相关论文: Lining up a Positive Semi-Definite Six-Point Boots…

We work out all of the details required for implementation of the conformal bootstrap program applied to the four-point function of two scalars and two vectors in an abstract conformal field theory in arbitrary dimension. This includes a…

We study local operator insertions on 1/2-BPS line defects in ABJM theory. Specifically, we consider a class of four-point correlators in the CFT$_1$ with SU$(1, 1|3)$ superconformal symmetry defined on the 1/2-BPS Wilson line. The relevant…

We introduce SDPB: an open-source, parallelized, arbitrary-precision semidefinite program solver, designed for the conformal bootstrap. SDPB significantly outperforms less specialized solvers and should enable many new computations. As an…

We introduce a new domain for finding precise numerical invariants of programs by abstract interpretation. This domain, which consists of level sets of non-linear functions, generalizes the domain of linear "templates" introduced by Manna,…

We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…

Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…

We evaluated all two-loop conformal integrals of scalar half-BPS six-point functions in $\mathcal{N} = 4$ SYM restricted to a configuration where all points lie on a line. Moreover, we also computed some of these integrals in the…

The N = 2, 4 superconformal symmetry constraints in d = 4 for four point functions of chiral primary 1/2-BPS operators are derived. The operators are described by symmetric traceless tensors of the internal R-symmetry group. A substantial…

We introduce PyCFTBoot, a wrapper designed to reduce the barrier to entry in conformal bootstrap calculations that require semidefinite programming. Symengine and SDPB are used for the most intensive symbolic and numerical steps…

Three-dimensional theories with cubic symmetry are studied using the machinery of the numerical conformal bootstrap. Crossing symmetry and unitarity are imposed on a set of mixed correlators, and various aspects of the parameter space are…

We initiate the S-matrix bootstrap analysis of theories with non-invertible symmetries in (1+1) dimensions. Our previous work showed that crossing symmetry of S-matrices in such theories is modified, with modification characterized by the…

We study the two-point function of the stress-tensor multiplet of $\mathcal{N}=4$ SYM in the presence of a line defect. To be more precise, we focus on the single-trace operator of conformal dimension two that sits in the $20'$ irrep of the…

We develop an algebraic approach to the analytic bootstrap in CFTs. By acting with the Casimir operator on the crossing equation we map the problem of doing large spin sums to any desired order to the problem of solving a set of recursion…

Understanding the link between correlation functions (CFs) of local operators and measurable collider correlators has emerged as a new opportunity in the study of gauge theory dynamics at colliders. While in Conformal Field Theories (CFTs)…

We propose an algorithm for computing the projection of a symmetric second-order tensor onto the cone of negative semidefinite symmetric tensors with respect to the inner product defined by an assigned positive definite symmetric…

We present a semidefinite programming approach to bound the measures of cross-independent pairs in a bipartite graph. This can be viewed as a far-reaching extension of Hoffman's ratio bound on the independence number of a graph. As an…

We study the fixed point problem for a system of multivariate operators that are coordinate-wise monotone (i.e., nondecreasing or nonincreasing in each of the variables, independently), in the setting of quasi-ordered sets. We show that…

We present a dispersion relation for defect CFT that reconstructs two-point functions in the presence of a defect as an integral of a single discontinuity. The main virtue of this formula is that it streamlines explicit bootstrap…

The four point function of Conformal Field Theories (CFT's) with global symmetry gives rise to multiple crossing symmetry constraints. We explicitly study the correlator of four scalar operators transforming in the fundamental…

We study the ternary quadratic problem (TQP), a quadratic optimization problem with linear constraints where the variables take values in $\{0, \pm 1\}$. While semidefinite programming (SDP) techniques are well established for $\{0,1\}$-…