arXiv subjects

Chris Hull

Publications and source records attributed to Chris Hull.

At least 19 recordsLinked to original sources

arXiv2026

Self-Dual Gauge Fields from Superstring Field Theory

The action for self-dual gauge fields that emerges from the recently constructed superstring field theory is found. The new superstring field theory reduces to that of Sen in a certain limit, and in this limit the new action for self-dual gauge fields reduces to Sen's action for such fields. The theory describes two decoupled self-dual gauge fields that couple to two metrics, with each gauge field coupling to only one of the metrics. The action also features a background metric, and the non-linear coupling to these three metrics is non-standard. There are two spin-two gauge invariances, and diffeomorphisms arise from the diagonal subgroup.

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arXiv2025

Non-renormalisation of coupling constants from categorical symmetries in two dimensions

We study the role of categorical symmetries in constraining the renormalisation of couplings in two-dimensional non-linear sigma models with Wess-Zumino term. A large class of these theories admit self-duality symmetries associated with discrete gauging and T-duality. They are generically non-conformal, but we argue that a particular coupling is protected from quantum corrections by the categorical symmetry. We give strong evidence for this claim by showing that the $\beta$-function for this coupling vanishes to 2-loop order if and only if this symmetry is present. Furthermore, in cases where the target space is a group manifold, the non-renormalisation result can be proven to hold non-perturbatively.

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arXiv2025

The Symplectic Geometry of p-Form Gauge Fields

We formulate interacting antisymmetric tensor gauge theory in a configuration space consisting of a pair of dual field strengths which has a natural symplectic structure. The field equations are formulated as the intersection of a pair of submanifolds of this infinite-dimensional symplectic configuration space, one of which is a Lagrangian submanifold while the other is either a coisotropic or Lagrangian submanifold, depending on the topology. Chern-Simons interactions give the configuration space an interesting global structure. We consider in detail the example of a six-dimensional theory of a 3-form field strength coupled to Yang-Mills theory via a Chern-Simons interaction. Our approach applies to a broad class of gauge systems.

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arXiv2025

Gravitational currents and charges from conformal Killing-Yano tensors

We construct a set of higher-form conserved currents on spacetimes admitting conformal Killing-Yano tensors. We find relations between these currents that allow the charge given by integrating one of these currents over a region to be re-expressed as an integral of a covariant quantity over the boundary. In many cases, only a non-covariant form of the boundary integral was previously known. For a special class of these currents the conservation does not rely on field equations, so they give conserved topological charges in any gravitational theory. We discuss the relation of our currents to the Komar current and derive several new properties of conformal Killing-Yano tensors. We study a number of applications of our construction to charges of black hole solutions of Einstein-Maxwell theory, and D-brane solutions of type II supergravity.

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arXiv2025

A New Action for Superstring Field Theory

Sen's superstring field theory successfully formulates perturbative superstring theory but has a number of unusual features. The action is not background independent and the resulting effective field theory does not appear to have standard diffeomorphsim symmetry - instead there is an exotic gauge symmetry that acts on some fields but not others. A new action is found that reduces to Sen's action in a certain limit and gives the same results as Sen's theory for physical superstring amplitudes. However, the new theory is background independent: there is a shift symmetry so that a change in the background can be compensated for by a corresponding shift in the string fields. Sen's theory has two string fields leading to the physical interacting superstring plus a free superstring that decouples from the physical superstring. The new terms in the action give self-interactions to the second superstring which remains decoupled from the physical superstring. The two superstrings each have a graviton and the effective action for the two gravitons coupled to a background metric is studied and shown to be background independent and diffeomorphism invariant, and the origin of further diffeomorphism-like symmetries is explained.

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arXiv2025

Quantising Chiral Bosons On Riemann Surfaces

Sen's action in two dimensions governs a chiral boson coupled to a two-dimensional metric together with a second chiral boson that couples to a flat two-dimensional metric. This second scalar decouples from the physical degrees of freedom. The generalisation of this action to one in which the second chiral scalar couples to an arbitrary second metric is used to formulate the theory on an arbitrary two-dimensional manifold. We use this action with both metrics Riemannian (or complex) to formulate the path integral on any Riemann surface. We calculate the partition function in this way and check the result with that calculated using canonical quantisation, and then extend this to multiple chiral bosons. The partition function for chiral scalars taking values on a rational torus is a sum of terms, each of which is the product of two holomorphic functions, one a function of the modulus of the first metric and the other a function of the modulus of the second metric. In particular, for the case of chiral bosons moving on a torus defined by an even self-dual lattice, the partition function is a single product of two such holomorphic functions, not a sum of such terms. This is applied to the heterotic string to give a world-sheet action whose quantisation is modular invariant and free from anomalies. We discuss modular invariance for the moduli of both metrics and the extension to higher genus Riemann surfaces.

