arXiv subjects

Troels Harmark

Publications and source records attributed to Troels Harmark.

At least 19 recordsLinked to original sources

arXiv2026

Finite scalar field theory with SU(1,1) spacetime symmetry from near-BPS limits of $\mathcal{N}=4$ SYM

In this work, we consider an interacting and matrix-valued scalar quantum field theory that emerges from a near-BPS decoupling limit of $\mathcal{N}=4$ super Yang-Mills. The theory is non-Lorentzian with SU(1,1) spacetime symmetry and admits a (semi-)local action formulation. The interaction can be viewed as arising from a non-abelian gauge field without propagating degrees of freedom. The proposed field theory action has previously been considered as classically equivalent to SU(1,1) Spin Matrix theory. In this work, we examine this equivalence at the quantum level. We show that the classical action is off-shell invariant under the SU(1,1) symmetry group. We then analyze the renormalization properties, showing the theory is finite at all orders in perturbation theory. This provides a rare example of a non-supersymmetric and non-Lorentzian quantum field theory where a non-renormalization theorem holds.

hep-th↗

arXiv2026

Tidal perturbations of an extreme mass ratio inspiral around a Kerr black hole

We determine the metric of a Kerr black hole subject to external tidal fields using metric reconstruction techniques. Working within the Newman-Penrose formalism, we solve the Teukolsky master equation for static, quadrupolar modes associated with a slowly varying tidal environment, and reconstruct the corresponding metric perturbation in the outgoing radiation gauge. As an application, we derive the secular Hamiltonian governing the motion of a test particle in the tidally deformed Kerr spacetime and investigate long-term tidal effects relevant to extreme-mass-ratio inspirals. In particular, we compute tidal-induced shifts of the innermost stable circular orbit and the light ring. We find that these tidal corrections are strongly spin dependent, with significantly larger effects for retrograde orbits around rapidly rotating black holes. Our results provide a fully analytic framework for studying tidal interactions and secular dynamics in rotating black-hole spacetimes, with direct applications to gravitational-wave modeling and tests of gravity in the strong-field regime.

gr-qc↗

arXiv2025

Observable signature of magnetic tidal coupling in hierarchical triple systems

We study hierarchical triple systems formed by a compact binary orbiting a supermassive black hole (SMBH), focusing on the role of relativistic magnetic tidal interactions. Extending previous analyses of precession resonances to 0.5 post-Newtonian order, we incorporate quadrupolar magnetic tidal moments, which have no Newtonian counterpart. We find that magnetic tides introduce new resonances absent at lower order, leading to additional eccentricity excitations and significantly modifying the binary's long-term evolution. Numerical solutions of the Lagrange Planetary Equations confirm these analytical predictions and reveal how resonance strength depends on orbital eccentricity and inclination. The resulting dynamics accelerates the binary merger and imprints distinctive signatures on gravitational waves, potentially observable by LISA. Our findings identify magnetic tidal coupling as a novel strong-gravity effect and establish its importance for the resonant dynamics of compact-object binaries near SMBHs.

gr-qc↗

arXiv2025

Strong-gravity precession resonances for binary systems orbiting a Schwarzschild black hole

Binary systems of compact objects in close orbit around a supermassive black hole (SMBH) may form in galactic nuclei, providing a unique environment to probe strong-gravity tidal effects on the binary's dynamics. In this work, we investigate precession resonances arising between the periastron precession frequency of a binary system and its orbital frequencies around the SMBH. By modeling the SMBH as a Schwarzschild black hole, we find that relativistic effects in the tidal field give rise to a significantly richer resonance spectrum compared to the Newtonian case. This result is supported by both perturbative and numerical analyses of the quadrupolar tidal interaction in the strong-gravity regime. Our results reveal new signatures for strong-gravity effects in such triple systems, with potential implications for gravitational-wave astronomy.

gr-qc↗

arXiv2025

Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory

We realize an explicit conformal mapping between the state and operator pictures in a class of (2+1)-dimensional non-Lorentzian field theories with SU(1,2)$\times$U(1) conformal symmetry. The state picture arises from null reducing four-dimensional relativistic conformal field theories on a three-sphere, yielding a non-Lorentzian geometry with the conformal Killing symmetry group SU(1,2). This is complementary to the operator picture recently studied by Lambert et al., where the geometry acquires an $Ω$-deformation. We then use the geometric mapping between the two pictures to derive a correspondence between the generators. This provides a concrete realization of the state-operator correspondence in non-Lorentzian conformal field theories.

