Derivative Expansion Research Articles

Q-state Potts model from the nonperturbative renormalization group.

We study the q-state Potts model for q and the space dimension d arbitrary real numbers using the derivative expansion of the nonperturbative renormalization group at its leading order, the local potential approximation (LPA and LPA^{'}). We determine the curve q_{c}(d) separating the first [q>q_{c}(d)] and second [q<q_{c}(d)] -order phase transition regions for 2.8<d≤4. At small ε=4-d and δ=q-2 the calculation is performed in a double expansion in these parameters, and we find q_{c}(d)=2+aε^{2} with a≃0.1. For finite values of ε and δ, we obtain this curve by integrating the LPA and LPA^{'} flow equations. We find that q_{c}(d=3)=2.11(7), which confirms that the transition is of first order in d=3 for the three-state Potts model.

Non-perturbative SQED beta function using the functional renormalization group approach and the NSVZ exact beta function

Abstract The renormalization group equations of massive $\mathcal {N}=1$ supersymmetric quantum electrodynamics are studied using the functional renormalization group approach. A non-perturbative form of the beta function has been computed via a derivative expansion of the effective action. In the local potential approximation, the functional form of the non-perturbative beta function is closely related to the form of the Novikov–Shifman–Vainshtein–Zakharov (NSVZ) exact beta function; this relationship is exact if an effective fine-structure constant is defined. The non-massive limit of the same is also analyzed. Furthermore, the calculation of the beta function has been improved by incorporating the influence of momentum modes on the propagation of the superfields in the non-perturbative running of the electric charge, applying a second-order truncation for the derivative expansion, which we use to find the momentum contributions to the β function. Again, we find the NSVZ relation for an effective fine-structure constant. It is with sadness that I say goodbye to my professor, Iván Schmidt Andrade, who left us during the course of this work. His passion for research and his special vision of physics work will remain with us. Thank you for everything.

The universal one-loop effective action with gravity

We complete the so-called Universal One-Loop Effective Action (UOLEA) with effects of gravity and provide a systematic approach to incorporate higher dimensional operators in curved spacetime. The functional determinant stemming from the path integral is computed using the Covariant Derivative Expansion (CDE), in a momentum representation that does not rely on a specific choice of coordinate to be defined, as it often is. This efficient approach manifests an interesting novelty as it allows to integrate out chiral fermions in curved spacetime in a direct manner leading to new operators involving the curvature, and provides a new alternative to the use of Feynman diagrams in that regard. The method presented would very well fit in a code that performs CDE, offering the possibility to integrate out at one-loop fields on a curved spacetime background, including spin-2 fields, like the graviton. Eventually these results should provide an interesting way to study low energy effects of UV completions of gravity.

Nitrene C-H Bond Insertion Approach to Carbazolones and Indolones, and a Reactivity Departure for 7-Membered Analogues.

A modular platform for facile access to 1,2,3,9-tetrahydro-4H-carbazol-4-ones (H4 -carbazolones) and 3,4-dihydrocyclopenta[b]indol-1(2H)-ones (H2 -indolones) is described. The requisite 6- and 5-membered 2-arylcycloalkane-1,3-dione precursors were readily obtained through a Cu-catalyzed arylation of 1,3-cyclohexanediones or by a ring expansion of aryl succinoin derivatives. Enolization of one carbonyl group in the diones, conversion to a leaving group, and subsequent azidation gave 2-aryl-3-azidocycloalk-2-en-1-ones. This two-step, one-pot azidation is highly regioselective with unsymmetrically substituted 2-arylcyclohexane-1,3-diones. The regioselectivity, which is important for access to single isomers of 3,3-disubstituted carbazolones, was analyzed mechanistically and computationally. Finally, a Rh-catalyzed nitrene/nitrenoid insertion into the ortho C-H bond of the aryl moiety gave the H4 -carbazolones and H2 -indolones. One carbazolone was elaborated to an intermediate reported in the total synthesis of N-decarbomethoxychanofruticosinate, (-)-aspidospermidine, (+)-kopsihainanine A. With 2-phenylcycloheptane-1,3-dione, prepared from cyclohexanone and benzaldehyde, the azidation reaction was readily accomplished. However, the Rh-catalyzed reaction unexpectedly led to a labile but characterizable azirine rather than the indole derivative. Computations were performed to understand the differences in reactivities of the 5- and 6-membered 2-aryl-3-azidocycloalk-2-en-1-ones in comparison to the 7-membered analogue, and to support the structural assignment of the azirine.

