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It was proven recently that JT gravity can be defined as an ensemble of L x L Hermitian matrices. We point out that the eigenvalues of the matrix correspond in JT gravity to FZZT-type boundaries on which spacetimes can end. We then…

High Energy Physics - Theory · Physics 2021-04-13 Andreas Blommaert , Thomas G. Mertens , Henri Verschelde

It is well known that a general two-point function cannot be uniquely determined in a theory with Poincar\'e symmetry. In this paper, we show that bulk-to-boundary correlators are highly constrained after imposing suitable fall-off…

High Energy Physics - Theory · Physics 2026-01-27 Jiang Long , Jing-Long Yang

The relationship between bulk and boundary properties is one of the founding features of (Rational) Conformal Field Theory. Our goal in this paper is to explore the possibility of having an equivalent relationship in the context of lattice…

High Energy Physics - Theory · Physics 2022-11-29 Jonathan Belletête , Azat M. Gainutdinov , Jesper L. Jacobsen , Hubert Saleur , Romain Vasseur

We present an interesting reformulation of a collection of dilaton gravity models in two space-time dimensions into a field theory of two decoupled Liouville fields in flat space, in the presence of a Maxwell gauge field. An effective…

High Energy Physics - Theory · Physics 2011-12-30 Simone Zonetti , Jan Govaerts

Any self-adjoint extension of a (singular) Sturm-Liouville operator bounded from below uniquely leads to an associated sesquilinear form. This form is characterized in terms of principal and nonprincipal solutions of the Sturm-Liouville…

Classical Analysis and ODEs · Mathematics 2025-09-10 Jussi Behrndt , Fritz Gesztesy , Seppo Hassi , Roger Nichols , Henk de Snoo

This paper studies a Sturm--Liouville boundary value problem in which one of the boundary conditions depends bilinearly on the spectral parameter. The differential equation is considered on the interval $(0,1)$ with a classical boundary…

Classical Analysis and ODEs · Mathematics 2026-04-01 Yagub N. Aliyev , Narmin N. Aliyeva

For the magnetic Laplacian on a bounded planar domain, imposing Neumann boundary conditions produces eigenvalues below the lowest Landau level. If the domain has two boundary components and one imposes a Neumann condition on one component…

Spectral Theory · Mathematics 2024-06-11 Soeren Fournais , Ayman Kachmar

In this article, the authors establish a general (two-weight) boundedness criterion for a pair of functions, $(F,f)$, on $\mathbb{R}^n$ in the scale of weighted Lebesgue spaces, weighted Lorentz spaces, (Lorentz--)Morrey spaces, and…

Analysis of PDEs · Mathematics 2021-12-09 Sibei Yang , Zhenyu Yang

By employing non-equispaced grid points near boundaries, boundary-optimized upwind finite-difference operators of orders up to nine are developed. The boundary closures are constructed within a diagonal-norm summation-by-parts (SBP)…

Numerical Analysis · Mathematics 2026-02-06 Ken Mattsson , David Niemelä , Andrew R. Winters

Recent results on the annulus partition function in Liouville field theory are applied to non-critical string theory, both below and above the critical dimension. Liouville gravity coupled to $c\le 1$ matter has a dual formulation as a…

High Energy Physics - Theory · Physics 2007-05-23 Emil J. Martinec

The Liouville action for two--dimensional quantum gravity coupled to interacting matter contains terms that have not been considered previously. They are crucial for understanding the renormalization group flow and can be observed in recent…

High Energy Physics - Theory · Physics 2009-10-22 Christof Schmidhuber

In this work we fully characterize the classes of matrix weights for which multilinear Calder\'on-Zygmund operators extend to bounded operators on matrix weighted Lebesgue spaces. To this end, we develop the theory of multilinear singular…

Functional Analysis · Mathematics 2024-12-20 Spyridon Kakaroumpas , Zoe Nieraeth

We provide a probabilistic approach to studying minimal surfaces in three-dimensional Euclidean space. Following a discussion of the basic relationship between Brownian motion on a surface and minimality of the surface, we introduce a way…

Differential Geometry · Mathematics 2011-01-20 Robert W. Neel

An analysis of the boundary representations and C$^*$-envelopes of some finite-dimensional operator systems $\mathcal R$ is undertaken by considering relationships between operator-theoretic properties of a $d$-tuple $\mathfrak…

Operator Algebras · Mathematics 2026-01-26 Douglas Farenick , Chi-Kwong Li , Sushil Singla

We derived the corresponding boundary condition on Fermi fields to the spin-1/2 Heisenberg chain with boundary magnetic fields. In order to obtain the correct boundary condition from the variation of the action at the edges, we carefully…

Statistical Mechanics · Physics 2014-12-09 Chihiro Matsui

We argue that topological matrix models (matrix models of the Kontsevich type) are examples of exact open/closed duality. The duality works at finite N and for generic `t Hooft couplings. We consider in detail the paradigm of the Kontsevich…

High Energy Physics - Theory · Physics 2014-11-18 Davide Gaiotto , Leonardo Rastelli

We construct a simple physical model of a particle moving on the infinite noncommutative 2-plane. The model consists of a pair of opposite charges moving in a strong magnetic field. In addition, the charges are connected by a spring. In the…

High Energy Physics - Theory · Physics 2009-10-07 Daniela Bigatti , Leonard Susskind

The structures in target space geometry that correspond to conformally invariant boundary conditions in WZW theories are determined both by studying the scattering of closed string states and by investigating the algebra of open string…

High Energy Physics - Theory · Physics 2009-10-31 G. Felder , J. Fröhlich , J. Fuchs , C. Schweigert

The $\XXZ$ spin chain with a boundary magnetic field $h$ is considered, using the vertex operator approach to diagonalize the Hamiltonian. We find explicit bosonic formulas for the two vacuum vectors with zero particle content. There are…

High Energy Physics - Theory · Physics 2009-10-28 M. Jimbo , R. Kedem , T. Kojima , H. Konno , T. Miwa

We study boundary renormalization group flows of N=2 minimal models using Landau-Ginzburg description of B-type. A simple algebraic relation of matrices is relevant. We determine the pattern of the flows and identify the operators that…

High Energy Physics - Theory · Physics 2007-05-23 Kentaro Hori