arXiv subjects

Matthew M. Roberts

Publications and source records attributed to Matthew M. Roberts.

At least 19 recordsLinked to original sources

arXiv2026

Spindle solutions with hyperscalars in $D=4$ gauged supergravity

We construct new classes of supersymmetric $AdS_2\times \Sigma$ solutions, where $\Sigma=\Sigma(n_N,n_S)$ is a spindle. Such solutions can arise as the near horizon limit of supersymmetric, accelerating black holes. The solutions are constructed using $D=4$ STU $U(1)^4$ gauged supergravity theory coupled to a charged hyperscalar, and can be uplifted to obtain smooth, supersymmetric $AdS_2\times Y_9$ solutions of $D=11$ supergravity. We allow $(n_N,n_S)$ to be non-coprime integers, including orbifolds of the round $S^2$. We also allow the hyperscalar to vanish at the poles. The $AdS_2$ solutions with non-vanishing hyperscalar can naturally arise as the endpoint of holographic RG flows, triggered by relevant hyperscalar deformations of the $AdS_2$ solutions of the STU model.

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arXiv2025

Spindle solutions, hyperscalars and smooth uplifts

We construct $AdS_3\times Y_7$ solutions of type IIB supergravity, where $Y_7$ is a smooth $S^5$ bundle over a spindle $\Sigma(n_N,n_S)$, which are dual to $\mathcal{N}=(0,2)$ SCFTs in $d=2$. The solutions are constructed using the $D=5$ STU $U(1)^3$ gauged supergravity theory coupled to a hyperscalar charged under $U(1)_B$. We investigate spindle solutions with two new features: first, we allow $(n_N,n_S)$ to be non-coprime integers, including orbifolds of the round $S^2$, which can lead to non-unique, inequivalent uplifts, distinguished by the hyperscalar spectra, for given magnetic flux through the spindle. Second, we also allow the hyperscalar to vanish at the poles leading to solutions carrying non-vanishing $U(1)_B$ flux. The new hyperscalar $AdS_3$ solutions can naturally arise as the endpoint of RG flows, triggered by relevant hyperscalar deformations of the $AdS_3$ solutions of the STU model.

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arXiv2024

Superconformal Monodromy Defects in ABJM and mABJM Theory

We study $D=11$ supergravity solutions which are dual to one-dimensional superconformal defects in $d=3$ SCFTs. We consider defects in ABJM theory with monodromy for $U(1)^4\subset SO(8)$ global symmetry, as well as in $\mathcal{N}=2$ mABJM SCFT, which arises from the RG flow of a mass deformation of ABJM theory, with monodromy for $U(1)^3\subset SU(3)\times U(1)$ global symmetry. We show that the defects of the two SCFTs are connected by a line of bulk marginal mass deformations and argue that they are also related by bulk RG flow. In all cases we allow for the possibility of conical singularities at the location of the defect. Various physical observables of the defects are computed including the defects conformal weight and the partition function, as well as associated supersymmetric Renyi entropies.

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arXiv2024

Superconformal Monodromy Defects in $\mathcal{N}$=4 SYM and LS theory

We study type IIB supergravity solutions that are dual to two-dimensional superconformal defects in $d=4$ SCFTs which preserve $\mathcal{N}=(0,2)$ supersymmetry. We consider solutions dual to defects in $\mathcal{N}=4$ SYM theory that have non-trivial monodromy for $U(1)^3\subset SO(6)$ global symmetry and we also allow for the possibility of conical singularities. In addition, we consider the addition of fermionic and bosonic mass terms that have non trivial dependence on the spatial directions transverse to the defect, while preserving the superconformal symmetry of the defect. We compute various physical quantities including the central charges of the defect expressed as a function of the monodromy, the on-shell action as well as associated supersymmetric Renyi entropies. Analogous computations are carried out for superconformal defects in the $\mathcal{N}=1$, $d=4$ Leigh-Strassler SCFT. We also show that the defects of the two SCFTs are connected by a line of bulk marginal mass deformations and argue that they are also related by bulk RG flow.

