Papers

Fermionic degrees of freedom are essential ingredients in cosmological collider physics and are well motivated by many phenomenological models beyond the Standard Model, but their signals remain largely unexplored due to the difficulty of computing loop diagrams. In this work, we ask how fermionic bubble loops contribute to cosmological collider signals and provide an exact answer for arbitrary couplings. We develop two parallel analytical methods whose agreement provides a non-trivial check of the result. The first method is similar in spirit to spectral decomposition and is built directly from an identity for the product of propagators, which turns the bubble signal into an infinite sum of tree-level exchange signals. The second method is based on the Mellin-Barnes representation, where the result is reconstructed from the residues of distinct families of poles. We also show that the fermionic bubble can be generated from the scalar bubble by the action of appropriate differential operators. As a phenomenologically important application, we consider Yukawa interactions between fermions and the inflaton, finding that the resulting bispectrum signal vanishes identically. Through the spectral decomposition, this vanishing can be traced to a field redefinition of the associated tree-level counterparts.

We consider the field theory of a quantum massless left handed fermion coupled to a background graviton field, $h_{\mu\nu}$, on four-dimensional Minkowski spacetime. By using the BPHZL renormalization scheme, we prove that, up to order four in the number of graviton fields, there are no parity-odd contributions to the renormalized gravitational effective action. As a side result, we show that, modulo arbitrary UV finite diffeomorphism invariant parity-even counterterms, the gravitational effective action in question is equal, up to order four in the number of graviton fields, to half the corresponding gravitational action for a Dirac fermion non-chirally coupled to gravity. Also as a side result, we conclude the the Weyl anomaly is purely parity-even and that its value is half the value of the Weyl anomaly for a Dirac fermion non-chirally coupled to gravity.

In this thesis we study embedding formalisms for $\mathcal{N}$-extended anti-de Sitter (AdS) superspaces in four and five dimensions. Specifically, building on earlier work in the four-dimensional case, we develop bi-supertwistor realisations for these AdS superspaces as well as their harmonic and projective extensions. We also describe the precise correspondence between such global approaches to AdS superspaces and their realisations within the supergravity setting. Finally, we present applications of our formalism, including new models for superparticles propagating in AdS superspaces in diverse dimensions.

We propose a worldline formulation of higher-spin gravity (HSG) in $\mathrm{AdS}_4$, based on a simple twistor action. Taken at face value, the model describes only the free propagation of massless higher-spin fields. The central observation of this work is that the model admits a natural double-line interpretation, which supplies a geometric prescription for gluing worldlines at interaction vertices, in close parallel with the joining of strings in string theory. Building on this picture, we construct $\mathrm{AdS}$-covariant vertex operators for all massless higher-spin fields, show that they satisfy the Bargmann-Wigner equations, and use them to compute the n-point correlation functions of type-A and type-B HSG as worldline path integrals of these vertex operators. In the boundary limit these correlators reproduce the higher-spin current correlators of free boson and free fermion vector models. We further discuss the embedding of the worldline theory into Poisson sigma model, where the doubled-line structure acquires a geometric origin as the two edges of an open string worldsheet, together with several consequences of this enlarged framework – fractional branes, loop expansion, unoriented projection, and the prospect of a worldsheet formulation of HSG.

Effective field theory (EFT) provides a systematic framework for parametrizing possible higher-energy corrections to general relativity through higher-curvature interactions. In this work, we investigate gravitational lensing in both weak- and strong-field regimes for EFT-corrected Reissner-Nordström black hole spacetimes, focusing on both weakly charged and near-extremal configurations. Using the strong deflection limit formalism, we derive the corresponding corrections to the deflection angle, photon sphere radius, critical impact parameter, and strong lensing coefficients induced by higher-derivative curvature-electromagnetic interactions. Our analysis is restricted to purely geometrical corrections associated with modifications of the background spacetime geometry, without including polarization-dependent corrections to the photon propagation law. We show that strong gravitational lensing observables in charged black hole backgrounds can provide complementary probes of effective interactions between gravity and electromagnetic fields. These results suggest that future high-precision observations of strong lensing phenomena may place constraints on higher-curvature EFT couplings beyond general relativity.

