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Abstract The quantum off-shell recursion provides an efficient and universal computational tool for loop-level scattering amplitudes. In this work, we present a new comprehensive computational framework based on the quantum off-shell recursion for binary black hole systems. Using the quantum perturbiner method, we derive the recursions and solve them explicitly up to two-loop order. We introduce an indicator that enables straightforward distinguishing diagrams and deriving integral families in the context of off-shell recursions. By employing the soft expansion technique, we remove irrelevant terms from the loop integrands and express them in terms of master integrals. We classify the one-loop and the two-loop classical diagrams, and their loop integrands are represented by linear combinations of the master integrals. Finally, we explicitly calculate the classical scalar 2 → 2 amplitudes in the potential region up to the 3PM order and reproduce the known results.

Abstract We verify the global Poincaré invariance of the Hamiltonian mechanics of gravitating binary dynamics at the second post Minkowskian (2PM) order. For spinless point particles, based on the known 2PM Hamiltonian in the center of momentum frame, we compute the general 2PM Hamiltonian valid in an arbitrary reference frame. An off-shell extension of the 1PM Hamiltonian, which contributes at the 2PM order through an iteration process, plays a crucial role. We then construct the 2PM boost generator that uniquely satisfies all the conditions imposed by the Poincaré algebra.

Abstract We derive all-order expressions for perturbations of the Einstein-Hilbert action and the Einstein equation with the general n-th order terms. To this end, we employ Cheung and Remmen’s perturbation conventions both in tensor density and the usual metric tensor formalisms, including the Einstein-dilaton theory. Remarkably, we find minimal building blocks that generate the entire perturbations for each of our formulations. We show that the number of terms of perturbations grows linearly as the order of perturbations increases. We regard our results as the reference and discuss how to derive perturbations in other conventions from the reference. As a consistency check, we compute graviton scattering amplitudes using the perturbiner method based on the perturbative Einstein equation. Finally we discuss how to generalise the results to curved backgrounds and incorporate additional matter.

Abstract We construct off-shell recursion relations for arbitrary loop-level scattering amplitudes beyond the conventional tree-level recursion relations for ϕ 4-theory and the Yang-Mills theory. We define a quantum perturbiner expansion that includes loop corrections from the quantum effective action formalism by identifying the external source. Our method clearly shows how the perturbiner expansion becomes an off-shell current generating function. Instead of using the classical equations of motion in the conventional perturbiner method, we exploit the Dyson-Schwinger equation to derive the quantum off-shell recursion relation to arbitrary order of loop-level scattering amplitudes. We solve the recursion relation and reproduce the results which agree up to one-loop six-point scattering amplitudes for ϕ 4-theory. Furthermore, we construct the recursions for computing loop-level correlation functions by replacing the choice of the external source.

Abstract We construct the off-shell recursion for gravity and the graviton current for the perturbative double field theory (DFT). We first formulate the perturbative DFT, which is equivalent but simpler to perturbative general relativity, to all-orders in fluctuations of generalised metric. The perturbative action and equations of motion (EoM) are derived to arbitrary order for pure gravity case. We then derive the graviton off-shell recursion, the gravity counterpart of the Berends-Giele recursion in Yang-Mills theory, through the so-called perturbiner method using the EoM of the perturbative DFT. We solve the recursion iteratively and obtain the graviton off-shell currents explicitly. We then discuss the classical double copy for the off-shell currents. We present the current KLT relation for gravity by extending the result proposed by Mizera and Skrzypek for the non-gravitational effective field theories. The relation represents graviton currents by squaring gluon currents with the KLT kernel up to gauge transformation and regular terms that do not have any pole. Finally we discuss the off-shell conservation of currents for nonlinear gauge choices.

Abstract We study the classical double copy for ungauged half-maximal supergravities using the Kaluza-Klein reduction of double field theory (DFT). We construct a general formula for the Kaluza-Klein (KK) reduction of the DFT Kerr-Schild ansatz. The KK reduction of the ansatz is highly nonlinear, but the associated equations of motion are linear. This linear structure implies that half-maximal supergravities admit a classical double copy. We show that their single copy is given by a pair of Maxwell-scalar theories, which are the KK reduction of a higher-dimensional single copy of DFT. We also investigate their T-duality transformations — both the Buscher rule and continuous O(D, D) rotations. Applying the Buscher rule to the Kerr BH, we obtain a solution with a nontrivial Kalb-Ramond field and dilaton. We also identify the single copy of Sen’s heterotic BH and the chiral null model and show that the chiral null model is self-dual under T-duality rotations.

