arXiv subjects

Chris Hull

Publications and source records attributed to Chris Hull.

At least 37 records · Page 2Linked to original sources

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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arXiv2023

Freely acting orbifolds of type IIB string theory on $T^5$

We study freely acting orbifolds of type IIB string theory on $T^5$ that spontaneously break supersymmetry from $\mathcal{N}=8$ to $\mathcal{N}=6,4,2$ or 0 in five dimensions. We focus on orbifolds that are a $\mathbb{Z}_p$ quotient by a T-duality acting on $T^4$ and a shift on the remaining $S^1$. Modular invariant partition functions are constructed and detailed examples of both symmetric and asymmetric orbifolds are presented, including new examples of five-dimensional non-supersymmetric string theories with no tachyons. The orbifolds we consider arise at special points in the moduli space of string theory compactifications with a duality twist. The supergravity limit of these are Scherk-Schwarz reductions which generate gauged supergravities with positive definite potentials on the moduli space in five dimensions. Both symmetric and asymmetric freely acting orbifolds give a landscape of Minkowski vacua. For gauged supergravities to belong to this landscape, we find a number of constraints and conditions. Firstly, the scalar potential should lead to a massive spectrum with masses that obey quantization conditions arising from a string theory orbifold, which we discuss in detail. Secondly, we find constraints on the massless sector, e.g. in the examples of orbifolds preserving sixteen supercharges in five dimensions that we consider, only an odd number of vector multiplets arise. Lastly, we present new examples of candidate asymmetric orbifolds with modular invariant partition functions, but with non-integral coefficients in the $q\bar{q}$-expansion in the twisted sector.

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arXiv2022

Gravity, Duality and Conformal Symmetry

The (4,0) supermultiplet in 6 dimensions contains a 4th rank tensor gauge field with the symmetries of the Riemann tensor and is superconformal, with 32+32 supersymmetries. Dimensional reduction on a circle gives the 5D N=8 supergravity multiplet, with the 4th rank tensor reducing to the graviton. If there is an interacting (4,0) theory it should reduce to the full N=8 supergravity theory and so would give a conformal theory of gravity that would reduce to conventional gravity with the usual 2-derivative action at low energies. This paper revisits the conjecture that a non-lagrangian interacting (4,0) superconformal theory arises from a strong coupling limit of 5D supergravity (suitably embedded in M-theory) describing M-theory at energies beyond the Planck scale. A key test for this is identified: M-theory toroidally compactified to 5D should have certain BPS states carrying a singlet central charge. These 1/2 BPS states are not related to any of the standard BPS states by dualities and do not correspond to non-singular soliton solutions -- they appear to correspond to singular solutions related to gravitational instantons. Such states are needed to provide the Kaluza-Klein modes for the compactified 6D theory. If there are no such states, then the conjecture is false, while the presence of such states would be strong indication that the conjecture could be true.

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arXiv2021

Homotopy Transfer and Effective Field Theory II: Strings and Double Field Theory

We continue our study of effective field theory via homotopy transfer of $L_\infty$-algebras, and apply it to tree-level non-Wilsonian effective actions of the kind discussed by Sen in which the modes integrated out are comparable in mass to the modes that are kept. We focus on the construction of effective actions for string states at fixed levels and in particular on the construction of weakly constrained double field theory. With these examples in mind, we discuss closed string theory on toroidal backgrounds and resolve some subtle issues involving vertex operators, including the proper form of cocycle factors and of the reflector state. This resolves outstanding issues concerning the construction of covariant closed string field theory on toroidal backgrounds. The weakly constrained double field theory is formally obtained from closed string field theory on a toroidal background by integrating out all but the doubly massless' states and homotopy transfer then gives a prescription for determining the theory's vertices and symmetries. We also discuss consistent truncation in the context of homotopy transfer.

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arXiv2020

Homotopy Transfer and Effective Field Theory I: Tree-level

We use the dictionary between general field theories and strongly homotopy algebras to provide an algebraic formulation of the procedure of integrating out of degrees of freedom in terms of homotopy transfer. This includes more general effective theories in which some massive modes are kept while other modes of a comparable mass scale are integrated out, as first explored by Sen in the context of closed string field theory. We treat $L_\infty$-algebras both in terms of a nilpotent coderivation and, on the dual space, in terms of a nilpotent derivation (corresponding to the BRST charge of the field theory) and provide explicit formulas for homotopy transfer. These are then shown to govern the integrating out of degrees of freedom at tree level, while the generalization to loop level will be explored in a sequel to this paper.