We revisit electric and magnetic surface charges and edge modes in four-dimensional Maxwell theory and QED on a spacetime with a finite spatial boundary. Using the S-wall, which implements electromagnetic duality, we clarify the dual structure of surface charges. We show that, for the standard Neumann and Dirichlet boundary conditions, large gauge transformations and the corresponding shifts of edge modes are gauge redundancies rather than physical boundary symmetries. We also consider singular large gauge transformations and interpret them as insertions of Wilson or 't Hooft loops on the boundary. For modified boundary conditions, we show that large gauge transformations can become genuine physical boundary symmetries generated by topological surface operators, and that the corresponding edge modes can become physical. We further construct new boundary conditions that are electromagnetic duals of the modified boundary conditions.

We study the low-energy properties of QCD-like theories in the presence of a $P$-odd and $U(1)$ axial breaking four-fermion operator $\left( \bar{\psi} \psi \right) \left( \bar{\psi} i \gamma_5 \psi \right)$. We apply the functional renormalization group for a low-energy effective theory involving the $CP$-violating operator. We find that allowing for the running gauge coupling, the $CP$-violating four-fermion interaction becomes relevant in the chirally broken phase. In the presence of a finite quark mass, the RG running of the $\theta$-parameter is shown to be strongly suppressed toward the infrared. The present work clarifies how strong-$CP$ effects generated at UV can non-trivially be transferred to the infrared physics in QCD-like theories.

In this paper, we present a detailed review/analysis of the Dirac quantisation of Hamiltonian systems with constraints. To this end, we use, as a guide, the physical example provided by the dynamics of a solid ball rolling, without slipping, down an inclined plane under the action of gravity. After all, however simple this physical system may be, it provides a rich framework for this analysis since, in addition to allowing us to discuss scenarios involving holonomic and non-holonomic constraints, it is also a gauge system. Indeed, due to this latter fact, we have carefully detailed how the transition, from classical to quantum mechanics, must be guided by the Dirac-Bergmann algorithm and by the consequent replacement of Dirac brackets with commutators. As a central result, we demonstrate that the restriction of the Hamiltonian operator of this system with constraints to the physical Hilbert subspace (which is identified with the quantisation of these constraints) reproduces the same Schrödinger equation that can be originally obtained in intrinsic terms, a fact that only reinforces the consistency of the Dirac quantisation method.

We introduce `dualGNN', an autoregressive message-passing GNN for sampling fine, regular triangulations of lattice polytopes. dualGNN operates on a generalization of the dual graph of a triangulation, with edges labeled by `signed circuits' – combinatorial invariants from the theory of oriented matroids. We show that these circuits are necessary and sufficient to determine a triangulation's regularity from the graph, provided certain magnitude information is retained. The model is independent of the polytope's point count and invariant under its orientation-preserving symmetries ($\mathrm{SL}(d,\mathbb{Z}) \ltimes \mathbb{Z}^d$), and our masking procedure further guarantees that every rollout produces a fine triangulation (in 2D). On unseen polygons with $N_\mathrm{pts} \leq 40$, dualGNN is the only sampler we tested that is consistent with uniform sampling across all our diagnostics (KL divergence from uniformity, collision counts, and sample autocorrelation). The model is small ($\sim92$k parameters) and trains in $\sim7.5$ hours on a single consumer GPU. We apply dualGNN to string theory, sampling Calabi-Yau threefolds uniformly at $h^{1,1}=86$; we also sample CYs at $h^{1,1}=128$, observing no deviations from uniformity, but our diagnostics are weaker here. Code, training scripts, and pretrained models are available at https://github.com/natemacfadden/dualGNN (pip install dualgnn), and dualGNN is integrated into CYTools.

We develop the (super)twistor approach to D$0$-brane, which is the massive type IIA superparticle in ten dimensional spacetime. The basic variables are hexadecuplet of constrained $OSp(32|1)$ supertwistors similar but not identical to the ones which have been used for the description of 11D massless superparticle, also known as M$0$-brane. We show how the constrained supertwistor formulation is related to the spinor moving frame approach to D$0$-brane. We perform the quantization of the model by two different methods and discuss the relation of the results with the quantization of the spinor moving frame formulation of D$0$-brane. The quantum state spectrum describes the massive counterpart of the linearized type IIA supergravity.