Approach to the lower critical dimension of the φ^{4} theory in the derivative expansion of the functional renormalization group.

We revisit the approach to the lower critical dimension d_{lc} in the Ising-like φ^{4} theory within the functional renormalization group by studying the lowest approximation levels in the derivative expansion of the effective average action. Our goal is to assess how the latter, which provides a generic approximation scheme valid across dimensions and found to be accurate in d≥2, is able to capture the long-distance physics associated with the expected proliferation of localized excitations near d_{lc}. We show that the convergence of the fixed-point effective potential is nonuniform in the field when d→d_{lc} with the emergence of a boundary layer around the minimum of the potential. This allows us to make analytical predictions for the value of the lower critical dimension d_{lc} and for the behavior of the critical temperature as d→d_{lc}, which are both found in fair agreement with the known results. This confirms the versatility of the theoretical approach.

Risk Management Case Analysis of ICBC's "Crude Oil Treasure" Incident

Driven by the marketization of interest rates and technological innovation, commercial banks in China continue to innovate various financial services businesses and devote more attention to attracting customers to purchase various investment and wealth management products in order to expand sources of bank performance and gain more benefits. In 2018, paper crude oil-linked wealth management products emerged. Paper crude oil products are linked to the prices of international crude oil futures contracts. The products feature controllable risks and relatively high returns, which are very popular among large numbers of customers. However, despite the continuous expansion of China's financial derivatives trading volume, the categories of derivative products and regulation still have many limitations. The development of innovative paper crude oil-linked products is not perfect and has many potential risks, which are highly susceptible to market fluctuations. Taking China Bank's "Crude Oil Treasure" product as the research focus, this paper analyzes the massive loss incident that occurred in late April 2020 through case study analysis and qualitative analysis methods. It is divided into four parts. The introduction part explains the research background, significance, content, methods and innovations and inadequacies of this paper. The first part sorts out the background and process of the "Crude Oil Treasure" case at China Bank and elaborates on the operating principles of this product. The second part analyzes the "Crude Oil Treasure" case in detail. It first focuses on the problems in the product's trading liquidity, domestic and international time differences and product promotion. Then it focuses on the internal and external causes of the case, discussing external factors such as international crude oil market turmoil and futures trading characteristics, and internal factors such as product design, risk control and lack of experience. It also evaluates the hedging strategy, contract design and compliance of the "Crude Oil Treasure" product. The third part mainly analyzes the impacts of the "Crude Oil Treasure" rollover incident and China Bank's subsequent response measures. The fourth part puts forward certain countermeasures and suggestions from the perspectives of bank management, investors and regulatory agencies to prevent such incidents from recurring based on the case analysis.

Anomaly cancellation in effective field theories from the covariant derivative expansion

Anomaly cancellation in effective field theories from the covariant derivative expansion

Entropy current and fluid-gravity duality in Gauss-Bonnet theory

Working within the approximation of small amplitude expansion, recently an entropy current has been constructed on the horizons of dynamical black hole solution in any higher derivative theory of gravity. In this note, we have dualized this horizon entropy current to a boundary entropy current in an asymptotically AdS black hole metric with a dual description in terms of dynamical fluids living on the AdS boundary. This boundary entropy current is constructed using a set of mapping functions relating each point on the horizon to a point on the boundary. We have applied our construction to black holes in Einstein-Gauss-Bonnet theory. We have seen that up to the first order in derivative expansion, Gauss-Bonnet terms do not add any extra corrections to fluid entropy as expected. However, at the second order in derivative expansion, the boundary current will non-trivially depend on how we choose our horizon to boundary map, which need not be expressible entirely in terms of fluid variables. So generically, the boundary entropy current generated by dualizing the horizon current will not admit a fluid dynamical description.