hep-th↗

arXiv2025

Gravitational solitons and non-relativistic string theory

We explore the non-relativistic string theory (NRST) limit of type II string theory and its action on gravitational solitons. As a start, we exhibit in detail that the NRST limit is T-dual to a discrete lightcone limit and can be viewed as a near-BPS limit. This also clarifies the nature of multi-string states of NRST and its connection to matrix string theory. We consider the NRST limit of the fundamental string soliton, confirming the recent finding that it corresponds to a relativistic near-horizon background, which we argue is the manifestation of a strong coupling phase of the NRST worldvolume theory. Furthermore, we consider the NRST limit of a class of D-branes as well as the NS5-brane. This reveals that they become gravitational solitons in NRST, as they are sourced torsional string Newton-Cartan (TSNC) geometries. Finally, for the NRST D-brane solitons we show that a further decoupling limit leads to new holographic correspondences between multicritical matrix theories and NRST in curved TSNC backgrounds.

hep-th↗

arXiv2024

Hagedorn temperature from the thermal scalar in AdS and pp-wave backgrounds

We propose a thermal scalar equation of motion (EOM) that takes into account curvature corrections for backgrounds supported by Ramond-Ramond fluxes. This can be used to obtain the Hagedorn temperature for type II string theory on AdS and pp-wave backgrounds. For Ramond-Ramond flux supported pp-waves we show that the proposed thermal scalar EOM reproduces the leading curvature correction in the Hagedorn temperature equation obtained from the type II string theory spectrum. Furthermore, we use the thermal scalar EOM to obtain curvature corrections to the Hagedorn temperature for the AdS$_5 \times S^5$ and AdS$_4 \times \mathbb{C} P^3$ backgrounds. These corrections match with strong coupling results of the integrable dual field theories, recently obtained by the Quantum Spectral Curve technique.

hep-th↗

arXiv2024

Binary mergers in strong gravity background of Kerr black hole

Binary-black-hole (BBH) mergers can take place close to a supermassive black hole (SMBH) while being in a bound orbit around the SMBH. In this paper, we study such bound triple systems and show that including the strong gravity effects of describing the SMBH with a Kerr metric can significantly modify the dynamics, as compared to a Newtonian point particle description of the SMBH. We extract the dynamics of the system, using a quadrupole approximation to the tidal forces due to the SMBH. We exhibit how the gyroscope precession is built into this dynamics, and find the secular Hamiltonian by both averaging over the inner and outer orbits, the latter being the orbit of the BBH around the SMBH. We study the long-time-scale dynamics, including the periastron precession and GW radiation-reaction of the binary system, finding that the strong gravity effects of the SMBH can enhance the von Zeipel-Lidov-Kozai mechanism, resulting in more cycles, higher maximum eccentricity, and thereby a shorter merger time, particularly when the binary is close to, or at, the innermost stable orbit of the SMBH. We end with an analysis of the peak frequency of the GW emission from the binary system, highlighting possible observable signatures in the LISA and ET frequency bands.

gr-qc↗

arXiv2024

Blandford-Znajek jets in MOdified Gravity

General relativity (GR) will be imminently challenged by upcoming experiments in the strong gravity regime, including those testing the energy extraction mechanisms for black holes. Motivated by this, we explore magnetospheric models and black hole jet emissions in MOdified Gravity (MOG) scenarios. Specifically, we construct new power emitting magnetospheres in a Kerr-MOG background which are found to depend non-trivially on the MOG deformation parameter. This may allow for high-precision tests of GR. In addition, a complete set of analytic solutions for vacuum magnetic field configurations around static MOG black holes are explicitly derived, and found to comprise exclusively Heun polynomials.

gr-qc↗

arXiv2023

Longitudinal Galilean and Carrollian limits of non-relativistic strings

It is well known that one can take an infinite speed of light limit that gives rise to non-relativistic strings with a relativistic worldsheet sigma model but with a non-relativistic target space geometry. In this work we systematically explore two further limits in which the worldsheet becomes non-Lorentzian. The first gives rise to a Galilean string with a Galilean structure on the worldsheet, extending previous work on Spin Matrix-related string theory limits. The second is a completely novel limit leading to a worldsheet theory with a Carrollian structure. We find the Nambu-Goto and Polyakov formulations of both limits and explore gauge fixing choices. Furthermore, we study in detail the case of the Galilean string for a class of target space geometries that are related to Spin Matrix target space geometries, for which the Nambu-Goto action (in static gauge) is quadratic in the fields.