Spontaneous symmetry breaking is a well-understood mechanism for generating distinct phases of matter. Recently, the notion of symmetry has been broadened to include operations without inverses, leading to the concept of non-invertible symmetries. How do symmetry-breaking phases associated with non-invertible symmetries differ from those arising from conventional invertible symmetries? We address this question using concrete lattice models of the gapped phases with non-invertible Rep($H_8$) symmetry as an example. We find that, despite the symmetry being non-invertible, the symmetry-breaking phases can still be characterized by the long-range correlation of local order parameters, which obey a more general algebraic structure than in the invertible setting. Furthermore, via generalized gauging, certain non-invertible symmetry-breaking transitions can be mapped to deconfined quantum critical points of invertible symmetries, and vice versa. We establish precise conditions under which this duality holds and illustrate them with several families of examples, providing a systematic route to studying beyond-Landau phase transitions.

We benchmark current annealing-based optimization workflows on a greenhouse-inspired quadratic unconstrained binary optimization problem for binary heater scheduling, where the horizon H denotes the number of hourly control decisions. For the main one-day instance (H=24), all solver outputs are decoded back into heater schedules and evaluated in the original greenhouse simulator using the same physical objective and feasibility criterion. Classical simulated annealing and path-integral simulated quantum annealing produce feasible near-optimal solutions in all repetitions, with best objectives close to the exact optimum. In contrast, the tested D-Wave Leap Hybrid BQM workflow is less reliable and does not outperform the classical baselines under 15–60~s requested time limits. Direct D-Wave QPU execution on reduced instances remains feasible in all runs and recovers the exact optimum for H=10 and H=12, but the exact-hit rate drops from 5/10 to 2/10 and then to 0/10 at H=14, with substantially higher variance than the classical baselines. The results do not indicate quantum advantage, but provide a reproducible, physically decoded benchmark that exposes the current strengths and limitations of classical, hybrid, and direct quantum annealing workflows on structured control QUBOs.

We investigate the charge and spin transport properties of a Weyl semimetal under an external magnetic field using a low-energy effective theory. By performing a chiral transformation, we remove the axial term from the fermionic Lagrangian, while its physical effects are retained through the system's electromagnetic response. This response, derived from integrating out the fermionic degrees of freedom, takes the form of axionic electrodynamics and enters the Dirac equation via minimal coupling. The resulting dynamics separate naturally into magnetic and electric components: the magnetic sector admits a supersymmetric factorization, while the electric part exhibits a PT-supersymmetric structure. Robin boundary conditions are applied to the spinor, setting the energy spectrum and defining exact spinor solutions. We obtain the chiral projections of probability and current densities, exhibiting a chiral imbalance in the material. We show that in the x-direction, only one chirality contributes to the chiral current ($j^x_l = 0$). Spin density and currents where also computed. Our results demonstrate how the interplay between axionic response and supersymmetry governs transport phenomena in our specific setup, offering novel insights into the effective field theory description of Weyl semimetals.

We construct the exact Robin bulk-to-boundary propagator for a Breitenlöhner–Freedman scalar on AdS$_{d+1}$ and the BTZ black hole, realizing the double-trace RG flow between standard and alternate quantization geometrically as a one-parameter family of bulk boundary conditions. We derive the UV and IR chain expansions of the kernel intrinsically from the boundary-value problem, without an auxiliary-field decoupling, and identify a branch split at each order that separates the local data the boundary CFT observes from finite-bulk-depth structure visible only to bulk probes – the part of $K_f$ that distinguishes holographic reconstruction from boundary calculation. On BTZ we obtain the closed-form Robin kernel and the corresponding family of quasinormal-mode trajectories, each connecting an alternate-quantization pole at $g=0$ to a standard one at $g\to\infty$. We locate an exceptional-point locus along this family at which two trajectories coalesce into a Jordan block, and show it acts as a non-Hermitian phase boundary for the double-trace flow itself: crossing it reorganizes the global pole-pairing topology of the spectrum. Unlike holographic EPs reached by analytic continuation in momentum or frequency, this transition lives on the interpolation between quantizations and is reachable at finite real momentum and temperature by tuning the physical Robin coupling.