Radiatively Induced Finite and (Un) Determined Chern-SimonsLike Terms

The problem of Chern-Simons-like term induction via quantum corrections in four-dimensions is investigated in two different cases. In the first case, we consider two distinct approaches to deal with the exact fermion propagator of the extended QED theory up to the first order in the b-coefficient. We find different results for distinct approaches in the same regularization scheme. In the second case, we show that when we use a modified derivative expansion method and another regularization scheme, we obtain a result that exactly coincides with one of the results obtained in the former case. This seems to imply an ambiguity absence as one treats the fermion propagator and the self-energy tensor properly

π0, η, η' → γγ Decays and the Explicit Chiral Symmetry Breaking

Corrections to the Wess–Zumino–Witten anomaly caused by the explicit breaking of the SU(3) times SU(3) chiral symmetry are studied using the effective meson Lagrangian based on the Nambu–Jona-Lasinio model with the simultaneous expansion in derivatives, current quark masses, and 1/Nc powers. The leading contribution and the first correction for the amplitudes of the π0, η, η' → γγ decays and the contact term in the eta {text{/}}eta {kern 1pt} ' to {{pi }^{ + }}{{pi }^{ - }}gamma amplitudes have been calculated. The results are compared with similar 1/Nc chiral perturbation calculations and existing experimental data.

Anomalies from the covariant derivative expansion

Anomalies from the covariant derivative expansion

Universal location of Yang-Lee edge singularity in classic O(N) universality classes

Employing the functional renormalization group approach at next-to-leading order of the derivative expansion, we refine our earlier findings for the location of the Yang-Lee edge singularity in classic O(N) universality classes. For the universality classes of interest to QCD, in three dimensions, we found $|z_c|/R_\chi^{1/\gamma} = 1.612(9),\ 1.597(3)$ for $N=2$, $4$ correspondingly. We also established $|z_c| = 2.04(8),\ 1.69(3)$ for $N=2$, $4$ albeit with greater systematic error.

Non-dissipative electrically driven fluids

Existing hydrodynamic models of charged fluids consider any external electric field acting on the fluid as either first order in the hydrodynamic derivative expansion and completely arbitrary or zeroth order but constrained by the fluid’s chemical potential. This is in tension with experiments on charged fluids, where the electric field is both zeroth order and completely arbitrary. In this work, we take the first step at resolving this conundrum by introducing a new class of hydrodynamic stationary states, including an arbitrary zeroth order electric field, upon which hydrodynamics can be built. We achieve this by first writing down the hydrostatic constitutive relations for a boost-agnostic charged fluid up to first order in derivatives. Then we introduce suitable energy and momentum relaxation terms to balance the influence of the electric field on the fluid. This analysis leads to a new hydrostatic constraint on the spatial fluid velocity, which can be used to define our class of states. This constraint generalizes to the realm of hydrodynamics a similar constraint on the velocity found in the Drude model of electronic transport. Our class of states exhibits non-trivial thermo-electric transport even at ideal order, since it hosts non-zero DC electric and heat currents. We derive the explicit form of the corresponding conductivities and show they depend non-linearly on the electric field.

Boost invariant spin hydrodynamics within the first order in derivative expansion

Boost-invariant equations of spin hydrodynamics confined to the first-order terms in gradients are numerically solved. The spin equation of state, relating the spin density tensor to the spin chemical potential, is consistently included in the first order. Depending on its form and the structure of the spin transport coefficients, we find solutions which are both stable and unstable within the considered evolution times of $10\text{ }\text{ }\mathrm{fm}/\mathrm{c}$. These findings are complementary to the recent identification of stable and unstable modes for perturbed uniform spin systems described by similar hydrodynamic frameworks.

