Conformal Field Research Articles

A new characterization of the Euclidean sphere.

In this paper, we obtain a new characterization of the Euclidean sphere as a compact Riemannian manifold with constant scalar curvature carrying a nontrivial conformal vector field which is also conformal Ricci vector field.

Scattering of conformal higher spin fields

We develop a formalism for describing the most general notion of tree-level scattering amplitudes in 4d conformal higher spin theory. As conformal higher spin fields obey higher-derivative equations of motion, there are many distinct on-shell external states which may contribute to their scattering, some of which grow polynomially with time, leading to ill-defined amplitudes. We characterize the set of admissible scattering states which produce finite tree amplitudes, noting that there are more such states than just standard massless higher spins obeying two-derivative equations of motion. We use conformal gravity as a prime example, where the set of scattering states includes the usual Einstein graviton and a ‘ghost’ massless spin 1 particle. An extension of the usual spinor helicity formalism allows us to encode these scattering states efficiently in terms of ‘twistor-spinors’. This leads to compact momentum space expressions for all finite tree-level 3-point amplitudes of conformal higher spin theory. While some of these 3-point amplitudes vanish (including all those with only standard two-derivative higher spin external states), there are many others which are non-vanishing. We also comment on the generalization to scattering of conformal higher spins in AdS4.

On the geometry of conformal vector fields

On the geometry of conformal vector fields

(OA04) Patterns of Failure After Postoperative Radiation Therapy for Locally Advanced NSCLC: Implications for Shifting Toward More Conformal Radiation Fields

Over the past decade, postoperative radiation therapy (PORT) volumes in locally advanced NSCLC have largely shifted from whole mediastinum to conformal fields as specified in the phase III Lung Adjuvant Radiotherapy Trial (Lung ART) trial. However, limited data is available on how this transition will affect locoregional recurrence rates (LRR) and overall survival (OS). We thus compared patterns of failure, survival outcomes, and toxicity with whole mediastinum (WM) radiation therapy vs. high-risk (HR) conformal fields in the postoperative setting. In this retrospective analysis, we identified the records of 200 consecutive patients with pT1-4 N1-2 NSCLC who were treated with PORT between July 1998 and November 2014. Medical records were reviewed for demographic, tumor- and treatment-specific, and outcome data. Patients underwent surgical resection with wedge resection (n=24, 12%), lobectomy (n=148, 74%), or pneumonectomy (n=28, 14%). The predominant T and N-stage was pT2 (n = 92, 46%) and pN2 (n = 159, 79.5%). PORT was delivered to a median dose of 50 Gy in 25 fractions, and patients were stratified into two groups according to PORT field size: WM (n=130, 65%) or HR (n=70, 35%) nodal regions (involved or involved plus adjacent regions). The most common treatment modality in the WM group was 2D (n=56, 43%) whereas IMRT (n=31, 41%) was utilized most frequently in the HR group. LRR was defined as failure in either the: a) bronchial stump/anastomosis, b) treated hilum, or c) mediastinum (levels 2-9) or supraclavicular region, treated or untreated. Patients with prior distant metastatic failure were censored at that time and were not defined as having LRR. The Kaplan-Meier method was used to calculate locoregional recurrence-free (LRRFS) and OS from the end of PORT. Comparisons between patient and treatment characteristics were made using log-rank tests. Univariate and multivariable analyses were calculated using Cox proportional hazards modeling. Median follow-up among patients treated with HR fields was 40.1 months (range, <1 month-167.2 months) and for WM patients was 33.6 months (range, <1 month-199.3 months). Median OS and LRRFS were not significant between groups but trended toward improvement with HR (48.6 months for HR and 28.3 months for WM and, p=0.11; 39.1 months for HR vs. 23.0 months for WM, p=0.20, respectively). However, on multivariable analysis, field size was not associated with significant differences in LRR, LRRFS, or OS (p=0.484, 0.146, and 0.196). Grade ≥2 toxicity was lower in the HR group (OR 0.32 [95% CI 0.14-0.77], p=0.010) and higher in patients who received concurrent chemotherapy (OR 5.45 [95% CI 1.55-19.19], p=0.008). Despite transitioning to more limited fields for PORT, LRRPFS and OS were not compromised. Toxicity was lower in patients treated with HR fields. This data supports the use of more conformal fields as per Lung ART in the setting of PORT.

Concircular vector fields on Lorentzian manifold of Bianchi type-I spacetimes

Our aim in this paper is to obtain concircular vector fields (CVFs) on the Lorentzian manifold of Bianchi type-I spacetimes. For this purpose, two different sets of coupled partial differential equations comprising ten equations each are obtained. The first ten equations, known as conformal Killing equations are solved completely and components of conformal Killing vector fields (CKVFs) are obtained in different possible cases. These CKVFs are then substituted into second set of ten differential equations to obtain CVFs. It comes out that Bianchi type-I spacetimes admit four-, five-, six-, seven- or 15-dimensional CVFs for particular choices of the metric functions. In many cases, the CKVFs of a particular metric are same as CVFs while there exists few cases where proper CKVFs are not CVFs.