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arXiv2023

Analog gravity and the continuum effective theory of the graphene tight binding lattice model

We consider the tight-binding model of graphene with slowly spatially varying hopping functions. We develop a low energy approximation as a derivative expansion in a Dirac spinor that is perturbative in the hopping function deformation. The leading description is the Dirac equation in flat 2+1-d spacetime with (strain-)gauge field. Prior work considered subleading corrections written as non-trivial frame and spin connection terms. We previously argued that such corrections cannot be considered consistently without taking all the terms at the same order of approximation, which due to the unconventional power counting originating from the large gauge field, involve also higher covariant derivative terms. Here we confirm this, explicitly computing subleading terms. To the order we explore, the theory is elegantly determined by the gauge field and frame, both given by the hopping functions, the torsion free spin connection of the frame, together with coefficients for the higher derivative terms derived from lattice invariants. For the first time we compute the metric that the Dirac field sees - the `electrometric' - to quadratic order in the deformation allowing us to describe the subleading corrections to the dispersion relation for inhomogeneous deformations originating from corrections to the frame. Focussing on in-plane inhomogeneous strain, we use a simple model to relate the hopping functions to the strain field, finding the electrometric becomes curved at this quadratic order. Thus this lattice model yields an effective analog gravity description as a curved space Dirac theory, with large magnetic field, and Lorentz violating higher covariant derivative terms. We check this by comparison to numerical diagonalization. From this we conjecture a form for the effective theory for monolayer graphene in terms of the strain tensor, consistent up to quadratic order in the deformation.

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arXiv2022

Leigh-Strassler compactified on a spindle

We construct a new class of supersymmetric $AdS_3\times Y_7$ solutions of type IIB supergravity, where $Y_7$ is an $S^5$ fibration over a spindle, which are dual to $d=2$, $\mathcal{N}=(0,2)$ SCFTs. The solutions are constructed in a sub-truncation of $D=5$, $SO(6)$ maximal gauged supergravity and they all lie within the anti-twist class. We show that the central charge computed from the gravity solutions agrees with an anomaly polynomial calculation associated with compactifying the $\mathcal{N}=1$, $d=4$ Leigh-Strassler SCFT on a spindle.

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arXiv2022

Curved-space Dirac description of elastically deformed monolayer graphene is generally incorrect

Undistorted monolayer graphene has energy bands which cross at protected Dirac points. It elastically deforms and much research has assumed the Dirac description persists, now in a curved space and coupled to a gauge field related to lattice strain. We show this is incorrect by using a real space gradient expansion to study how the Dirac equation derives from the tight binding model. Generic spatially varying hopping functions give rise to large magnetic fields which spoil the truncation in derivatives. In the perturbative regime, the only consistent truncation to Dirac is one with nontrivial gauge field but in flat space. One can instead fine tune the magnetic field to be small, and we derive the resulting differential condition that the hopping functions must satisfy to yield a consistent truncation to Dirac in curved space. We consider whether mechanical effects might impose this fine tuning, but find this is not the case for a simple elastic membrane model.

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arXiv2021

Marginal deformations and RG flows for type IIB S-folds

We construct a continuous one parameter family of $AdS_4\times S^1\times S^5$ S-fold solutions of type IIB string theory which have nontrivial $SL(2,\mathbb{Z})$ monodromy in the $S^1$ direction. The solutions span a subset of a conformal manifold that contains the known $\mathcal{N}=4$ S-fold SCFT in $d=3$, and generically preserve $\mathcal{N}=2$ supersymmetry. We also construct RG flows across dimensions, from $AdS_5\times S^5$, dual to $\mathcal{N}=4$, $d=4$ SYM compactified with a twisted spatial circle, to various $AdS_4\times S^1\times S^5$ S-fold solutions, dual to $d=3$ SCFTs. We construct additional flows between the $AdS_5$ dual of the Leigh-Strassler SCFT and an $\mathcal{N}=2$ S-fold as well as RG flows between various S-folds.