Abstract We construct the classical double copy formalism for M-theory. This extends the current state of the art by including the three form potential of eleven dimensional supergravity along with the metric. The key for this extension is to construct a Kerr-Schild type Ansatz for exceptional field theory. This Kerr-Schild Ansatz then allows us to find the solutions of charged objects such as the membrane from a set of single copy fields. The exceptional field theory formalism then automatically produces the IIB Kerr-Schild ansatz allowing the construction of the single copy for the fields of IIB supergravity (with manifest SL(2) symmetry).

Abstract The classical double copy relates solutions to the equations of motion in gauge theory and in gravity. In this paper, we present two double-copy formalisms for relating the Coulomb solution in gauge theory to the two-parameter Janis-Newman-Winicour solution in gravity. The latter is a static, spherically symmetric, asymptotically fiat solution that generically includes a dilaton field, but also admits the Schwarzschild solution as a special case. We first present the classical double copy as a perturbative construction, similar to its formulation for scattering amplitudes, and then present it as an exact map, with a novel generalisation of the Kerr-Schild double copy motivated by double field theory. The latter formalism exhibits the relation between the Kerr-Schild classical double copy and the string theory origin of the double copy for scattering amplitudes.

This paper presents a application system using imperceptible metamer markers. The proposed system is based on metamer markers that are invisible to the human eye but visible to infrared (IR) cameras. The metamer means the indistinguishable colors with different spectrums. RGB cameras cannot capture the different spectrums of metamer markers, but IR cameras can detect the metamer markers printed under the color image. This paper describes how to create metamer markers using a ordinary color printer. First, uniformly select color samples from the RGB color space, analyze the visibility of RGB colors and metamer color printed by the printer, and then design a color mapping model between color printers to produce the effective metamer color. After confirming successful detection of a metamer marker under various infrared lightings and filters, the exact color differences were analyzed and the validity of the proposed method was clarified. To verify its applicability, a prototype of fairytale book was published and demonstrated as an AR-book. The metamer markers are expected to be very useful for AR applications, projector-camera systems, human-computer interaction systems, and so on.

A new type of interface using a conduction hot spot reflecting the user’s intention is presented. Conventional methods using fingertips to generate conduction hot points cannot be applied to those who have difficulty using their hands or cold hands. In order to overcome this problem, an exhaling interaction using a hollow rod is proposed and extensively analyzed in this paper. A preliminary study on exhaling interaction demonstrated the possibility of the method. This paper is an attempt to develop and extend the concept and provide the necessary information for properly implementing the interaction method. We have repeatedly performed conduction hot-point-generation experiments on various materials that can replace walls or screens to make wide use of the proposed interfaces. Furthermore, a lot of experiments have been conducted in different seasons, considering that the surface temperature of objects also changes depending on the season. Based on the results of an extensive amount of experiments, we provide key observations on important factors such as material, season, and user condition, which should be considered for realizing contactless exhaling interfaces.

Abstract We discuss the generalization of the Kerr-Schild (KS) formalism for general relativity and double field theory (DFT) to the heterotic DFT and supergravity. We first introduce a heterotic KS ansatz by introducing a pair of null O (d, d+G) generalized tangent vectors. The pair of null vectors are represented by a pair of d-dimensional vector fields, and one of the vector fields is not a null vector. This implies that the null property of the usual KS formalism, which plays a crucial role in linearizing the field equations, can be partially relaxed in a consistent way. We show that the equations of motion under the heterotic KS ansatz in a flat background can be reduced to linear equations. Using the heterotic KS equations, we establish the single and zeroth copy for heterotic supergravity and derive the Maxwell and Maxwell-scalar equations. This agrees with the KLT relation for heterotic string theory.

Abstract The Kerr-Schild (KS) formalism is a powerful tool for constructing exact solutions in general relativity. In this paper, we present a generalization of the conventional KS formalism to double field theory (DFT) and supergravities. We introduce a generalized KS ansatz for the generalized metric in terms of a pair of null vectors. Applying this ansatz to the equations of motion of DFT, we construct the generalized KS field equation. While the generalized KS equations are quadratic in the fields, we show that it is possible to find solutions by considering linear equations only. Furthermore, we construct a Killing spinor equation under the generalized KS ansatz. Based on this formalism, we show that the classical double copy structure, which represents solutions of the Einstein equation in terms of solutions of the Maxwell equation, can be extended to the entire massless string NS-NS sector. We propose a supersymmetric classical double copy which shows that solutions of the Killing spinor equation can be realized in terms of solutions of the BPS equation of the supersymmetric Maxwell theory.