Möbius Moduli for Fingerprint Orientation Fields

We propose a novel fingerprint descriptor, namely Mobius moduli, measuring local deviation of orientation fields (OF) of fingerprints from conformal fields, and we propose a method to robustly measure them, based on tetraquadrilaterals to approximate a conformal modulus locally with one due to a Mobius transformation. Conformal fields arise by the approximation of fingerprint OFs given by zero-pole models, which are determined by the singular points and a rotation. This approximation is very coarse, e.g., for fingerprints with no singular points (arch type), the zero-pole model’s OF has parallel lines. Quadratic differential (QD) models, which are obtained from zero-pole models by adding suitable singularities outside the observation window, approximate real fingerprints much better. For example, for arch type fingerprints, parallel lines along the distal joint change slowly into circular lines around the nail furrow. Still, QD models are not fully realistic because, for example along the central axis of arch type fingerprints, ridge line curvatures usually first increase and then decrease again. It is impossible to model this with QDs, which, due to complex analyticity, also produce conformal fields only. In fact, as one of many applications of the new descriptor, we show, using histograms of curvatures and conformality indices (log of the absolute values of the Mobius moduli), that local deviation from conformality in fingerprints occurs systematically at high curvature which is not reflected by state-of-the-art fingerprint models as are used, for instance, in the well-known synthetic fingerprint generation tool SFinGe and these differences robustly discriminate real prints from SFinGe’s synthetic prints.

54. Stereotactic plans quality assurance with Delta 4PT phantom

Introduction As treatment plans of intra and extracranial stereotactic radiotherapy do not benefit in vivo dosimetry, it is a common practice to perform a pretreatment quality control of the dose calculated by the treatment planning system (TPS). In the midst of the different solutions proposed in terms of detectors, we wanted to evaluate the performances of the Delta 4PT (Scandidos) phantom for the measurement of dynamic conformal arctherapy fields. We were then able to define evaluation criteria which proved to be suitable for the whole range of field dimensions in stereotactic radiotherapy (fields of 10 × 10 mm and more). Methods At the Jean PERRIN center, stereotactic radiotherapy treatment plans are mainly calculated with the iPlan TPS from Brainlab (v4.5). A dedicated module, “Phantom Mapping 4.5.4”, allows to calculate the plan on the Delta 4PT phantom CT image. The treatments were then delivered by a Novalis TrueBeam STX linear accelerator (Varian) for 6 MV photon beams in FFF (Flattening Filter Free) mode. The Delta 4PT used for the measurement is a cylindrical PMMA phantom containing 2 planes of orthogonal p-Si detectors. These very small volume detectors are spaced 5 mm apart on a surface of 6 × 6 cm in the center then every 10 mm on the perimeter. The Delta 4PT has been previously calibrated for energy 6 FFF to take into account the energy response. We also took advantage of the “High Resolution” option of the Delta 4PT phantom to double the longitudinal resolution (2.5 mm). Several sets of parameters were tested for the studied treatment plans. For the analysis, we choosed four parameters: the gamma score, the mean gamma, the number of detectors taken into account in the statistics and the median dose. A comparison with the results obtained by VARIAN’s Portal Dose Image Prediction (PDIP) solution was also carried out to indicate the limits of these two pretreatment control methods. Results Statistical and rational analyzes show that an optimal parameter set makes it possible to verify that the Delta 4PT can be used for all types of dynamic conformal arctherapy treatment plans. Initial results show that the absolute dose measured with The Delta 4PT is correct with an average median dose of −0.4% and a standard deviation of 0.75%. The gamma score (2%/2 mm) systematically passes the criteria of the 95% of points having a gamma of less than 1. Moreover, the results obtained for the PDIP are similar. Conclusions A threshold of 30% with a 2%/2 mm criteria on the local gamma seems to be a good compromise for all field sizes. The physical and dosimetric characteristics of the Delta 4PT phantom allow it to be integrated into a quality assurance plan, whether in classic VMAT or stereotactic radiotherapy.

