Circle Reduction Research Articles

The minimal weak gravity conjecture

We examine the minimal constraints imposed by the Weak Gravity Conjecture (WGC) on the particle spectrum of a quantum gravity theory. Towers of super-extremal states have previously been argued to be required for consistency of the WGC under circle reduction. At the same time, there exist classes of theories where no tower of super-extremal particle states below the black hole threshold has been established with current techniques. We resolve this tension by arguing for the existence of a minimal radius for circle reductions of generic quantum gravity theories. Below this threshold, the notion of a circle compactification breaks down, bypassing the need for a tower of super-extremal states to satisfy the WGC after circle reduction. Based on this we propose that if a theory satisfies the WGC at the particle level below the black hole threshold, these states are sufficient for consistency under dimensional reduction, even in absence of a tower of super-extremal particles. Apart from general arguments, we provide independent evidence for this main result in F-, M- and string theory compactifications. According to the Emergent String Conjecture the only exception to the appearance of a minimal radius arises in asymptotically weak-coupling limits for heterotic strings, which aligns with the appearance of a weakly coupled super-extremal tower of particle states. This observation motivates a Minimal Weak Gravity Conjecture which states that towers of super-extremal particles occur if and only if they are required by consistency of the WGC under dimensional reduction.

Boosted rotating dyonic strings in Salam-Sezgin model

We show that the bosonic sector of the N = (1, 0), 6D Salam-Sezgin gauged supergravity model possesses a T-duality symmetry upon a circle reduction to D = 5. We then construct a simple magnetic rotating string solution with two equal angular momenta. Applying the T-duality transformation to this solution, we obtain the general boosted rotating dyonic black string solutions whose global structures and thermodynamic quantities are also analyzed. Owing to the fact that the solutions are not asymptotically flat, we find that there are two distinct globally-different non-extremal solutions with two different sets of thermal dynamic variables, with both satisfying the thermodynamic first law and the corresponding Small relations. However, their BPS limit becomes the same and we show that it preserves one quarter of supersymmetry by directly solving the corresponding Killing spinor equations.

More on closed string effective actions at order α′2

Recent progress in string theory has unveiled the discovery of Neveu Schwarz-Neveu Schwarz couplings in bosonic and heterotic effective actions at order α′2, which were achieved by imposing O(1,1) symmetry on the circle reduction of classical effective actions. While the bosonic theory features 25 couplings, the heterotic theory encompasses 24 parity-even and 3 parity-odd couplings, excluding the pure gravity couplings. In this study, we redefine the even-parity couplings in the bosonic and heterotic theories through the application of appropriate field redefinitions, resulting in 10 and 8 couplings, respectively. To establish the validity of these couplings, a cosmological reduction is conducted, demonstrating that the cosmological couplings in the heterotic theory vanish, subject to one-dimensional field redefinitions that include the lapse function and total derivative terms. Additionally, it is observed that the cosmological couplings in the bosonic theory can be expressed as tr(S˙6). These results are consistent with existing literature, where such behavior is attributed to the pure gravity component of the couplings. Furthermore, the consistency of the obtained couplings with 4-point string theory S-matrix elements is confirmed. Published by the American Physical Society 2024

Back to heterotic strings on ALE spaces. Part II. Geometry of T-dual little strings

This work is the second of a series of papers devoted to revisiting the properties of Heterotic string compactifications on ALE spaces. In this project we study the geometric counterpart in F-theory of the T-dualities between Heterotic ALE instantonic Little String Theories (LSTs) extending and generalising previous results on the subject by Aspinwall and Morrison. Since the T-dualities arise from a circle reduction one can exploit the duality between F-theory and M-theory to explore a larger moduli space, where T-dualities are realised as inequivalent elliptic fibrations of the same geometry. As expected from the Heterotic/F-theory duality the elliptic F-theory Calabi-Yau we consider admit a nested elliptic K3 fibration structure. This is central for our construction: the K3 fibrations determine the flavor groups and their global forms, and are the key to identify various T-dualities. We remark that this method works also more generally for LSTs arising from non-geometric Heterotic backgrounds. We study a first example in detail: a particularly exotic class of LSTs which are built from extremal K3 surfaces that admit flavor groups with maximal rank 18. We find all models are related by a so-called T-hexality (i.e. a 6-fold family of T-dualities) which we predict from the inequivalent elliptic fibrations of the extremal K3.