We discuss a number of problems associated with the circle compactification of the bosonic tensile ambitwistor string with the asymmetric vacuum choice. By considering the spectrum and physical state conditions, we show that the circle radius plays a role as a tuning parameter which determines the low energy effective field theory. At the self dual point, we construct the current operators and compute OPEs between them. While the final outcome remains as yet inconclusive, several new results are obtained. Through the current algebra analysis we show that there is a subsector of the massless states where the gauge symmetry is enhanced to ISO(2)L×SU(2)R. Using the fact that the one loop partition function is not modular invariant, we show that tensile ambitwistor string partition function is exactly the same as a field theory partition function. Our result proves that despite the existence of winding modes, which is a typical characteristic of a string, the tensile ambitwistor string behaves as a point particle theory.

Erdheim-Chester disease (ECD) is a form of non-Langerhans cell histiocytosis that most commonly involves the skeletal system. We report an unusual case of ECD presenting as an anterior mediastinal tumor without skeletal involvement. A 60-year-old man with no remarkable medical history was referred for evaluation of a mediastinal mass. The patient underwent surgical excision of the tumor via video-assisted thoracoscopic surgery. Histologic examination revealed marked proliferation of atypical histiocytes with sclerosis, and the results of immunohistochemical staining were suggestive of ECD.

Abstract Quantization of closed string proceeds with a suitable choice of worldsheet vacuum. A priori, the vacuum may be chosen independently for left-moving and right-moving sectors. We construct ab initio quantized bosonic string theory with left-right asymmetric worldsheet vacuum and explore its consequences and implications. We critically examine the validity of new vacuum and carry out first-quantization using standard operator formalism. Remarkably, the string spectrum consists only of a finite number of degrees of freedom: string gravity (massless spin-two, Kalb-Ramond and dilaton fields) and two massive spin-two Fierz-Pauli fields. The massive spin-two fields have negative norm, opposite mass-squared, and provides a Lee-Wick type extension of string gravity. We compute two physical observables: tree-level scattering amplitudes and one-loop cosmological constant. Scattering amplitude of four dilatons is shown to be a rational function of kinematic invariants, and in D = 26 factorizes into contributions of massless spin-two and a pair of massive spin-two fields. The string one loop partition function is shown to perfectly agree with one loop Feynman diagram of string gravity and two massive spin-two fields. In particular, it does not exhibit modular invariance. We critically compare our construction with recent studies and contrast differences.

Abstract The (heterotic) double field theories and the exceptional field theories are manifestly duality covariant formulations, describing low-energy limit of various super-string and M-theory compactifications. These field theories are known to be reduced to the standard descriptions by introducing appropriately parameterized generalized metric and by applying suitably chosen section conditions. In this paper, we apply these formulations to non-geometric backgrounds. We introduce different parameterizations for the generalized metric in terms of the dual fields which are pertinent to non-geometric fluxes. Under certain simplifying assumptions, we construct new effective action for non-geometric backgrounds. We then study the non-geometric backgrounds sourced by exotic branes and find their U -duality monodromy matrices. The charge of exotic branes obtained from these monodromy matrices agrees with the charge obtained from the non-geometric flux integral.

Background: This study assessed the efficacy of pulmonary metastasectomy for synovial sarcoma in adult patients. Methods: Fifty patients, diagnosed with pulmonary metastasis from June 1990 to August 2010, were reviewed retrospectively. Twenty-eight patients underwent complete pulmonary metastasectomy, and their survival was evaluated. Age, sex, time to metastatic progression, laterality, number of tumors, size of largest nodule, and number of metastasectomies were analyzed as potential prognostic factors. Results: I n all, 2 9 patients underwent at least one pulmonary metastasectomy, and 51 resections were performed. One intraoperative mortality occurred, and the 5-year survival rate was 58.4%. Bilateral metastases and early metastatic progression were associated with poor survival in multivariate analyses. Conclusion: Surgical resection can be a good option for treating pulmonary metastasis in patients with synovial sarcoma. Repeated resection was feasible with low mortality and morbidity.

We show that it is possible to construct a well-defined effective field theory incorporating string winding modes without using strong constraint in double field theory. We show that X-ray (Radon) transform on a torus is well-suited for describing weakly constrained double fields, and any weakly constrained fields are represented as a sum of strongly constrained fields. Using inverse X-ray transform we define a novel binary operation which is compatible with the level matching constraint. Based on this formalism, we construct a consistent gauge transform and gauge invariant action without using strong constraint. We then discuss the relation of our result to the closed string field theory. Our construction suggests that there exists an effective field theory description for massless sector of closed string field theory on a torus in an associative truncation.

We investigate α′-corrections of heterotic double field theory up to quadratic order in the language of supersymmetric O(D,D+dim⁡G) gauged double field theory. After introducing double-vielbein formalism with a parametrization which reproduces heterotic supergravity, we show that supersymmetry for heterotic double field theory up to leading order α′-correction is obtained from supersymmetric gauged double field theory. We discuss the necessary modifications of the symmetries defined in supersymmetric gauged double field theory. Further, we construct supersymmetric completion at quadratic order in α′.