Abstract ID: 108 Study on conformal proton therapy using multileaf collimated beams without tumour-specific range compensators via flat dose-layer stacking

Purpose In traditional conformal proton therapy (CPT), proximal dose conformity of tumours is sacrificed for achieving distal dose conformity due to tumour-specific range compensators. This study investigated whether CPT can be realized without tumour-specific range compensators using multileaf-collimated proton beams, and whether range-compensator-free CPT (RCF-CPT) can improve the proximal dose conformity without sacrificing distal conformity. Methods First, geometric configurations of a virtual multileaf-collimator (MLC) and three tumour cases (brain, liver, and prostate) were adopted during Geant4 geometry setup. Second, conformal proton radiation fields were generated for tumour CT slices based on the predesigned MLC using Geant4. Third, flat dose-layers corresponding to these tumour slices were produced using dose patching method in which MLC-collimated subbeams can be utilized to modulate the dose uniformity of these flat dose-layers. Forth, these flat dose-layers were stacked and integrated throughout the tumours for obtaining sufficient tumour dose coverages. Furthermore, dosimetric comparisons between the RCF-CPT and traditional CPT were performed to detail the dosimetric advantages of RCF-CPT. Results For the three tumour cases, the tumours can be sufficiently covered by 95% relative doses through RCF-CPT, and the maximum tumour doses were smaller than 110% relative doses. Approximately, the proximal doses of RCF-CPT were controlled to 60% relative doses, and 95% dose lines fit with the tumour profiles at proximal tumour regions. Conclusions Compared with traditional CPT, RCF-CPT can highly enhance the proximal dose conformity of tumours without sacrificing distal conformity. Moreover, the workflows of CPT can be largely simplified based on the range-compensator-free characteristic of RCF-CPT.

Bernstein type results for complete spacelike hypersurfaces immersed in a weighted conformally stationary spacetime

In this paper, we deal with complete noncompact spacelike hypersurfaces immersed in a weighted conformally stationary spacetime endowed with a closed conformal timelike vector field [Formula: see text]. Under suitable constraints on the weighted mean curvature of such a spacelike hypersurface, we establish sufficient conditions to ensure that it must be an integral leaf of the foliation orthogonal to [Formula: see text].

On the Kerr-AdS/CFT correspondence

We review the relation between four-dimensional global conformal blocks and field propagation in AdS5. Following the standard argument that marginal perturbations should backreact in the geometry, we turn to the study of scalar fields in the generic Kerr-AdS5 geometry. On one hand, the result for scattering coefficients can be obtained exactly using the isomonodromy technique, giving exact expressions in terms of c = 1 chiral conformal blocks. On the other hand, one can use the analogy between the scalar field equations to the Level 2 null field Ward identity in two dimensional Liouville field theory to write approximate expressions for the same coefficients in terms of semi-classical chiral Liouville conformal blocks. Surprisingly, the conformal block thus constructed has a well-behaved interpretation in terms of Liouville vertex operators.

{{SO(d,1)}}-Invariant Yang\u2013Baxter Operators and the dS/CFT Correspondence

We propose a model for the dS/CFT correspondence. The model is constructed in terms of a “Yang–Baxter operator” R for unitary representations of the de Sitter group {SO(d,1)}. This R-operator is shown to satisfy the Yang–Baxter equation, unitarity, as well as certain analyticity relations, including in particular a crossing symmetry. With the aid of this operator we construct: (a) a chiral (light-ray) conformal quantum field theory whose internal degrees of freedom transform under the given unitary representation of {SO(d,1)}. By analogy with the O(N) non-linear sigma model, this chiral CFT can be viewed as propagating in a de Sitter spacetime. (b) A (non-unitary) Euclidean conformal quantum field theory on {mathbb{R}^{d-1}}, where SO(d, 1) now acts by conformal transformations in (Euclidean) spacetime. These two theories can be viewed as dual to each other if we interpret {mathbb{R}^{d-1}} as conformal infinity of de Sitter spacetime. Our constructions use semi-local generator fields defined in terms of R and abstract methods from operator algebras.

Conformal vector fields on submanifolds of a Euclidean space

Conformal vector fields on submanifolds of a Euclidean space

F-stability of spacelike hypersurfaces in weighted spacetimes

We establish the notions of f-stability and strong f-stability concerning closed spacelike hypersurfaces immersed with constant f-mean curvature in a conformally stationary spacetime endowed with a conformal timelike vector field V and a weight function f. When V is closed, with the aid of the f-Laplacian of a suitable support function, we characterize f-stable closed spacelike hypersurfaces through the analysis of the first eigenvalue of the Jacobi operator associated to the corresponding variational problem. Furthermore, we obtain sufficient conditions which assure that a strongly f-stable closed spacelike hypersurface must be either f-maximal or isometric to a leaf orthogonal to V.

