Nonperturbative Methods for Quantum Field Theory: Holographic Wilson Loops and S-Matrix Bootstrap

In this thesis, we explore nonperturbative methods of quantum field theory through two topics: holographic Wilson loops and S-matrix bootstrap. In the first part, we study the holographic calculation of Wilson loops using Ad-S/CFT correspondence, which is a duality between a string theory in AdS space and a gauge theory living on the conformal boundary of the AdS space. Under this duality, the expectation value of the Wilson loop operator in the gauge theory at strong t’Hooft coupling limit is given by the area of a string worldsheet ending on a boundary curve defined by the shape of the Wilson loop. We exploit the conformal symmetry and integrability properties of this problem and study the equivalent problem of finding the conformal reparametrization of a boundary curve. In (Euclidean) AdS3, we find analytic solutions in terms of Mathieu functions and implement numerical procedures for finding the conformal reparametrization in general. We also generalize the formalism to higher dimensional case and identify conformal invariants of the boundary curve which provide boundary conditions for the Pohlmeyer reduction of the string sigma model. In the second part, we study the S-matrix bootstrap program. In particular, we consider generic S-matrices in 2d relativistic quantum field theory with O(N) global symmetry and under crossing, real analyticity and unitarity constraints. We search for a maximization problem with these constraints that defines the 2dO(N) nonlinear sigma model which is an integrable theory. We find that the defining feature of this theory is that it resides at a vertex of the convex space defined by the constraints. Our numerical results reproduce the exact analytic S-matrix without assuming integrability

Bootstrapping gauge theories

We consider asymptotically free gauge theories with gauge group $SU(N_c)$ and $N_f$ quarks with mass $m_q\ll \Lambda_{\text{QCD}}$ that undergo chiral symmetry breaking and confinement. We propose a bootstrap method to compute the S-matrix of the pseudo-Goldstone bosons (pions) that dominate the low energy physics. For the important case of $N_c=3$, $N_f=2$, a numerical implementation of the method gives the phase shifts of the $S0$, $P1$ and $S2$ waves in good agreement with experimental results. The method incorporates gauge theory information ($N_c$, $N_f$, $m_q$, $\Lambda_{\text{QCD}}$) by using the form-factor bootstrap recently proposed by Karateev, Kuhn and Penedones together with a finite energy version of the SVZ sum rules. This requires, in addition, the values of the quark and gluon condensates. At low energy we impose constraints from chiral symmetry breaking which additionally require knowing the pion mass $m_\pi$.Comment: 39 pages, 10 figure

Interpretable Graph Anomaly Detection using Gradient Attention Maps

Detecting unusual patterns in graph data is a crucial task in data mining. However, existing methods often face challenges in consistently achieving satisfactory performance and lack interpretability, which hinders our understanding of anomaly detection decisions. In this paper, we propose a novel approach to graph anomaly detection that leverages the power of interpretability to enhance performance. Specifically, our method extracts an attention map derived from gradients of graph neural networks, which serves as a basis for scoring anomalies. In addition, we conduct theoretical analysis using synthetic data to validate our method and gain insights into its decision-making process. To demonstrate the effectiveness of our method, we extensively evaluate our approach against state-of-the-art graph anomaly detection techniques. The results consistently demonstrate the superior performance of our method compared to the baselines

Market-based Financing Reforms and Shareholder Valuations: Event Study Evidence from the Chinese Science and Technology Innovation Board

This paper studies the impact of the newly introduced science and technology innovation board (STIB) on stock valuations in China. This Nasdaq-style board features a market-based IPO system that contrasts with the current approved-based arrangement. Event study approach shows that A-share firms pertaining to STIB related industries increased significantly after the reform announcement. The effect is stronger for Non-SOEs and firms with higher R&D capacity. Public shareholders of the firms filing STIB IPO applications experienced salient growth in their abnormal returns while their industry competitors suffered price drops. Financial analysts also broadened their company coverages in STIB related industries and revised their market valuation forecasts positively in line with the market investors