Related papers: Generalized monodromy method in gauge/gravity dual…
Motivated by the two-dimensional massive gravity description of $T\overline{T}$ deformations, we propose a direct generalization in $d$ dimensions. Our methodology indicates that all terms up to order $d$ are present in the deformation. In…
We study monodromy defects in $O(N)$ symmetric scalar field theories in $d$ dimensions. After a Weyl transformation, a monodromy defect may be described by placing the theory on $S^1\times H^{d-1}$, where $H^{d-1}$ is the hyperbolic space,…
We consider the monodromy problem for the four-punctured sphere in which the character of one composite monodromy is fixed, by looking at the expansion of the accessory parameter in the modulus $x$ directly, without taking the limit of the…
We use the numerical bootstrap to study conformal line defects with $O(2)$ global symmetry. Our results are very general and capture in particular conformal line defects originating from bulk CFTs with a continuous global symmetry, which…
We have classified special solutions around the origin for the two-dimensional degenerate Garnier system G(1112) with generic values of complex parameters, whose linear monodromy can be calculated explicitly.
In this paper, we develop and explore recursive methods to investigate the 2d CFT 5-point conformal block with a level 2 degenerate insertion, as well as its AGT dual, by solving the BPZ differential equation. First, we represent the…
We develop a monotone, two-scale discretization for a class of integrodifferential operators of order $2s$, $s \in (0,1)$. We apply it to develop numerical schemes, and derive pointwise convergence rates, for linear and obstacle problems…
We introduce a generalized forward-backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of maximally monotone operators and the normal cone to the nonempty set of zeros of…
This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…
We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the…
We develop a representation-theoretic framework for the relation between asymptotic symmetry evolution and monodromy in critical topologically massive gravity at the chiral point $\mu \ell=1$. We show that continuous evolution generated by…
We propose new linear combinations of compositions of a basic second-order scheme with appropriately chosen coefficients to construct higher order numerical integrators for differential equations. They can be considered as a generalization…
We propose a geometric framework to describe and analyze a wide array of operator splitting methods for solving monotone inclusion problems. The initial inclusion problem, which typically involves several operators combined through…
We classified finite orbits of monodromies of the Fuchsian system for five $2\times 2$ matrices. The explicit proof of this result is given. We have proposed a conjecture for a similar classification for $6$ or more $2\times 2$ matrices.…
We study the generalized forward-reflected-backward (GFRB) method, an extension of the forward-reflected-backward (FRB) scheme due to Malitsky and Tam, for solving monotone inclusion problems in real Hilbert spaces. We first analyze GFRB…
The notion of monodromy was introduced by J. J. Duistermaat as the first obstruction to the existence of global action coordinates in integrable Hamiltonian systems. This invariant was extensively studied since then and was shown to be…
The notion of fractional monodromy was introduced by Nekhoroshev, Sadovski\'{i} and Zhilinski\'{i} as a generalization of standard (`integer') monodromy in the sense of Duistermaat from torus bundles to singular torus fibrations. In the…
Using the monodromy method, a compact expression is obtained for the identity block contribution to the expectation value of two low-energy probe operators on a broad class of time-dependent heavy pure states in large-$c$ 2d CFTs. It will…
The generalized alternating direction method of multipliers (ADMM) of Xiao et al. [{\tt Math. Prog. Comput., 2018}] aims at the two-block linearly constrained composite convex programming problem, in which each block is in the form of…
In this paper, we introduce some adaptive methods for solving variational inequalities with relatively strongly monotone operators. Firstly, we focus on the modification of the recently proposed, in smooth case [1], adaptive numerical…