hep-th↗

arXiv2021

A new family of $AdS_4$ S-folds in type IIB string theory

We construct infinite new classes of $AdS_4\times S^1\times S^5$ solutions of type IIB string theory which have non-trivial $SL(2,\mathbb{Z})$ monodromy along the $S^1$ direction. The solutions are supersymmetric and holographically dual, generically, to $\mathcal{N}=1$ SCFTs in $d=3$. The solutions are first constructed as $AdS_4\times \mathbb{R}$ solutions in $D=5$ $SO(6)$ gauged supergravity and then uplifted to $D=10$. Unlike the known $AdS_4\times \mathbb{R}$ S-fold solutions, there is no continuous symmetry associated with the $\mathbb{R}$ direction. The solutions all arise as limiting cases of Janus solutions of $d=4$, $\mathcal{N}=4$ SYM theory which are supported both by a different value of the coupling constant on either side of the interface, as well as by fermion and boson mass deformations. As special cases, the construction recovers three known S-fold constructions, preserving $\mathcal{N}=1,2$ and 4 supersymmetry, as well as a recently constructed $\mathcal{N}=1$ $AdS_4\times S^1\times S^5$ solution (not S-folded). We also present some novel "one-sided Janus" solutions that are non-singular.

hep-th↗

arXiv2020

Spatially modulated and supersymmetric mass deformations of $\mathcal{N}=4$ SYM

We study mass deformations of $\mathcal{N}=4$, $d=4$ SYM theory that are spatially modulated in one spatial dimension and preserve some residual supersymmetry. We focus on generalisations of $\mathcal{N}=1^*$ theories and show that it is also possible, for suitably chosen supersymmetric masses, to preserve $d=3$ conformal symmetry associated with a co-dimension one interface. Holographic solutions can be constructed using $D=5$ theories of gravity that arise from consistent truncations of $SO(6)$ gauged supergravity and hence type IIB supergravity. For the mass deformations that preserve $d=3$ superconformal symmetry we construct a rich set of Janus solutions of $\mathcal{N}=4$ SYM theory which have the same coupling constant on either side of the interface. Limiting classes of these solutions give rise to RG interface solutions with $\mathcal{N}=4$ SYM on one side of the interface and the Leigh-Strassler (LS) SCFT on the other, and also to a Janus solution for the LS theory. Another limiting solution is a new supersymmetric $AdS_4\times S^1\times S^5$ solution of type IIB supergravity.

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arXiv2020

Superconformal RG interfaces in holography

We construct gravitational solutions that holographically describe two different $d=4$ SCFTs joined together at a co-dimension one, planar RG interface and preserving $d=3$ superconformal symmetry. The RG interface joins $\mathcal{N}=4$ SYM theory on one side with the $\mathcal{N}=1$ Leigh-Strassler SCFT on the other. We construct a family of such solutions, which in general are associated with spatially dependent mass deformations on the $\mathcal{N}=4$ SYM side, but there is a particular solution for which these deformations vanish. We also construct a Janus solution with the Leigh-Strassler SCFT on either side of the interface. Gravitational solutions associated with superconformal interfaces involving ABJM theory and two $d=3$ $\mathcal{N}=1$ SCFTs with $G_2$ symmetry are also discussed and shown to have similar properties, but they also exhibit some new features.

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arXiv2019

Supersymmetric space-time symmetry breaking sources

We construct new families of deformed supersymmetric field theories which break space-time symmetries but preserve half of the original supersymmetry. We do this by writing deformations as couplings to background multiplets. In many cases it is important to use the off-shell representation as auxiliary fields of the non-dynamical fields must be turned on to preserve supersymmetry. We also consider backgrounds which preserve some superconformal symmetry, finding scale-invariant field profiles, as well as $\mathcal{N} =2$ theories on $S^3$. We discuss how this is related to previous work on interface SCFTs and other holographic calculations.

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arXiv2018

Mass deformed ABJM and $\mathcal{PT}$ symmetry

We consider real mass and FI deformations of ABJM theory preserving supersymmetry in the large $N$ limit, and compare with holographic results. On the field theory side, the problems amounts to a spectral problem of a non-Hermitian Hamiltonian. For certain values of the deformation parameters this is invariant under an antiunitary operator (generalised $\mathcal{PT}$ symmetry), which ensures the partition function remains real and allows us to calculate the free energy using tools from statistical physics. The results obtained are compatible with previous work, the important new feature being that these are obtained directly from the real deformations, without analytic continuation.