We introduce a minimally coupled dark sector based on a nonlinear electrodynamics to generate regular spacetime textures that interpolate from a regular core to an asymptotic Lorentz-violating conical geometry. This construction provides a simple mechanism, in Einstein gravity with minimally coupled matter, for obtaining Lorentz-violating Schwarzschild and Reissner-Nordström black holes. The framework further allows us to construct Lorentz-violating regular black holes, including the Bardeen and Hayward black holes, as well as a class of electrically-charged regular black holes.

We show that the local gauge-invariance of the quantum geometric tensor (QGT) defined in the two-dimensional Block-momentum (BM) space of a generic $N$-band (arising out of sub-lattice degrees of freedom) insulator represented by a tight-binding hamiltonian, leads to the existence of zero modes of non-abelian Dirac operator in such BM space. These zero modes in the two-dimensional Brillouin zone torus $T^{2}$, determines the probability amplitudes associated with the $N$-component ground state wave-function under adiabatic approximation. We analytically derive the expansion coefficients of maximally localized Wannier function in one-dimension from the solutions of these zero mode equations, and obtain momentum-space generalization of celebrated Laughlin gauge condition as a by-product.The commutator of these non-abelian Dirac operators define the algebra of the guiding center co-ordinates which provide a more general frame-work to study such systems than one based on the Landau-level analogues. In the ideal quantum geometric limit, these zero-mode solutions become self-dual momentum-space instantons, and can be linked to the non-abelian generalization of the vortexability criterion of Chern bands in momentum-space. We derive some exact solutions of such zero-mode on the complex torus geometry, and discuss implications of this framework for realistic systems such as two-dimensional topological insulators, rhombohedral $N_{L}$-layer graphene.

The ring wormhole is the zero-mass limit of the Kerr metric. Its geometry is locally flat, but the topology is nontrivial, with a throat connecting two asymptotic regions and a distributional curvature singularity on the ring encircling the throat. We construct stationary generalizations of this static wormhole that are different from Kerr and invariant under reflections across the wormhole throat. The problem reduces to solving the vacuum Ernst equations subject to the corresponding symmetry conditions. The slowly rotating perturbative solutions were constructed previously, while we now present a detailed analysis of non-perturbative solutions obtained within a numerical framework. For slow rotation, they exhibit the non-relativistic relation $M\sim J^2$ between the mass and angular momentum, which transforms into the Regge relation $J=M^2$ in the fast-rotation regime, when $J\to\infty$ and the ring is stretched without bound by the centrifugal force. However, if the ring size in the static limit is sent to zero at the same time, then $M$ and $J$ remain bounded as the throat linear velocity approaches unity. The wormhole geometry then approaches the extremal Kerr solution, thus “mimicking” it. The wormholes carry a curvature singularity at the ring, but this can be removed by via simple “scalarization” procedure that promotes the vacuum solutions to regular wormholes with a phantom scalar field.

We present a field-theoretic construction of a class of artificial neural networks from solitonic degrees of freedom in nonlinear scalar field theory. The purpose is not to rename a standard neural layer in the language of solitons, but to start from a continuum action, restrict the theory to a nonperturbative sector containing localized stable solutions, perform a collective-coordinate reduction, and derive the neural layer as the finite-dimensional input-output map of the reduced solitonic dynamics. In this construction, the computational unit is a projected collective coordinate of a localized field configuration rather than an elementary point variable; the activation function is the solitonic response profile or scattering map; the weight matrix is the Hessian or overlap matrix of an effective interaction energy among solitons; the bias is induced by external sources, vacuum asymmetry, or boundary forcing; and depth is a discrete evolution parameter on the solitonic moduli space. We develop the construction explicitly for the \(\phi^4\) kink, where the \(\tanh\) activation and the logistic sigmoid arise from the kink profile, and then derive the multilayer feedforward form from an operator-splitting approximation to collective-coordinate gradient flow. We emphasize the novelty criterion: the neural architecture is obtained only after specifying the field action, the solitonic ansatz, the moduli-space metric, the interaction functional, and the projection map. The result is a controlled route from nonlinear field theory to neural-network structure, with robustness tied to the energetic and topological stability of the solitonic sector.