Intrinsic conformal symmetries in Szekeres models

We show that Spatially Inhomogeneous (SI) and Irrotational dust models admit a six-dimensional algebra of Intrinsic Conformal Vector Fields (ICVFs) [Formula: see text] satisfying [Formula: see text], where [Formula: see text] is the associated metric of the two-dimensional distribution [Formula: see text] normal to the fluid velocity [Formula: see text] and the radial unit space-like vector field [Formula: see text]. The Intrinsic Conformal (IC) algebra is determined for each of the curvature value [Formula: see text] that characterizes the structure of the screen space [Formula: see text]. In addition the conformal flatness of the hypersurfaces [Formula: see text] indicates the existence of a ten-dimensional algebra of ICVFs of the three-dimensional metric [Formula: see text]. We illustrate this expectation and propose a method to derive them by giving explicitly the seven proper ICVFs of the Lemaître–Tolman–Bondi (LTB) model which represents the simplest subclass within the Szekeres family.

Trace anomaly and invariance under transformation of units

Paying attention to conformal invariance as the invariance under local transformations of units of measure, we take a conformal invariant quantum field as a quantum matter theory in which one has the freedom to choose the values of units of mass, length and time arbitrarily at each point. To be able to have this view, it is necessary that the background on which the quantum field is based be conformal invariant as well. Consequently, defining the unambiguous expectation value of the energy-momentum tensor of such a quantum field through the Wald renormalizing prescription necessitates breaking down the conformal symmetry of the background. Then, noticing the field equations suitable for describing the back-reaction effect, we show that the existence of trace anomaly, known for indicating the brokenness of conformal symmetry in quantum field theory, can also indicate the above gravitational conformal symmetry brokenness

The Schouten tensor as a connection in the unfolding of 3D conformal higher-spin fields

A first-order differential equation is provided for a one-form, spin-s connection valued in the two-row, width-(s − 1) Young tableau of GL(5). The connection is glued to a zero-form identified with the spin-s Cotton tensor. The usual zero-Cotton equation for a symmetric, conformal spin-s tensor gauge field in 3D is the flatness condition for the sum of the GL(5) spin-s and background connections. This presentation of the equations allows to reformulate in a compact way the cohomological problem studied in arXiv:1511.07389, featuring the spin-s Schouten tensor. We provide full computational details for spin 3 and 4 and present the general spin-s case in a compact way.

Pelvic Reirradiation for the Treatment of Locally Recurrent Rectal Cancer

This study aims to summarize the literature on pelvic reirradiation for the treatment of locally recurrent rectal cancer. Symptom palliation, rates of local progression after reirradiation with or without surgery, overall survival, and toxicity outcomes are discussed. The majority of patients received total doses of 30–40 Gy given in 1.2 or 1.5 Gy twice-daily fractions. Treatment evolved over time to include more conformal fields. The overall rates of local control generally range from 25 to 70% and surgical salvage after reirradiation was performed in 20–79% of patients. Some studies suggest that patients treated with reirradiation may have a higher rate of a complete R0 resection, which is an important predictor of overall survival. Survival outcomes have improved over time along with increased use of reirradiation. Pelvic reirradiation can offer effective symptom palliation and be part of a curative salvage treatment strategy for locally recurrent rectal cancer.

On symmetries of generalized Robertson-Walker spacetimes and applications

ABSTRACTThe purpose of the present article is to study and characterize several types of symmetries of generalized Robertson-Walker spacetimes. Conformal vector fields, curvature and Ricci collineations are studied. Many implications for existence of these symmetries on generalized Robertson-Walker spacetimes are obtained. Finally, Ricci solitons on generalized Robertson-Walker spacetimes admitting conformal vector fields are investigated.

The Bekenstein-Hawking Corpuscular Cascading from the Back-Reacted Black Hole

Exciting peculiarities of Planck-scale physics have immediate effects on the Bekenstein-Hawking radiation emitted from black holes (BHs). In this paper, using the tunneling formalism, we determine the Bekenstein-Hawking temperature for the vector particles from a back-reacted black hole (BBH) constructed from a conformal scalar field surrounded by a BTZ (Banados-Teitelboim-Zanelli) BH. Then, under the effect of the generalized uncertainty principle, we extend our calculations for scalar particles to understand the effects of quantum gravity. Then, we calculate an evaporation time for the BBH, the total number of Bekenstein-Hawking particles, and the quantum corrections of the number. We observe that remnants of the BH evaporation occur and that they affect the Bekenstein-Hawking temperature of the BBH as well as the total number of Bekenstein-Hawking particles.

Iterating free-field AdS/CFT: higher spin partition function relations

We find a simple relation between a free higher spin partition function on the thermal quotient of and the partition function of the associated d-dimensional conformal higher spin field defined on the thermal quotient of . Starting with a conformal higher spin field defined in , one may also associate to with another conformal field in dimensions, thus iterating AdS/CFT. We observe that in the case of , this iteration leads to a trivial 3d higher spin conformal theory with parity-even non-local action: it describes a zero total number of dynamical degrees of freedom and the corresponding partition function is equal to 1.