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arXiv2025

The CFT of Sen's Formulation of Chiral Gauge Fields

Sen's action for chiral bosons in 2 dimensions describes two chiral scalars, one of which couples to the physical metric and one of which couples to a flat metric. It has a generalisation in which the flat metric is replaced by an arbitrary second metric and so can be formulated on any curved world-sheet. When the two metrics are equal, the theory reduces to a $\beta \gamma$ system, giving a non-unitary $c=2$ conformal field theory. We argue that the relation between this and the theory of two chiral bosonic scalars of the same chirality can be viewed as a \lq bosonisation'. We show that the standard vertex operators for the chiral scalars are vertex operators and line operators in the Sen formulation and derive the formulation in the Sen theory of correlation functions in the chiral scalar theory. The flat space Sen theory can be coupled to two different world-sheet metrics in such a way that one scalar couples to one metric and the other to the other metric, so obtaining the general formulation with two metrics. In $d=4k+2$ dimensions, the bi-metric action for a $2k$-form gauge field with self-dual field strength reduces, when the two metrics are equal, to a conformal field theory with a $BF$-type action, except that $B$ is a self-dual $d/2$-form and $F$ is a $d/2$-form field strength, $F=dP$. The self-duality of $B$ means that this is not a topological theory but instead represents two self-dual gauge fields. This has a generalisation to a democratic action for $p$-form gauge fields in any dimension.

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arXiv2025

Duality and Infinite Distance Limits in Asymmetric Freely Acting Orbifolds

We use freely acting asymmetric orbifolds of type IIB string theory to construct a class of theories in four dimensions with eight supercharges. Their low energy effective field theories resemble $STU$ models, but have different duality groups: the orbifold's free action reduce the duality groups to congruence subgroups of the modular group. The fundamental domain is consequently larger and contains new interesting points at infinite distance on the real axis bounding the upper half plane. We verify that the distance conjectures hold in the non-geometric compactification of string theory studied here. In particular, we find points at infinite distance in moduli space at which the theory decompactifies to a different orbifold construction.

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arXiv2025

Duality Symmetries

Duality symmetries in supergravity theories, together with their implications for string theory, are reviewed.

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arXiv2025

Non-invertible symmetries of two-dimensional Non-Linear Sigma Models

Global symmetries can be generalised to transformations generated by topological operators, including cases in which the topological operator does not have an inverse. A family of such topological operators are intimately related to dualities via the procedure of half-space gauging. In this work we discuss the construction of non-invertible defects based on T-duality in two dimensions, generalising the well-known case of the free compact boson to any Non-Linear Sigma Model with Wess-Zumino term which is T-dualisable. This requires that the target space has an isometry with compact orbits that acts without fixed points. Our approach allows us to include target spaces without non-trivial 1-cycles, does not require the NLSM to be conformal, and when it is conformal it does not need to be rational; moreover, it highlights the microscopic origin of the topological terms that are responsible for the non-invertibility of the defect. An interesting class of examples are Wess-Zumino-Witten models, which are self-dual under a discrete gauging of a subgroup of the isometry symmetry and so host a topological defect line with Tambara-Yamagami fusion. Along the way, we discuss how the usual 0-form symmetries match across T-dual models in target spaces without 1-cycles, and how global obstructions can prevent locally conserved currents from giving rise to topological operators.

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arXiv2025

Coupling Self-Dual p-Form Gauge Fields to Self-Dual Branes

In $d=4k+2$ dimensions, $p$-form gauge fields (with $p=2k$) with self-dual field strengths couple naturally to dyonic branes with equal electric and magnetic charges. Sen's action for a $p$-form gauge field with self-dual field strength coupled to a spacetime metric $g$ involves an explicit Minkowski metric; however, this action can be generalised to provide a theory in which the Minkowski metric is replaced by a second metric $\bar g$ on spacetime. This theory describes a physical sector, consisting of the chiral $p$-form gauge field coupled to the dynamical metric $g$, plus an auxiliary sector consisting of a second chiral $p$-form and the second metric $\bar g$. The fields in this auxiliary sector only couple to each other and have no interactions with the physical sector. However, in this theory, the standard coupling to a brane given by integrating the gauge potential over the world-volume of the brane is problematic as the physical gauge potential depends non-locally on the fields appearing in the action. A consistent coupling is given by introducing Dirac branes (generalising Dirac strings), and is shown to have generalised symmetries corresponding to invariance under deforming the positions of the Dirac branes, provided the Dirac branes do not intersect any physical brane world-volumes.