hep-th↗

arXiv2023

2.5PN accurate waveform information for generic-planar-orbit binaries in effective one-body models

We provide the post-Newtonian (PN) waveform for binary systems in motion along generic planar orbits at 2.5PN accuracy, in terms of the dynamical variables of the effective one-body (EOB) formalism. In addition to the calculation of the higher order terms for all the contributions to the waveform that have been already considered in previous avatars of EOB models, we also compute the EOB expression of the oscillatory memory terms. These are purely non-circular contributions, first appearing at 1.5PN order, that have been so far neglected in the EOB literature. This should foster their inclusion in EOB models and the definitive assessment of their role in shaping gravitational wave signals at infinity. To further promote the application of our results, we also derive associated non-circular factors according to the waveform factorization prescription of the non-circular EOB model TEOBResumS-DALI; the result is a set of ready-to-use non-circular factors that can be directly implemented as extra non-circular corrections in the waveform of TEOBResumS-DALI.

gr-qc↗

arXiv2023

The Panorama of Spin Matrix Theory

Spin Matrix theory describes near-BPS limits of $\mathcal{N}=4$ SYM theory, which enables us to probe finite $N$ effects like D-branes and black hole physics. In previous works, we have developed the spherical reduction and spin chain methods to construct Spin Matrix theory for various limits. In this paper, by considering a supercharge $\mathcal{Q}$ which is cubic in terms of the letters, we construct the Hamiltonian of the largest Spin Matrix theory of $\mathcal{N}=4$ SYM, called the PSU$(1,2|3)$ Spin Matrix theory, as $H = \{\mathcal{Q}, \mathcal{Q}^\dagger \}$. We show the resulting Hamiltonian is automatically positive definite and manifestly invariant under supersymmetry. The Hamiltonian is made of basic blocks which transform as supermultiplets. A novel feature of this Hamiltonian is its division into D-terms and F-terms that are separately invariant under PSU$(1,2|3)$ symmetry and positive definite. As all the other Spin Matrix theories arising from $\mathcal{N}=4$ SYM can be acquired by turning off certain letters in the theory, we consider our work as revealing the "Panorama" of Spin Matrix theory.

hep-th↗

arXiv2023

Tidal deformations of a binary system induced by an external Kerr black hole

The dynamics of a binary system moving in the background of a black hole is affected by tidal forces. In this work, for the Kerr black hole, we derive the electric and magnetic tidal moments at quadrupole order, where the latter are computed for the first time in full generality. We make use of these moments in the scenario of a hierarchical triple system made of a Kerr black hole and an extreme-mass ratio binary system consisting of a Schwarzschild black hole and a test particle. We study how the secular dynamics of the test particle in the binary system is distorted by the presence of tidal forces from a much larger Kerr black hole. Our treatment includes strong gravitational effects beyond the post-Newtonian approximation both for the binary system and for the tidal forces since the binary system is allowed to be close to the event horizon of the Kerr black hole. We compute the shifts in the physical quantities for the secular dynamics of the test particle and show that they are gauge-invariant. In particular, we apply our formalism to the innermost stable circular orbit for the test particle and to the case of the photon sphere. Our results are relevant for the astrophysical situation in which the binary system is in the vicinity of a supermassive black hole.

gr-qc↗

arXiv2022

Blandford--Znajek monopole expansion revisited: novel non-analytic contributions to the power emission

The Blandford and Znajek (BZ) split-monopole serves as an important theoretical example of the mechanism that can drive the electromagnetic extraction of energy from Kerr black holes. It is constructed as a perturbative low spin solution of Force Free Electrodynamics (FFE). Recently, Armas $et~al.$ put this construction on a firmer footing by clearing up issues with apparent divergent asymptotics. This was accomplished by resolving the behavior around the outer light surface, a critical surface of the FFE equations. Building on this, we revisit the BZ perturbative expansion, and extend the perturbative approach to higher orders in the spin parameter of the Kerr black hole. We employ matched-asymptotic-expansions and semi-analytic techniques to extend the split-monopole solution to the sixth-order in perturbation theory. The expansion necessarily includes novel logarithmic contributions in the spin parameter. We show that these higher order terms result in non-analytic contributions to the power and angular momentum output. In particular, we compute for the first time the perturbative contributions to the energy extraction at seventh- and eighth-order in the spin parameter. The resulting formula for the energy extraction improves the agreement with numerical simulations at finite spin. Moreover, we present a novel numerical procedure for resolving the FFE equations across the outer light surface, resulting in significantly faster convergence and greater accuracy, and extend this to higher orders as well. Finally, we include a general discussion of light surfaces as critical surfaces of the FFE equations.