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arXiv2017

Particle-hole symmetry and composite fermions in fractional quantum Hall states

We study fractional quantum Hall states at filling fractions in the Jain sequences using the framework of composite Dirac fermions. Synthesizing previous work, we write down an effective field theory consistent with all symmetry requirements, including Galilean invariance and particle-hole symmetry. Employing a Fermi liquid description, we demonstrate the appearance of the Girvin--Macdonlald--Platzman algebra and compute the dispersion relation of neutral excitations and various response functions. Our results satisfy requirements of particle-hole symmetry. We show that while the dispersion relation obtained from the HLR theory is particle-hole symmetric, correlation functions obtained from HLR are not. The results of the Dirac theory are shown to be consistent with the Haldane bound on the projected structure factor, while those of the HLR theory violate it.

cond-mat.mes-hall↗

arXiv2017

Electrons and composite Dirac fermions in the lowest Landau level

We construct an action for the composite Dirac fermion consistent with symmetries of electrons projected to the lowest Landau level. First we construct a generalization of the $g=2$ electron that gives a smooth massless limit on any curved background. Using the symmetries of the microscopic electron theory in this massless limit we find a number of constraints on any low-energy effective theory. We find that any low-energy description must couple to a geometry which exhibits nontrivial curvature even on flat space-times. Any composite fermion must have an electric dipole moment proportional and orthogonal to the composite fermion's wavevector. We construct the effective action for the composite Dirac fermion and calculate the physical stress tensor and current operators for this theory.

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arXiv2017

Physical stress, mass, and energy for non-relativistic matter

For theories of relativistic matter fields there exist two possible definitions of the stress-energy tensor, one defined by a variation of the action with the coframes at fixed connection, and the other at fixed torsion. These two stress-energy tensors do not necessarily coincide and it is the latter that corresponds to the Cauchy stress measured in the lab. In this note we discuss the corresponding issue for non-relativistic matter theories. We point out that while the physical non-relativistic stress, momentum, and mass currents are defined by a variation of the action at fixed torsion, the energy current does not admit such a description and is naturally defined at fixed connection. Any attempt to define an energy current at fixed torsion results in an ambiguity which cannot be resolved from the background spacetime data or conservation laws. We also provide computations of these quantities for some simple non-relativistic actions.

hep-th↗

arXiv2016

Higher-Spin Theory of the Magnetorotons

Fractional quantum Hall liquids exhibit a rich set of excitations, the lowest-energy of which are the magnetorotons with dispersion minima at a finite momentum. We propose a theory of the magnetorotons on the quantum Hall plateaux near half filling, namely, at filling fractions $ν=N/(2N+1)$ at large $N$. The theory involves an infinite number of bosonic fields arising from bosonizing the fluctuations of the shape of the composite Fermi surface. At zero momentum there are $O(N)$ neutral excitations, each carrying a well-defined spin that runs integer values $2,3,\ldots$. The mixing of modes at nonzero momentum $q$ leads to the characteristic bending down of the lowest excitation and the appearance of the magnetoroton minima. A purely algebraic argument shows that the magnetoroton minima are located at $q\ell_B=z_i/(2N+1)$, where $\ell_B$ is the magnetic length and $z_i$ are the zeros of the Bessel function $J_1$, independent of the microscopic details. We argue that these minima are universal features of any two-dimensional Fermi surface coupled to a gauge field in a small background magnetic field.

cond-mat.mes-hall↗

arXiv2016

Covariant effective action for a Galilean invariant quantum Hall system

We construct effective field theories for gapped quantum Hall systems coupled to background geometries with local Galilean invariance i.e. Bargmann spacetimes. Along with an electromagnetic field, these backgrounds include the effects of curved Galilean spacetimes, including torsion and a gravitational field, allowing us to study charge, energy, stress and mass currents within a unified framework. A shift symmetry specific to single constituent theories constraints the effective action to couple to an effective background gauge field and spin connection that is solved for by a self-consistent equation, providing a manifestly covariant extension of Hoyos and Son's improvement terms to arbitrary order in $m$.

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