Twisted Fibrations in M/F-theory

In this work we investigate 5-dimensional theories obtained from M-theory on genus one fibered threefolds which exhibit twisted algebras in their fibers. We provide a base-independent algebraic description of the threefolds and compute light 5D BPS states charged under finite sub-algebras of the twisted algebras. We further construct the Jacobian fibrations that are associated to 6-dimensional F-theory lifts, where the twisted algebra is absent. These 6/5-dimensional theories are compared via twisted circle reductions of F-theory to M-theory. In the 5-dimensional theories we discuss several geometric transitions that connect twisted with untwisted fibrations. We present detailed discussions of {mathfrak{e}}_6^{(2)} , {mathfrak{so}}_8^{(3)} and {mathfrak{su}}_3^{(2)} twisted fibers and provide several explicit example threefolds via toric constructions. Finally, limits are considered in which gravity is decoupled, including Little String Theories for which we match 2-group symmetries across twisted T-dual theories.

Transgluteal Ultrasonography in Spica Cast in the Post-reduction Assessment of Hip Developmental Dysplasia

Concentric circle reduction is one of the outcomes after reduction of developmental dysplasia of the hip (DDH). Radiography and magnetic resonance imaging (MRI) are used to confirm the reduction results. In this study, we evaluated the reduction results of the coronal section of the hip using transgluteal ultrasonography. We enrolled 46 children admitted to our hospital for closed or open reduction plaster fixation of DDH between January 2021 and December 2022. Thirty-eight patients had unilateral DDH, and eight patients had bilateral DDH. Transgluteal ultrasonography, radiography and MRI were done on the patients during the 7 d after reduction, and the results were interpreted by different radiologists. The covering of the femoral head and the distance between the medial margin of the femoral head and the acetabulum (HSD) were measured after calculating the maximum coronal surface of the iliac bone. MRI is regarded as the gold standard for determining hip reduction or dislocation. The sensitivity, specificity, positive predictive value (PPV) and negative predictive value (NPV) of ultrasound and radiography were determined and compared. The sensitivity, specificity, PPV and NPV of transgluteal ultrasonography were 100% (confidence interval [CI]: 69.2%-100%), 97.7% (CI: 88%-99.9%), 90.9% (CI: 59%-98.6%) and 100%, respectively, higher than those of radiography, which were 50% (CI: 18.7%-81.3%), 86.4% (CI: 72.6%-94.8%), 45.5% (CI: 24%-68.7%) and 88.4% (CI: 80.2%-93.5%), respectively. Ultrasonography had a higher sensitivity (100% vs. 50%, p < 0.01) and positive predictive rate (90.9% vs. 45.5%, p < 0.01) than radiography. Ultrasonography revealed that a distance between the head and socket (HSD) >8 mm indicated a strong suspicion for a poor reduction. Transgluteal coronal ultrasound scan with semiquantitative assessment of acetabular femoral head coverage and measurement of HSD can effectively monitor the reduction relationship between the two in children after DDH reduction.

Higgs branches of Argyres-Douglas theories as quiver varieties

We present a general prescription for constructing 3d mathcal{N} = 4 Lagrangians for the IR SCFTs that arise from the circle reduction of a large class of Argyres-Douglas theories. The resultant Lagrangian gives a realization of the Higgs branch of the 4d SCFT as a quiver variety, up to a set of decoupled interacting SCFTs with empty Higgs branches. As representative examples, we focus on the families (Ap−N−1, AN−1) and Dp(SU(N)). The Lagrangian in question is generically a non-ADE-type quiver gauge theory involving only unitary gauge nodes with fundamental and bifundamental hypermultiplets, as well as hypermultiplets which are only charged under the U(1) subgroups of certain gauge nodes. Our starting point is the Lagrangian 3d mirror of the circle-reduced Argyres-Douglas theory, which can be read off from the class mathcal{S} construction. Using the toolkit of the S-type operations, developed in [1], we show that the mirror of the 3d mirror for any Argyres-Douglas theory in the aforementioned families is guaranteed to be a Lagrangian theory of the above type, up to some decoupled free sectors. We comment on the extension of this procedure to other families of Argyres-Douglas theories. In addition, for the case of Dp(SU(N)) theories, we compare these 3d Lagrangians to the ones found in [2] and propose that the two are related by an IR duality. We check the proposed IR duality at the level of the three-sphere partition function for specific examples. In contrast to the 3d Lagrangians in [2], which are linear chains involving unitary-special unitary nodes, we observe that the Coulomb branch global symmetries are manifest in the 3d Lagrangians that we find.