Holographic entanglement entropy for relativistic hydrodynamic flows

We study the behaviour of holographic entanglement entropy (HEE) in near equilibrium thermal states which are macroscopically described by conformal relativistic hydrodynamic flows dual to dynamical black brane geometries. We compute HEE for strip-shaped subsystems in boundary dimensions d = 2, 3, 4, which provides us with general qualitative inferences on the interplay between fluid flows and entanglement dynamics. At first, we consider the zeroth order in hydrodynamic derivative expansion, holographically described by stationary boosted black branes. Working non-perturbatively in fluid velocity, we find that, as the fluid velocity approaches its relativistic upper limit, the UV regulated HEE exhibits a divergence at arbitrary temperature. Also, the holographic mutual information between two relatively close subsystems vanishes at some critical fluid velocity and remains zero beyond it. We then compute HEE in an excited state of the fluid in the presence of the sound mode. As a simplified setup, we first work with non-dissipative dynamics in d = 2, where the time evolution of HEE is studied in the presence of the sound mode and a propagating pressure pulse. In d = 4, working upto first order in derivative expansion, we find that dissipative sound modes produce an additional dynamical UV divergence which is subleading compared to the ‘area law divergence’. No such divergence is observed for dissipative sound mode in d = 3.

On the effective action for scalars in a general manifold to any loop order

Functional methods and a derivative expansion are employed for laying out a procedure to compute the effective action to any loop order, for scalar fields parametrising an arbitrary Riemannian manifold, while maintaining explicit field-space covariance. These results are of use in the characterization of effective field theories for electroweak symmetry breaking and extend a geometric perspective in field space beyond one loop.

Analytical propagation on relative motion of geostationary earth orbit satellites with orbital perturbations

AbstractAn accurate description of the relative motion of satellites is critical for space missions in the complex geostationary earth orbit space environment. Here, a new relative motion model is established considering major perturbations. To avoid the singularity of the classical orbital elements, a set of quasi‐non‐singular orbital elements are used to represent the relative motion states, which is further extended by considering the SRP coefficient difference. On the basis of existing classical model, an analytical model is derived by taking the Taylor expansion of the time derivative of the perturbation functions to the first order in the neighbourhood of the reference satellite, which contains the earth's oblateness perturbation, the third‐body perturbations and the solar radiation pressure perturbation. This method avoids solving the complex differential equations of relative motion directly and provides a general framework for including arbitrary perturbations into the model. The new model is verified in uncontrolled natural relative motion scenarios and position‐keeping control scenario, respectively. The results show that the proposed model has high accuracy and strong competitiveness.

Synthesis of Clausena Alkaloids Using Unique Ring Expansion of Dihydroisoquinolines and Their Cholinesterase Inhibitory Activity

AbstractA facile and direct synthetic entry to the carbon skeleton of Clausena alkaloids, the benzo[d]azocin-4-one, is reported featuring the ring expansion of 1-phenyldihydroisoquinoline derivatives initially triggered by oxazolone under environmentally benign conditions in a one-pot procedure. Functionalization of the eight-membered lactam framework provided a set of Clausena alkaloid derivatives. Some derivatives show a promising inhibition toward acetylcholinesterase and a better selectivity index than the previously used Alzheimer’s disease (AD) drug, tacrine, and the currently used AD drug, galantamine.