By examining the transition from freeze-out to freeze-in dark matter (DM) production within the framework of perturbative reheating, where DM interacts with the visible sector through effective operators of dimension six, we have investigated how a broad range of new physics probes can reveal the nature of the pre-BBN Universe. Incorporating constraints from direct and indirect DM searches, invisible decay measurements, collider experiments, and gravitational wave observations, our analysis demonstrates that both current and forthcoming experimental sensitivities can serve as powerful tools for probing as well as constraining the post-inflationary era, together with new physics beyond the SM. Our analysis demonstrates that collider experiments at both the intensity and energy frontiers can impose strong bounds on derivative operators whose interactions are typically p-wave suppressed, and therefore only weakly constrained by astrophysical observations. In particular, these complementary searches can significantly restrict the allowed reheating temperature, DM mass and effective interaction scale required to reproduce the observed DM abundance for DM produced during the epoch of reheating.

We study the possibility of probing the dynamical inverse seesaw mechanism for the origin of light neutrino masses via the detection of stochastic gravitational waves (GW) in the low-frequency regime currently being probed by pulsar timing arrays. As the lepton number-violating term in inverse seesaw typically remains in the sub-MeV ballpark, its dynamical origin naturally brings the possibility of a low-scale first-order phase transition, which can be probed at low-frequency GW experiments. We also find interesting complementarity with heavy neutral lepton searches, as GW experiments remain sensitive to parameter space with small active-sterile mixing, which is out of reach for most particle physics experiments.

We describe the dynamics of many-body quantum chaotic systems at all time scales by studying the Green's and out-of-time order correlation (OTOC) functions of the four-body, $N$-Majorana Sachdev-Ye-Kitaev model. By combining the scramblon formalism and random-matrix-theory techniques, we obtain analytical expressions for these functions at all times. The early exponential growth of the OTOC is followed by an exponential decay at a rate governed by that of the Green's function (the real part of the leading complex Ruelle-Pollicott resonances). For late times that scale exponentially with $N$, both functions have a dip-ramp-plateau pattern for $N \mathrm{mod}8 = 2, 6$ that deviates substantially from the ergodic prediction due to local-in-energy correlations of matrix elements and eigenvalues, even after the Heisenberg time.

Motivated by trans-Planckian issues in inflation, we determine the Hilbert space and amplitudes of quantum perturbations in the general low-energy effective theory of (multi-)field inflation without relying on the sub-horizon limit. The scalar sector is the most intricate, featuring field mixings and second-class constraints, which we handle using Dirac brackets. These results enable us to estimate the magnitude of higher-derivative corrections. In the specific case of slow-roll inflation, such estimate can be expressed in terms of the first slow-roll parameter $\epsilon$ for a given cutoff $\Lambda$. We apply our results to several inflationary models with finite $\Lambda$: Higgs inflation, the Starobinsky model, natural inflation and hilltop inflation.

Matrix string theory (arXiv:hep-th/9703030, arXiv:hep-th/9701025, arXiv:hep-th/9710009) is a conjectured duality between two-dimensional maximally supersymmetric $U(N)$ Yang-Mills theory and type-IIA string theory in ten-dimensional Minkowski spacetime. The IR description of this gauge theory is governed by the symmetric product orbifold $(\mathbb{R}^8)^N/S_N$ CFT. The leading irrelevant deformation from this IR fixed point is the Dijkgraaf-Verlinde-Verlinde operator, which comes with an unknown Wilson coefficient. We determine this coefficient using non-renormalization arguments from the UV gauge theory. The result is consistent with the matrix string theory conjecture and gives a first-principles check of the relation between $g_{\rm YM}$ and the string coupling. We also comment on the prospects for fixing further Wilson coefficients using similar methods.