Back to heterotic strings on ALE spaces. Part I. Instantons, 2-groups and T-duality

In this paper we begin revisiting the little string theories (LSTs) which govern the dynamics of the instantonic heterotic E8 × E8 five-branes probing ALE singularities, building on and extending previous results on the subject by Aspinwall and Morrison as well as Blum and Intriligator. Our focus are the cases corresponding to choices of non-trivial flat connections at infinity. The latter are in particular interesting for the exceptional ALE singularities, where a brane realization in Type I′ is lacking. Our approach to determine these models is based on 6d conformal matter: we determine these theories as generalized 6d quivers. All these LSTs have a higher-one form symmetry which forms a 2-group with the zero-form Poincaré symmetry, the R-symmetry and the other global symmetries: the matching of the R-symmetry two-group structure constant is a stringent constraint for T-dualities, which we use in combination with the matching of 5d Coulomb branches and flavor symmetries upon circle reduction, as a consistency check for the realization of the 6d LSTs we propose.

Anomalies as obstructions: from dimensional lifts to swampland

We revisit the relation between the anomalies in four and six dimensions and the Chern-Simons couplings one dimension below. While the dimensional reduction of chiral theories is well-understood, the question which three and five-dimensional theories can come from a general circle reduction, and are hence liftable, is more subtle. We argue that existence of an anomaly cancellation mechanism is a necessary condition for liftability. In addition, the anomaly cancellation and the CS couplings in six and five dimensions respectively determine the central charges of string-like BPS objects that cannot be consistently decoupled from gravity, a.k.a. supergravity strings. Following the completeness conjecture and requiring that their worldsheet theory is unitary imposes bounds on the admissible theories. We argue that for the anomaly-free six-dimensional theories it is more advantageous to study the unitarity constraints obtained after reduction to five dimensions. In general these are slightly more stringent and can be cast in a more geometric form, highly reminiscent of the Kodaira positivity condition (KPC). Indeed, for the F-theoretic models which have an underlying Calabi-Yau threefold these can be directly compared. The unitarity constraints (UC) are in general weaker than KPC, and maybe useful in understanding the consistent models without F-theoretic realisation. We catalogue the cases when UC is more restrictive than KPC, hinting at more refined hidden structure in elliptic Calabi-Yau threefolds with certain singularity structure.

O(9,9) symmetry of NS-NS couplings at order α′3

Recently, imposing the $O(1,1)$ symmetry on the circle reduction of the classical effective action of string theory, we have found all NS-NS couplings of type II superstring theories at order $\alpha'^3$. In this paper we use the cosmological reduction on the couplings and show that, up to field redefinitions and total derivative terms, they are invariant under the $O(9,9)$ transformations.

O(25,\xa025) symmetry of bosonic string theory at order alpha '^2

It has been recently observed that the imposition of the O(1, 1) symmetry on the circle reduction of the classical effective action of string theory, can fix the effective action of the bosonic string theory at order alpha '^2, up to an overall factor. In this paper, we use the cosmological reduction on the action and show that, up to one-dimensional field redefinitions and total derivative terms, it can be written in the O(25, 25)-invariant form proposed by Hohm and Zwiebach.

5d SCFTs from (En, Em) conformal matter

We determine 5d mathcal{N} = 1 SCFTs originating from 6d (En, Em) conformal matter theories with n ≠ m by circle reduction and mass deformations. The marginal geometries are constructed and we derive their combined fiber diagrams (CFDs). The CFDs allow for an enumeration of descendant SCFTs obtained by decoupling matter hypermultiplets and a description of candidate weakly coupled quivers.

