Bootstrap Method in Theoretical Physics

In the realm of contemporary physics, the bootstrap method is typically associated with an optimization-based approach to problem-solving. This method leverages our understanding of a specific physical problem, which is used as the constraints for the optimization problem, to carve out the allowed region of our physical theory. Notably, this method often yields not only precise numerical bounds for physical quantities but also offers theoretical insights into the nature of the problem at hand. The modern numerical bootstrap method has seen its greatest success in the fields of conformal field theory (via the conformal bootstrap) and Scattering amplitude (through the S-matrix bootstrap). This dissertation presents the application of the bootstrap method to matrix models (random matrices), Yang-Mills theory, and conformal field theory. We will commence with a review of the fundamental elements of these theories. Following this, we will delve into the bootstrap studies of these models.Comment: Zechuan Zheng's Ph.D. thesis, defended on September 15th at \'Ecole Normale Sup\'erieure (ENS), Pari

Numerical Conformal bootstrap with Analytic Functionals and Outer Approximation

This paper explores the numerical conformal bootstrap in general spacetime dimensions through the lens of a distinct category of analytic functionals, previously employed in two-dimensional studies. We extend the application of these functionals to a more comprehensive backdrop, demonstrating their adaptability and efficacy in general spacetime dimensions above two. The bootstrap is implemented using the outer approximation methodology, with computations conducted in double precision. The crux of our study lies in comparing the performance of this category of analytic functionals with conventional derivatives at crossing symmetric points. It is worth highlighting that in our study, we identified some novel kinks in the scalar channel during the maximization of the gap in two-dimensional conformal field theory. Our numerical analysis indicates that these analytic functionals offer a superior performance, thereby revealing a potential alternative paradigm in the application of conformal bootstrap.Comment: 59 pages, 16 tables and 12 figure

Analytic and Numerical Bootstrap for One-Matrix Model and "Unsolvable" Two-Matrix Model

We propose the relaxation bootstrap method for the numerical solution of multi-matrix models in the large $N$ limit, developing and improving the recent proposal of H.Lin. It gives rigorous inequalities on the single trace moments of the matrices up to a given "cutoff" order (length) of the moments. The method combines usual loop equations on the moments and the positivity constraint on the correlation matrix of the moments. We have a rigorous proof of applicability of this method in the case of the one-matrix model where the condition of positivity of the saddle point solution appears to be equivalent to the presence of supports of the eigenvalue distribution only on the real axis and only with positive weight. We demonstrate the numerical efficiency of our method by solving the analytically "unsolvable" two-matrix model with $\mathrm{tr}[A,B]^2$ interaction and quartic potentials, even for solutions with spontaneously broken discrete symmetry. The region of values for computed moments allowed by inequalities quickly shrinks with the increase of the cutoff, allowing the precision of about 6 digits for generic values of couplings in the case of $\mathbb{Z}_2$ symmetric solutions. Our numerical data are checked against the known analytic results for particular values of parameters.Comment: 60 pages, 15 figure

Bounding 3d CFT correlators

We consider the problem of bounding CFT correlators on the Euclidean section. By reformulating the question as an optimization problem, we construct functionals numerically which determine upper and lower bounds on correlators under several circumstances. A useful outcome of our analysis is that the gap maximization bootstrap problem can be reproduced by a numerically easier optimization problem. We find that the 3d Ising spin correlator takes the minimal possible allowed values on the Euclidean section. Turning to the maximization problem we find that for d > 2 there are gap-independent maximal bounds on CFT correlators. Under certain conditions we show that the maximizing correlator is given by the generalized free boson for general Euclidean kinematics. In our explorations we also uncover an intriguing 3d CFT which saturates gap, OPE maximization and correlator value bounds. Finally we comment on the relation between our functionals and the Polyakov bootstrap.Comment: 34 pages, 14 figure

Co-infusion of haplo-identical CD19-chimeric antigen receptor T cells and stem cells achieved full donor engraftment in refractory acute lymphoblastic leukemia

Abstract Background Elderly patients with relapsed and refractory acute lymphoblastic leukemia (ALL) have poor prognosis. Autologous CD19 chimeric antigen receptor-modified T (CAR-T) cells have potentials to cure patients with B cell ALL; however, safety and efficacy of allogeneic CD19 CAR-T cells are still undetermined. Case presentation We treated a 71-year-old female with relapsed and refractory ALL who received co-infusion of haplo-identical donor-derived CD19-directed CAR-T cells and mobilized peripheral blood stem cells (PBSC) following induction chemotherapy. Undetectable minimal residual disease by flow cytometry was achieved, and full donor cell engraftment was established. The transient release of cytokines and mild fever were detected. Significantly elevated serum lactate dehydrogenase, alanine transaminase, bilirubin and glutamic-oxalacetic transaminase were observed from days 14 to 18, all of which were reversible after immunosuppressive therapy. Conclusions Our preliminary results suggest that co-infusion of haplo-identical donor-derived CAR-T cells and mobilized PBSCs may induce full donor engraftment in relapsed and refractory ALL including elderly patients, but complications related to donor cell infusions should still be cautioned. Trial registration Allogeneic CART-19 for Elderly Relapsed/Refractory CD19+ ALL. NCT0279955