Future gravitational wave (GW) standard siren catalogues will probe the late-time expansion history of the Universe across redshift ranges largely inaccessible to traditional electromagnetic observations. To determine how effectively this background distance information can distinguish between viable cosmological models, we introduce a model-independent reconstruction framework utilizing Gaussian Process Regression (GPR). Analyzing mock LISA and Einstein Telescope (ET) catalogues across six fiducial cosmological backgrounds-$\Lambda$CDM, CPL, CPL+$\Lambda$, interacting dark matter, interacting dark energy and axion inspired early dark energy. We reconstruct the comoving distance and its derivatives. Crucially, we propagated the full GP covariance, including derivative cross-covariances, to robustly evaluate the Hubble parameter $H(z)$ and other diagnostics such as $q(z)$, $\mathcal{O}_{m}(z)$ $w_{\rm total}(z)$ and $\kappa(z)$. While our analysis demonstrates that GW bright standard sirens faithfully recover fiducial expansion histories, applying pointwise marginal Hellinger distance reveals that background measurements alone do not provide decisive statistical separation among models. Instead, derivative sensitive diagnostics pinpoint specific redshift windows (e.g., $z\simeq1.6-1.8$ for ET and $z\simeq2.6-2.9$ for LISA) where future catalogues will maximize their discriminatory power. As machine learning methodologies become increasingly integral to astrophysics and cosmology, this Bayesian GPR pipeline offers a principled, nonparametric approach to precisely identifying where the most valuable cosmological information lies.

In observational cosmology, the dark energy density and equation of state are effective quantities reconstructed at the background level under a set of assumptions. These include the FLRW framework, the standard Friedmann equation of General Relativity, and separately conserved non-relativistic matter at late times. Recent analyses involving DESI BAO measurements combined with CMB and supernova data have shown mild preference for dynamical dark energy featuring phantom or phantom-crossing behaviour. While the statistical significance of these trends remains limited, and unresolved systematics or modelling uncertainties may still be important, the resulting discussions have highlighted the need for a clearer interpretation of effective dark energy reconstruction. In particular, effective phantom behaviour does not necessarily imply the existence of a fundamental phantom field, microscopic ghost instabilities, violation of the null energy condition by the fundamental stress tensor, or a catastrophic cosmic future. The purpose of this work is to clarify these distinctions, independently of whether the current observational preference for dynamical dark energy survives future data. We discuss the definition of effective dark energy in cosmology, the interpretation of phantom and phantom-crossing behaviour, introduce a simple kinematic criterion for identifying effective phantom evolution directly from the expansion history, and review physical mechanisms through which effective phantom behaviour may arise without fundamental pathologies. While familiar within the dark energy reconstruction community, these distinctions are often left implicit in broader discussions of dynamical dark energy. We hope that this work will remain useful beyond the present observational situation as a clarification of what observationally reconstructed dark energy does and does not imply.

We establish a correspondence between conformal partial waves on flat, thermal, and defect backgrounds using the shadow formalism. We demonstrate that scalar one-point thermal blocks can be systematically obtained from their four-point flat-space and two-point defect counterparts by considering specific operator configurations. This framework allows us to derive the thermal Casimir equation as a diagonal reduction of the flat-space Casimir system without introducing chemical potentials. We further show that defect two-point blocks with a spin-$l$ exchange operator correspond to thermal one-point blocks for an external spin-$l$ operator.