3d mirrors of the circle reduction of twisted A2N theories of class S

Mirror symmetry has proven to be a powerful tool to study several properties of higher dimensional superconformal field theories upon compactification to three dimensions. We propose a quiver description for the mirror theories of the circle reduction of twisted A2N theories of class S in four dimensions. Although these quivers bear a resemblance to the star-shaped quivers previously studied in the literature, they contain unitary, symplectic and special orthogonal gauge groups, along with hypermultiplets in the fundamental representation. The vacuum moduli spaces of these quiver theories are studied in detail. The Coulomb branch Hilbert series of the mirror theory can be matched with that of the Higgs branch of the corresponding four dimensional theory, providing a non-trivial check of our proposal. Moreover various deformations by mass and Fayet-Iliopoulos terms of such quiver theories are investigated. The fact that several of them flow to expected theories also gives another strong support for the proposal. Utilising the mirror quiver description, we discover a new supersymmetry enhancement renormalisation group flow.

Phases of 5d SCFTs from M-/F-theory on non-flat fibrations

We initiate the systematic investigation of non-flat resolutions of non-minimal singularities in elliptically fibered Calabi-Yau threefolds. Compactification of M-theory on these geometries provides an alternative approach to studying phases of five-dimensional superconformal field theories (5d SCFTs). We argue that such resolutions capture non-trivial holonomies in the circle reduction of the 6d conformal matter theory that is the F-theory interpretation of the singular fibration. As these holonomies become mass deformations in the 5d theory, non-flat resolutions furnish a novel method in the attempt to classify 5d SCFTs through 6d SCFTs on a circle. A particularly pleasant aspect of this proposal is the explicit embedding of the 5d SCFT’s enhanced flavor group inside that of the parent 6d SCFT, which can be read off from the geometry. We demonstrate these features in toric examples which realize 5d theories up to rank four.

Holographic glueballs from the circle reduction of Romans supergravity

We reconsider a one-parameter class of known solutions of the circle compactification of Romans six-dimensional half-maximal supergravity. The gauge-theory duals of these solutions are confining four-dimensional field theories. Their UV completions consist of the compactification on a circle of a higher-dimensional field theory that is flowing between two fixed points in five dimensions. We systematically study the bosonic fluctuations of the supergravity theory, corresponding to the bosonic glueballs of the dual field theory.We perform numerically the calculation of the spectrum of excitations of all the bosonic fields, several of which had been disregarded in earlier work on the subject. We discuss the results as a function of the one parameter characterising the class of background solutions, hence further extending known results. We show how certain towers of states are independent of the background, and compare these states to existing lattice literature on four-dimensional Yang-Mills (pure) gauge theories, confirming the existence of close similarities.For the aforementioned analysis, we construct gauge-invariant combinations of the fields appearing in the reduction to five dimensions of the supergravity theory, and hence focus on the 32 physical bosonic degrees of freedom. We show explicitly how to implement gauge-fixing of the supergravity theory. The results of such technical work could be used to analyse the spectra of other theories proposed in the context of top-down holography. For example, it could be applied to holographic realisations of composite-Higgs and light-dilaton scenarios.

Development of control strategies of a multi-wheeled combat vehicle

This work develops a vehicle dynamics controller for vehicle stability, manoeuvrability and turning circle reduction for an 8 × 8 heavy combat vehicle utilising both torque vectoring and third and fourth axle steering. The proposed control scheme is composed of two distinct controllers, each with their own range of operation based on vehicle speed. A feedforward zero side slip (ZSS) controller actuates the third and fourth axle steering angles. It is used for manoeuvring at speeds of 30 kph and below and for turning circle reduction. A two degrees of freedom (DOF) linear parameter varying (LPV) H∞ controller that monitors steering wheel angle and yaw rate error and uses both the rear axle steering and torque vectoring to enhance vehicle stability and manoeuvrability at speeds above 40 kph. Gaussian distribution functions are used to switch from one controller to the other. The proposed control scheme is evaluated by running simulations using a validated computer simulation (TruckSim) full vehicle model in co-simulation with the controller and developed electric powertrain in Simulink. The proposed control system is able to greatly improve vehicle stability and manoeuvrability. A turning circle reduction of 30% is obtained using the ZSS feedforward method.