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arXiv2020

Black holes in string theory with duality twists

We consider 5D supersymmetric black holes in string theory compactifications that partially break supersymmetry. We compactify type IIB on $T^4$ and then further compactify on a circle with a duality twist to give Minkowski vacua preserving partial supersymmetry ($\mathcal{N}=6,4,2,0$) in five dimensions. The effective supergravity theory is given by a Scherk-Schwarz reduction with a Scherk-Schwarz supergravity potential on the moduli space, and the lift of this to string theory imposes a quantization condition on the mass parameters. In this theory, we study black holes with three charges that descend from various ten-dimensional brane configurations. For each black hole we choose the duality twist to be a transformation that preserves the solution, so that it remains a supersymmetric solution of the twisted theory with partially broken supersymmetry. We discuss the quantum corrections arising from the twist to the pure gauge and mixed gauge-gravitational Chern-Simons terms in the action and the resulting corrections to the black hole entropy.

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arXiv2019

Noncommutative gauge theories on D-branes in non-geometric backgrounds

We investigate the noncommutative gauge theories arising on the worldvolumes of D-branes in non-geometric backgrounds obtained by T-duality from twisted tori. We revisit the low-energy effective description of D-branes on three-dimensional T-folds, examining both cases of parabolic and elliptic twists in detail. We give a detailed description of the decoupling limits and explore various physical consequences of the open string non-geometry. The T-duality monodromies of the non-geometric backgrounds lead to Morita duality monodromies of the noncommutative Yang-Mills theories induced on the D-branes. While the parabolic twists recover the well-known examples of noncommutative principal torus bundles from topological T-duality, the elliptic twists give new examples of noncommutative fibrations with non-geometric torus fibres. We extend these considerations to D-branes in backgrounds with R-flux, using the doubled geometry formulation, finding that both the non-geometric background and the D-brane gauge theory necessarily have explicit dependence on the dual coordinates, and so have no conventional formulation in spacetime.

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arXiv2019

Strong Kähler with Torsion as Generalised Geometry

Strong Kähler with Torsion is the target space geometry of $(2,1)$ and $(2,0)$ supersymmetric nonlinear sigma models. We discuss how it can be represented in terms of Generalised Complex Geometry in analogy to the Gualtieri map from the geometry of $(2,2)$ supersymmetric nonlinear sigma models to Generalised Kähler Geometry.

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arXiv2018

Non-geometric Calabi-Yau Backgrounds and K3 automorphisms

We consider compactifications of type IIA superstring theory on mirror-folds obtained as K3 fibrations over two-tori with non-geometric monodromies involving mirror symmetries. At special points in the moduli space these are asymmetric Gepner models. The compactifications are constructed from non-geometric automorphisms that arise from the diagonal action of an automorphism of the K3 surface and of an automorphism of the mirror surface. We identify the corresponding gaugings of N=4 supergravity in four dimensions, and show that the minima of the potential describe the same four-dimensional low-energy physics as the worldsheet formulation in terms of asymmetric Gepner models. In this way, we obtain a class of Minkowski vacua of type II string theory which preserve N=2 supersymmetry. The massless sector consists of N=2 supergravity coupled to 3 vector multiplets, giving the STU model. In some cases there are additional massless hypermultiplets.

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arXiv2018

The Generalised Complex Geometry of $(p,q)$ Hermitian Geometries

We define $(p,q)$ hermitian geometry as the target space geometry of the two dimensional $(p,q)$ supersymmetric sigma model. This includes generalised Kähler geometry for $(2,2)$, generalised hyperkähler geometry for $(4,2)$, strong Kähler with torsion geometry for $(2,1)$ and strong hyperkähler with torsion geometry for $(4,1)$. We provide a generalised complex geometry formulation of hermitian geometry, generalising Gualtieri's formulation of the $(2,2)$ case. Our formulation involves a chiral version of generalised complex structure and we provide explicit formulae for the map to generalised geometry.

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arXiv2017

All $(4,0)$: Sigma Models with $(4,0)$ Off-Shell Supersymmetry

Off-shell $(4,0)$ supermultiplets in 2-dimensions are formulated. These are used to construct sigma models whose target spaces are vector bundles over manifolds that are hyperkähler with torsion. The off-shell supersymmetry implies that the complex structures are simultaneously integrable and allows us to write actions using extended superspace and projective superspace, giving an explicit construction of the target space geometries.