Abstract 156: An ascitic fluid-derived organoid platform for Hispanic ovarian cancer patients to capture heterogeneity and disparity

Abstract Introduction: Ovarian cancer (OC) is a fatal gynecological and heterogeneous disease usually diagnosed at stages after peritoneal seeding. Current medical intervention involves surgical removal of both ovaries and the uterus followed by chemotherapy. Thus, experimental models, established from primary tumor, may not mimic the real-time characteristics, heterogeneity, and disparity of OC after surgical debulking; a stage where OC survive and grow in peritoneal lavage fluid and form malignant ascites. Therefore, we present a protocol that enables efficient derivation and long-term expansion of ascites-derived organoids (AsO) culture to study their heterogeneity and disparity. Methods: Malignant ascites, fresh tumors and whole blood were obtained at the time of surgical debulking and drainage of ascites/pleural effusion under an approved IRB protocol; patients characteristic included ethnicity: Hispanic and pathology: Mucinous Adenocarcinoma, Serous Grade 3, Carcinosarcoma grade 3, FIGO Stage IIB/IIIC (N = 3; treatment naïve). Within four hours of collection, an aliquot of tumors/ascites were used, and the cellular components were collected and resuspended in Matrigel®/complete organoid culture media (60:40) that is supplemented with B-27 supplement, N-acetyl-cysteine, R-spondin 1, Noggin, Nicotamide, EGF, FGF 10, Forksolin, A8301, hydrocorticosone, Heregulin β-1, β-Estradiol, Y27632, and N2; 30,000 cells per well were seeded and grown for 10 days before passaging. RNA sequencing was performed on AsO and tumor-derived organoids (TuO), and that of whole tissues as controls. Single-cell RNA sequencing (scRNAseq) was performed on 1 million live cells collected from malignant ascites (N = 3 patients). Tissues and organoids were fixed and sectioned for H&amp;E, IHC, and IF staining. Results: At the time of submission of this abstract, we have established 6 organoid lines from 3 Hispanic OC patients, representing different subtypes of OC. AsO or TuO recapitulate histological and genomic features from which they were derived, illustrating interpatient heterogeneity. Organoids were positive for OC protein biomarkers, such as PAX8 and cytokeratin. AsO showed morphological variation between patient subtypes, mostly forming dense organoid structure. The scRNAseq data have been analyzed to understand the distinctive features of individual cells and subcellular heterogeneity. RNA sequencing data confirmed that AsO and TuO recapitulated the features of their tissue of origin, but also illustrated genomic and phenotypical differences between both organoid types. Conclusion: Our efforts to make Hispanic-centered AsO biobank faithfully recapitulates OC hallmarks and can be subjected to real-time drug screening against chemoresistant tumors, genetic manipulations and cancer disparity research by comparing the AsO of non-Hispanic Whites. Citation Format: Md Mynul Hassan, Riajul Wahab, Sheralyn Sanchez, Eugene P. Toy, Sireesha Y. Reddy, Sourav Roy, Taslim A. Al-Hilal. An ascitic fluid-derived organoid platform for Hispanic ovarian cancer patients to capture heterogeneity and disparity [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 156.

Computing first-passage times with the functional renormalisation group

We use Functional Renormalisation Group (FRG) techniques to analyse the behaviour of a spectator field, σ, during inflation that obeys an overdamped Langevin equation. We briefly review how a derivative expansion of the FRG can be used to obtain Effective Equations of Motion (EEOM) for the one- and two-point function and derive the EEOM for the three-point function. We show how to compute quantities like the amplitude of the power spectrum and the spectral tilt from the FRG. We do this explicitly for a potential with multiple barriers and show that in general many different potentials will give identical predictions for the spectral tilt suggesting that observations are agnostic to localised features in the potential. Finally we use the EEOM to compute first-passage time (FPT) quantities for the spectator field. The EEOM for the one- and two-point function are enough to accurately predict the average time taken 〈\U0001d4a9〉 to travel between two field values with a barrier in between and the variation in that time δ\U0001d4a9 2. It can also accurately resolve the full PDF for time taken ρ(\U0001d4a9), predicting the correct exponential tail. This suggests that an extension of this analysis to the inflaton can correctly capture the exponential tail that is expected in models producing Primordial Black Holes.