3d Chern--Simons theories wrapped on a spindle.

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arXiv2022

A tale of (M)2 twists

We study the parameter space of magnetically charged AdS$_2\times\mathbb{WCP}^{1}_{[n_-,n_+]}$ solutions in 4d U$(1)^4$ gauged STU supergravity. We show that both \emph{twist} and \emph{anti-twist} solutions are realised and give constraints for their existence in terms of the magnetic charges of the solution. We provide infinite families of both classes of solution in terms of their magnetic charges and weights of the orbifold. As a byproduct of our analysis we obtain a closed form expression for the free-energy of the 4-charge magnetic solution in terms of the magnetic charges and weights $n_{\pm}$. We also show that the AdS$_2$ solution is the near-horizon of an asymptotically AdS$_4$ black hole which can be found in the literature.

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arXiv2022

N=(0,4) Black String Chains

We construct black string solutions in Type IIA supergravity arising from intersecting D2-D4-D6-NS5 branes in the presence of fractional D4-branes. The fractional D4-branes arise from D6-branes wrapping (collapsing) two-cycles in a Calabi--Yau two-fold. In the near horizon limit these solutions give rise to AdS$_3$ geometries preserving $\mathcal{N}=(0,4)$ supersymmetry and fall within the recent classification of \cite{Lozano:2019emq}. We interpret our solutions as describing chains of black strings stacked on top of each other along an interval. We construct 2d quiver CFTs dual to our solutions that reproduce the Bekenstein-Hawking entropy microscopically.

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arXiv2022

On Type IIA AdS$_3$ solutions and massive GK geometries

We give the necessary and sufficient conditions for warped AdS$_3$ (and Mink$_3$) solutions of Type II supergravities to preserve ${\cal N}=(2,0)$ supersymmetry, in terms of geometric conditions on their internal space M$_7$. Such solutions possess a canonical ten-dimensional Killing vector that can be either time-like or null. In this work we classify the null case in massive Type IIA supergravity which necessitates that M$_7$ decomposes as a circle fibration over a six-dimensional base with orthogonal SU(2)-structure containing a complex four-manifold. We narrow our focus to solutions for which M$_7$ becomes $\mathbb{T}^2$ fibred over a foliation of a K\"{a}hler manifold over an interval. We find a class of solutions which are the massive Type IIA version of GK geometries and present an extremal problem which computes the central charge of the solution using just topology. Finally, we present geometric conditions for AdS$_3$ solutions to preserve arbitrary extended chiral supersymmetry.

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arXiv2022

${\cal N}=(2,2)$ AdS$_3$ from D3-branes wrapped on Riemann surfaces

We construct $\mathcal{N}=(2,2)$ supersymmetric AdS$_3$ solutions of type IIB supergravity, dual to twisted compactifications of 4d $\mathcal{N}=4$ super-Yang--Mills on Riemann surfaces. We consider both theories with a regular topological twist, and a twist involving the isometry group of the Riemann surface. These solutions are interpreted as the near-horizon of black strings asymptoting to AdS$_5\times \text{S}^5$. As evidence for the proposed duality we compute the central charge of the gravity solutions and show that it agrees with the field theory result.

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arXiv2021

M2-branes on Discs and Multi-Charged Spindles

We study supersymmetric AdS$_2\times Y_9$ solutions of 11d supergravity where $Y_9$ is an $S^7$ fibration over a Riemann surface equipped with a metric of non-constant curvature. We consider two classes of Riemann surface: the first is a spindle and the second is a topological disc. These solutions are interpreted as the near-horizon limit of M2 branes wrapped on the Riemann surface and describe the near-horizon of a 4d black hole. In the case of the topological disc there are additional flavour M2 branes smeared on a five-sphere embedded in the transverse $S^7$. We perform a full global analysis of both classes of solutions, both from a 4d and an 11d viewpoint. Finally we compute the two-dimensional Newton's constant from which we obtain a prediction for the entropy of the black hole.

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