gr-qc↗

arXiv2022

Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: Chemical potentials and deformations

We describe how to calculate the Hagedorn temperature of $\mathcal{N}=4$ SYM theory and type IIB superstring theory on $AdS_5\times S^5$ via the Quantum Spectral Curve (QSC) -- providing further details on our previous letters 1706.03074 and 1803.04416. We solve the QSC equations perturbatively at weak 't Hooft coupling $λ$ up to seven-loop order and numerically at finite coupling, finding that the perturbative results can be expressed in terms of single-valued harmonic polylogarithms. Moreover, we generalize the QSC to describe the Hagedorn temperature in the presence of chemical potentials. Finally, we show that the Hagedorn temperature in certain deformations of $\mathcal{N}=4$ SYM theory (real-$β$ and $γ_i$ deformation) agrees with the one in $\mathcal{N}=4$ SYM theory at any value of $λ$.

hep-th↗

arXiv2021

Spin Matrix Theory in near $\frac{1}{8}$-BPS corners of $\mathcal{N} = 4$ super-Yang-Mills

We consider limits of $\mathcal{N} = 4$ super-Yang-Mills (SYM) theory that approach BPS bounds. These limits result in non-relativistic theories that describe the effective dynamics near the BPS bounds and upon quantization are known as Spin Matrix Theories. The near-BPS theories can be obtained by reducing $\mathcal{N}=4$ SYM on a three-sphere and integrating out the fields that become non-dynamical in the limits. In previous works we have considered various SU(1,1) and SU(1,2) types of subsectors in this limit. In the current work, we will construct the remaining Spin Matrix Theories defined near the $\frac{1}{8}$-BPS subsectors, which include the PSU(1,1|2) and SU(2|3) cases. We derive the Hamiltonians by applying the spherical reduction algorithm and show that they match with the spin chain result, coming from the loop corrections to the dilatation operator. In the PSU(1,1|2) case, we prove the positivity of the spectrum by constructing cubic supercharges using the enhanced PSU$(1|1)^2$ symmetry and show that they close to the interacting Hamiltonian. We finally analyse the symmetry structure of the sectors in view of an interpretation of the interactions in terms of fundamental blocks.

hep-th↗

arXiv2021

The Hagedorn temperature of AdS5/CFT4 at finite coupling via the Quantum Spectral Curve

Building on the recently established connection between the Hagedorn temperature and integrability [Phys.Rev.Lett. 120 (2018) no.7, 071605], we show how the Quantum Spectral Curve formalism can be used to calculate the Hagedorn temperature of AdS5/CFT4 for any value of the 't Hooft coupling. We solve this finite system of finite-difference equations perturbatively at weak coupling and numerically at finite coupling. We confirm previous results at weak coupling and obtain the previously unknown three-loop Hagedorn temperature. Our finite-coupling results interpolate between weak and strong coupling and allow us to extract the first perturbative order at strong coupling. Our results indicate that the Hagedorn temperature for large 't Hooft coupling approaches that of type IIB string theory in ten-dimensional Minkowski space.

hep-th↗

arXiv2021

Torsional string Newton-Cartan geometry for non-relativistic strings

We revisit the formulation of non-relativistic (NR) string theory and its target space geometry. We obtain a new formulation in which the geometry contains a two-form field that couples to the tension current and that transforms under string Galilei boosts. This parallels the Newton-Cartan one-form that couples to the mass current of a non-relativistic point particle. We show how this formulation of the NR string arises both from an infinite speed of light limit and a null reduction of the relativistic closed bosonic string. In both cases, the two-form originates from a combination of metric quantities and the Kalb-Ramond field. The target space geometry of the NR string is seen to arise from the gauging of a new algebra that is obtained by an Inonu-Wigner contraction of the Poincaré algebra extended by the symmetries of the Kalb-Ramond field. In this new formulation, there are no superfluous target space fields that can be removed by fixing a Stückelberg symmetry. Classically, there are no foliation/torsion constraints imposed on the target space geometry.

hep-th↗