Bootstrap for Lattice Yang-Mills theory

We study the $SU(\infty)$ lattice Yang-Mills theory at the dimensions $D=2,3,4$ via the numerical bootstrap method. It combines the Makeenko-Migdal loop equations, with a cut-off $L_{\mathrm{max}}$ on the maximal length of loops, and positivity conditions on certain matrices of Wilson loops. Our algorithm is inspired by the pioneering paper of P.Anderson and M.Kruczenski but it is significantly more efficient, as it takes into account the symmetries of the lattice theory and uses the relaxation procedure in line with our previous work on matrix bootstrap. We thus obtain rigorous upper and lower bounds on the plaquette average at various couplings and dimensions. For $D=4$, the lower bound data appear to be close to the MC data in the strong coupling phase and the upper bound data in the weak coupling phase reproduce well the 3-loop perturbation theory. Our results suggest that this bootstrap approach can provide a tangible alternative to the, so far uncontested, Monte Carlo approach.Comment: 7 pages, 6 figures, and 2 table

Bounding scattering of charged particles in 1+11+1 dimensions

We obtain general bounds on scattering processes involving charged particles in 1+1 spacetime dimensions. After a general analysis we derive mostly numerical bounds on couplings in theories with $O(N)$ and $U(N)$ global symmetries. The bounds are consistently saturated by $S$-matrices without particle production, and in many cases by known integrable $S$-matrices. Our work provides a blueprint for a similar analysis in higher dimensions

Biodegradable ZnLiCa ternary alloys for critical-sized bone defect regeneration at load-bearing sites: In vitro and in vivo studies

A novel biodegradable metal system, ZnLiCa ternary alloys, were systematically investigated both in vitro and in vivo. The ultimate tensile strength (UTS) of Zn0.8Li0.1Ca alloy reached 567.60 ± 9.56 MPa, which is comparable to pure Ti, one of the most common material used in orthopedics. The elongation of Zn0.8Li0.1Ca is 27.82 ± 18.35%, which is the highest among the ZnLiCa alloys. The in vitro degradation rate of Zn0.8Li0.1Ca alloy in simulated body fluid (SBF) showed significant acceleration than that of pure Zn. CCK-8 tests and hemocompatibility tests manifested that ZnLiCa alloys exhibit good biocompatibility. Real-time PCR showed that Zn0.8Li0.1Ca alloy successfully stimulated the expressions of osteogenesis-related genes (ALP, COL-1, OCN and Runx-2), especially the OCN. An in vivo implantation was conducted in the radius of New Zealand rabbits for 24 weeks, aiming to treat the bone defects. The Micro-CT and histological evaluations proved that the regeneration of bone defect was faster within the Zn0.8Li0.1Ca alloy scaffold than the pure Ti scaffold. Zn0.8Li0.1Ca alloy showed great potential to be applied in orthopedics, especially in the load-bearing sites

Biodegradable Zn–Sr alloy for bone regeneration in rat femoral condyle defect model: In vitro and in vivo studies

Bone defects are commonly caused by severe trauma, malignant tumors, or congenital diseases and remain among the toughest clinical problems faced by orthopedic surgeons, especially when of critical size. Biodegradable zinc-based metals have recently gained popularity for their desirable biocompatibility, suitable degradation rate, and favorable osteogenesis-promoting properties. The biphasic activity of Sr promotes osteogenesis and inhibits osteoclastogenesis, which imparts Zn–Sr alloys with the ideal theoretical osteogenic properties. Herein, a biodegradable Zn–Sr binary alloy system was fabricated. The cytocompatibility and osteogenesis of the Zn–Sr alloys were significantly better than those of pure Zn in MC3T3-E1 cells. RNA-sequencing illustrated that the Zn-0.8Sr alloy promoted osteogenesis by activating the wnt/β-catenin, PI3K/Akt, and MAPK/Erk signaling pathways. Furthermore, rat femoral condyle defects were repaired using Zn-0.8Sr alloy scaffolds, with pure Ti as a control. The scaffold-bone integration and bone ingrowth confirmed the favorable in vivo repair properties of the Zn–Sr alloy, which was verified to offer satisfactory biosafety based on the hematoxylin-eosin (H&E) staining and ion concentration testing of important organs. The Zn-0.8Sr alloy was identified as an ideal bone repair material candidate, especially for application in critical-sized defects on load-bearing sites due to its favorable biocompatibility and osteogenic properties in vitro and in vivo