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arXiv2017

Stringy AdS3 from the Worldsheet

We investigate the behaviour of the bosonic string on AdS3 with H-flux at stringy scales, looking in particular for a `tensionless' limit in which there are massless higher spin gauge fields. We do this by revisiting the physical spectrum of the sl(2,R)$_k$ WZW model and considering the limit in which k becomes small. At k=3 we find that there is an infinite stringy tower of massless higher spin fields which are part of a continuum of light states. This can be viewed as a novel tensionless limit, which appears to be distinct from that inferred from the symmetric orbifold description of superstring AdS3 vacua.

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arXiv2017

All $(4,1)$: Sigma Models with $(4,q)$ Off-Shell Supersymmetry

Off-shell $(4,q)$ supermultiplets in 2-dimensions are constructed for $q=1,2,4$. These are used to construct sigma models whose target spaces are hyperkähler with torsion. The off-shell supersymmetry implies the three complex structures are simultaneously integrable and allows us to construct actions using extended superspace and projective superspace, giving an explicit construction of the target space geometries.

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arXiv2012

Generalized Kähler Geometry in (2,1) superspace

Two-dimensional (2,2) supersymmetric nonlinear sigma models can be described in (2,2), (2,1) or (1,1) superspaces. Each description emphasizes different aspects of generalized Kähler geometry. We investigate the reduction from (2,2) to (2,1) superspace. This has some interesting nontrivial features arising from the elimination of nondynamical fields. We compare quantization in the different superspace formulations.

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arXiv2010

Generalized metric formulation of double field theory

The generalized metric is a T-duality covariant symmetric matrix constructed from the metric and two-form gauge field and arises in generalized geometry. We view it here as a metric on the doubled spacetime and use it to give a simple formulation with manifest T-duality of the double field theory that describes the massless sector of closed strings. The gauge transformations are written in terms of a generalized Lie derivative whose commutator algebra is defined by a double field theory extension of the Courant bracket.

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arXiv2010

Background independent action for double field theory

Double field theory describes a massless subsector of closed string theory with both momentum and winding excitations. The gauge algebra is governed by the Courant bracket in certain subsectors of this double field theory. We construct the associated nonlinear background-independent action that is T-duality invariant and realizes the Courant gauge algebra. The action is the sum of a standard action for gravity, antisymmetric tensor, and dilaton fields written with ordinary derivatives, a similar action for dual fields with dual derivatives, and a mixed term that is needed for gauge invariance.

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arXiv2009

The gauge algebra of double field theory and Courant brackets

We investigate the symmetry algebra of the recently proposed field theory on a doubled torus that describes closed string modes on a torus with both momentum and winding. The gauge parameters are constrained fields on the doubled space and transform as vectors under T-duality. The gauge algebra defines a T-duality covariant bracket. For the case in which the parameters and fields are T-dual to ones that have momentum but no winding, we find the gauge transformations to all orders and show that the gauge algebra reduces to one obtained by Siegel. We show that the bracket for such restricted parameters is the Courant bracket. We explain how these algebras are realised as symmetries despite the failure of the Jacobi identity.

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arXiv2009

Double Field Theory

The zero modes of closed strings on a torus --the torus coordinates plus dual coordinates conjugate to winding number-- parameterize a doubled torus. In closed string field theory, the string field depends on all zero-modes and so can be expanded to give an infinite set of fields on the doubled torus. We use the string field theory to construct a theory of massless fields on the doubled torus. Key to the consistency is a constraint on fields and gauge parameters that arises from the L_0 - \bar L_0=0 condition in closed string theory. The symmetry of this double field theory includes usual and 'dual diffeomorphisms', together with a T-duality acting on fields that have explicit dependence on the torus coordinates and the dual coordinates. We find that, along with gravity, a Kalb-Ramond field and a dilaton must be added to support both usual and dual diffeomorphisms. We construct a fully consistent and gauge invariant action on the doubled torus to cubic order in the fields. We discuss the challenges involved in the construction of the full nonlinear theory. We emphasize that the doubled geometry is physical and the dual dimensions should not be viewed as an auxiliary structure or a gauge artifact.

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