Monopole quivers and new 3D [formula omitted] dualities

We present a new family of dualities for three-dimensional gauge theories, motivated by the brane realization of the reduction of four-dimensional dualities on a circle. This family can be understood as a generalization of Aharony duality to quiver gauge theories whose nodes interact via monopole terms in the superpotential. We refer to this family of theories as monopole quivers. We corroborate the new dualities by checking the equivalence of the three-sphere partition functions, obtained from the standard circle reduction of the four-dimensional superconformal index. As a special case, we recover some dualities recently discussed in the literature.

The gravitational sector of 2d (0, 2) F-theory vacua

F-theory compactifications on Calabi-Yau fivefolds give rise to two-dimensional N = (0, 2) supersymmetric field theories coupled to gravity. We explore the dilaton supergravity defined by the moduli sector of such compactifications. The massless moduli spectrum is found by uplifting Type IIB compactifications on Calabi-Yau fourfolds. This spectrum matches expectations from duality with M-theory on the same elliptic fibration. The latter defines an N = 2 Supersymmetric Quantum Mechanics related to the 2d (0, 2) F-theory supergravity via circle reduction. Using our recent results on the gravitational anomalies of duality twisted D3-branes wrapping curves in Calabi-Yau fivefolds we show that the F-theory spectrum is anomaly free. We match the classical Chern-Simons terms of the M-theory Super Quantum Mechanics to one-loop contributions to the effective action by S1 reduction of the dual F-theory.

Shift-symmetries and gauge coupling functions in orientifolds and F-theory

We investigate the field dependence of the gauge coupling functions of four-dimensional Type IIB orientifold and F-theory compactifications with space-time filling seven-branes. In particular, we analyze the constraints imposed by holomorphicity and covariance under shift-symmetries of the bulk and brane axions. This requires introducing quantum corrections that necessarily contain Riemann theta functions on the complex torus spanned by the D7-brane Wilson line moduli. Our findings hint towards a new underlying geometric structure for gauge coupling functions in string compactifications. We generalize this discussion to a genuine F-theory compactification on an elliptically fibered Calabi-Yau fourfold. We perform the first general dimensional reduction of eleven-dimensional super-gravity and dualization to the F-theory frame. The resulting effective action is compared with the circle reduction of a four-dimensional mathcal{N} = 1 supergravity theory. The F-theory geometry elegantly unifies bulk and brane degrees of freedom and allows us to infer non-trivial results about holomorphicity and shift-symmetries. For instance, we gain new insight into kinetic mixing of bulk and brane gauge fields.

AdS2 holographic dictionary

We construct the holographic dictionary for both running and constant dilaton solutions of the two dimensional Einstein-Maxwell-Dilaton theory that is obtained by a circle reduction from Einstein-Hilbert gravity with negative cosmological constant in three dimensions. This specific model ensures that the dual theory has a well defined ultraviolet completion in terms of a two dimensional conformal field theory, but our results apply qualitatively to a wider class of two dimensional dilaton gravity theories. For each type of solutions we perform holographic renormalization, compute the exact renormalized one-point functions in the presence of arbitrary sources, and derive the asymptotic symmetries and the corresponding conserved charges. In both cases we find that the scalar operator dual to the dilaton plays a crucial role in the description of the dynamics. Its source gives rise to a matter conformal anomaly for the running dilaton solutions, while its expectation value is the only non trivial observable for constant dilaton solutions. The role of this operator has been largely overlooked in the literature. We further show that the only non trivial conserved charges for running dilaton solutions are the mass and the electric charge, while for constant dilaton solutions only the electric charge is non zero. However, by uplifting the solutions to three dimensions we show that constant dilaton solutions can support non trivial extended symmetry algebras, including the one found by Compère, Song and Strominger [1], in agreement with the results of Castro and Song [2]. Finally, we demonstrate that any solution of this specific dilaton gravity model can be uplifted to a family of asymptotically AdS2 × S 2 or conformally AdS2 × S 2 solutions of the STU model in four dimensions, including non extremal black holes. The four dimensional solutions obtained by uplifting the running dilaton solutions coincide with the so called ‘subtracted geometries’, while those obtained from the uplift of the constant dilaton ones are new.