In this article we study the structure of the $\mathcal{N}=2$ abelian higher-spin cubic $(\mathbf{s_1}, \mathbf{s_2}, \mathbf{s_2})$ vertices and the corresponding $\mathcal{N}=2$ higher-spin supercurrents, introduced in arXiv:2408.00668. These interactions are possible only for $\mathbf{s_1} \geq 2 \mathbf{s_2}$. Conserved supercurrents are constructed as descendants of the principal supercurrent, which is uniquely characterized by simple differential conditions and admits an explicit representation in terms of $\mathcal{N}=2$ higher-spin super-Weyl tensors. We derive the analytic form of the abelian vertices and identify the corresponding analytic higher-spin $\mathcal{N}=2$ supercurrents. We show that the vertex structure is fully determined by the analytic supercurrents $J^{++}_{\alpha(s-1)\dot{\alpha}(s-1)}$, $J^+_{\alpha(s-1)\dot{\alpha}(s-2)}$, and $\bar{J}^+_{\alpha(s-2)\dot{\alpha}(s-1)}$. The analytic form of the vertices provides a simple framework for analyzing their component structure. As an example, we explore the component content of such interactions on the Bel–Robinson diagonal. Using the superfield inverse Noether procedure, we study higher-spin gauge transformations for the $\mathcal{N}=2$ vector multiplet associated with the $(\mathbf{s}, \mathbf{1}, \mathbf{1})$ interaction. In the rigid limit, for odd $\mathbf{s}$ these transformations reduce to the $\mathcal{N}=2$ superspace generalization of zilch-type higher-spin symmetries.

The relative entropy between two states is a key concept in quantum information theory and quantum field theory. In the setting of quantum field theory, its computation requires the handling of relative modular Hamiltonians, which are typically very difficult to compute explicitly. In this paper, we exploit locality properties of general algebraic QFTs to estimate relative modular Hamiltonians between two states, $\omega$ and $\tilde{\omega}$, and hence also their relative entropy, in terms of the modular Hamiltonian of a reference state $\hat{\omega}$, which might be better understood. For suitable pairs of states we can estimate the relative modular Hamiltonian for the algebra of a region $V_2$ from above, resp. from below, in terms of the modular Hamiltonian of $\hat{\omega}$ on a larger region $V_3$, resp. a smaller region $V_1$. Pairs of states and choices of regions which are susceptible to our scheme are related to the presence of superluminal signalling in the sense of Sorkin's paradox. If $\omega=\hat{\omega}$, then there exists a unitary that maps $\omega$ to $\tilde{\omega}$ on $V_3$ and that does not allow superluminal signalling from the spacelike complement $V_3'$ to $V_2$, resp. from $V_1$ to $V_2'$, if our upper, resp. lower, bound applies. To investigate the strength of our estimates we consider coherent states for CCR systems, focussing particularly on free scalar fields. Our estimates apply even if the relative modular Hamiltonian cannot be computed exactly. For sufficiently regular excitations we recover an exact result by squeezing. Our method thus yields an independent proof for the relative entropy formula in cases where the relative modular Hamiltonian cannot be computed exactly. For massless fields we establish the analogous result also for double cone regions. These results indicate that our estimates do not lose too much information.

We study order parameters in one-dimensional quantum lattice models with finite invertible or non-invertible symmetry. We investigate what properties a string operator must satisfy in order to acquire a non-vanishing expectation value in a given gapped phase. We deduce that multiplets of string order parameters organise into a Lagrangian algebra in the Drinfel'd centre of the symmetry category. In particular, we highlight the role of the multiplication rule as governing the fusion of the twisted sector local operators that constitute the string operator in the infrared limit. Our derivations exploit the tensor network approach to the classification of gapped phases and its reformulation in terms of module categories over the symmetry category. Within this framework, a gapped phase is associated with a pattern of spontaneous symmetry breaking wherein a Morita class of algebras of topological lines is preserved in the ground state subspace. The crux of the proof is to show that the expectation value of any string operator explicitly depends on the tube algebra module associated with the Lagrangian algebra, which is realised as the full centre of the corresponding module category. Finally, we demonstrate that these techniques extend to phases of symmetric mixed states.

We give an introduction to the cosmological multiverse, aimed at an audience of artists. We discuss general relativity – our modern theory of gravity – and the cosmological constant, which is widely believed to be responsible for the observed accelerated expansion of the universe. We then turn to a big puzzle that the cosmological constant poses, and, eventually, how the multiverse could solve this puzzle. There's no such thing as a free lunch, however: the multiverse can become arbitrarily large and old. The unsolved problem of making unambiguous predictions for observations in eternally accelerating universes is known as the measure problem of eternal inflation.