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arXiv2024

Gauge-invariant charges of the dual graviton

The free graviton theory given by linearising Einstein's theory has a dual formulation in terms of a dual graviton field. The dual graviton theory has two gauge invariances giving rise to two conserved charges, while the ADM charges of the graviton theory become magnetic charges for the dual graviton theory. These charges can be ill-defined in topologically non-trivial settings and we find improvement terms that can be added to these to give gauge-invariant conserved charges. These gauge-invariant charges, which have local expressions in both the graviton and dual graviton formulation, give topological operators of the theory that should be considered as the generators of the genuine symmetries of the theory.

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arXiv2024

Gauging generalised symmetries in linear gravity

The theory of a free spin-2 field on Minkowski spacetime has 1-form and $(d-3)$-form symmetries associated with conserved currents formed by contractions of the linearised Riemann tensor with conformal Killing-Yano 2-forms. We show that a subset of these can be interpreted as Noether currents for specific shift symmetries of the graviton that involve a Killing vector and a closed 1-form parameter. We give a systematic method to gauge these 1-form symmetries by coupling the currents to background gauge fields and introducing a particular set of counter-terms involving the background fields. The simultaneous gauging of certain pairs of 1-form and $(d-3)$-form symmetries is obstructed by the presence of mixed 't Hooft anomalies. The anomalous pairs of symmetries are those which are related by gravitational duality. The implications of these anomalies are discussed.

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arXiv2024

Generalised symmetries in linear gravity

Linearised gravity has a global symmetry under which the graviton is shifted by a symmetric tensor satisfying a certain flatness condition. There is also a dual symmetry that can be associated with a global shift symmetry of the dual graviton theory. The corresponding conserved charges are shown to satisfy a centrally-extended algebra. We discuss the gauging of these global symmetries, finding an obstruction to the simultaneous gauging of both symmetries which we interpret as a mixed 't Hooft anomaly for the ungauged theory. We discuss the implications of this, analogous to those resulting from a similar structure in Maxwell theory, and interpret the graviton and dual graviton as Nambu-Goldstone modes for these shift symmetries.

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arXiv2024

Gauge-invariant magnetic charges in linearised gravity

Linearised gravity has magnetic charges carried by (linearised) Kaluza-Klein monopoles. A gauge-invariant expression is found for these charges that is similar to Penrose's gauge-invariant expression for the ADM charges. A systematic search is made for other gauge-invariant charges.

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arXiv2024

$N=(2,2)$ superfields and geometry revisited

We take a fresh look at the relation between generalised K\"ahler geometry and $N=(2,2)$ supersymmetric sigma models in two dimensions formulated in terms of $(2,2)$ superfields. Dual formulations in terms of different kinds of superfield are combined to give a formulation with a doubled target space and both the original superfield and the dual superfield. For K\"ahler geometry, we show that this doubled geometry is Donaldson's deformation of the holomorphic cotangent bundle of the original K\"ahler manifold. This doubled formulation gives an elegant geometric reformulation of the equations of motion. We interpret the equations of motion as the intersection of two Lagrangian submanifolds (or of a Lagrangian submanifold with an isotropic one) in the infinite dimensional symplectic supermanifold which is the analogue of phase space. We then consider further extensions of this formalism, including one in which the geometry is quadrupled, and discuss their geometry.

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arXiv2024

Exact moduli spaces for $\mathcal{N}=2, D=5$ freely acting orbifolds

We use freely acting asymmetric orbifolds of type IIB string theory to construct a class of theories in five dimensions with eight supercharges whose moduli spaces for vector multiplets and hypermultiplets can be determined exactly. We argue that no quantum corrections to these moduli spaces arise. We focus on examples in which all moduli are in the NS-NS sector, while all fields from the R-R sector become massive. The full symmetry group of the moduli space is then determined by the subgroup of the T-duality group that survives the orbifold action. We illustrate this for freely acting orbifolds of type IIB string theory on $T^5$ with $0,1$ or $2$ hypermultiplets.

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arXiv2024

Charges and topology in linearised gravity

Covariant conserved 2-form currents for linearised gravity are constructed by contracting the linearised curvature with conformal Killing-Yano tensors. The corresponding conserved charges were originally introduced by Penrose and have recently been interpreted as the generators of generalised symmetries of the graviton. We introduce an off-shell refinement of these charges and find the relation between these improved Penrose charges and the linearised version of the ADM momentum and angular momentum. If the graviton field is globally well-defined on a background Minkowski space then some of the Penrose charges give the momentum and angular momentum while the remainder vanish. We consider the generalisation in which the graviton has Dirac string singularities or is defined locally in patches, in which case the conventional ADM expressions are not invariant under the graviton gauge symmetry in general. We modify them to render them gauge-invariant and show that the Penrose charges give these modified charges plus certain magnetic gravitational charges. We discuss properties of the Penrose charges, generalise to toroidal Kaluza-Klein compactifications and check our results in a number of examples.

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