scholarly journals Category theory for conformal boundary conditions

2003 ◽  
pp. 25-70 ◽  
Author(s):  
Jürgen Fuchs ◽  
Christoph Schweigert
Keyword(s):  
Boundary Conditions ◽  
Category Theory ◽  
Conformal Boundary

scholarly journals Bootstrapping boundary-localized interactions

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Connor Behan ◽  
Lorenzo Di Pietro ◽  
Edoardo Lauria ◽  
Balt C. van Rees
Keyword(s):  
Boundary Condition ◽  
Scalar Field ◽  
Boundary Conditions ◽  
Parameter Space ◽  
Three Dimensional ◽  
Conformal Boundary ◽  
Dimensional Boundary ◽  
Dirichlet And Neumann Conditions ◽  
Boundary Fields ◽  
Boundary Dynamics

Abstract We study conformal boundary conditions for the theory of a single real scalar to investigate whether the known Dirichlet and Neumann conditions are the only possibilities. For this free bulk theory there are strong restrictions on the possible boundary dynamics. In particular, we find that the bulk-to-boundary operator expansion of the bulk field involves at most a ‘shadow pair’ of boundary fields, irrespective of the conformal boundary condition. We numerically analyze the four-point crossing equations for this shadow pair in the case of a three-dimensional boundary (so a four-dimensional scalar field) and find that large ranges of parameter space are excluded. However a ‘kink’ in the numerical bounds obeys all our consistency checks and might be an indication of a new conformal boundary condition.

scholarly journals Conformal boundary conditions from cutoff AdS3

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Evan Coleman ◽  
Vasudev Shyam
Keyword(s):  
Boundary Conditions ◽  
Ground State ◽  
State Energy ◽  
Growth Characteristic ◽  
Temperature Limit ◽  
Flow Equation ◽  
Legendre Transform ◽  
Conformal Boundary ◽  
Deformation Parameters ◽  
Metric Fluctuations

Abstract We construct a particular flow in the space of 2D Euclidean QFTs on a torus, which we argue is dual to a class of solutions in 3D Euclidean gravity with conformal boundary conditions. This new flow comes from a Legendre transform of the kernel which implements the T$$ \overline{T} $$ T ¯ deformation, and is motivated by the need for boundary conditions in Euclidean gravity to be elliptic, i.e. that they have well-defined propagators for metric fluctuations. We demonstrate equivalence between our flow equation and variants of the Wheeler de-Witt equation for a torus universe in the so-called Constant Mean Curvature (CMC) slicing. We derive a kernel for the flow, and we compute the corresponding ground state energy in the low-temperature limit. Once deformation parameters are fixed, the existence of the ground state is independent of the initial data, provided the seed theory is a CFT. The high-temperature density of states has Cardy-like behavior, rather than the Hagedorn growth characteristic of T$$ \overline{T} $$ T ¯ -deformed theories.

scholarly journals Properties of RG interfaces for 2D boundary flows

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Anatoly Konechny
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Variational Method ◽  
Boundary Conditions ◽  
The Other ◽  
Two Dimensional ◽  
Conformal Boundary ◽  
First Approximation ◽  
Local Operators

Abstract We consider RG interfaces for boundary RG flows in two-dimensional QFTs. Such interfaces are particular boundary condition changing operators linking the UV and IR conformal boundary conditions. We refer to them as RG operators. In this paper we study their general properties putting forward a number of conjectures. We conjecture that an RG operator is always a conformal primary such that the OPE of this operator with its conjugate must contain the perturbing UV operator when taken in one order and the leading irrelevant operator (when it exists) along which the flow enters the IR fixed point, when taken in the other order. We support our conjectures by perturbative calculations for flows between nearby fixed points, by a non-perturbative variational method inspired by the variational method proposed by J. Cardy for massive RG flows, and by numerical results obtained using boundary TCSA. The variational method has a merit of its own as it can be used as a first approximation in charting the global structure of the space of boundary RG flows. We also discuss the role of the RG operators in the transport of states and local operators. Some of our considerations can be generalised to two-dimensional bulk flows, clarifying some conceptual issues related to the RG interface put forward by D. Gaiotto for bulk 𝜙1,3 flows.

scholarly journals Integrable boundaries, conformal boundary conditions and A-D-E fusion rules

1998 ◽  
Vol 31 (50) ◽  
pp. L763-L770 ◽  
Author(s):  
Roger E Behrend ◽  
Paul A Pearce ◽  
Jean-Bernard Zuber
Keyword(s):  
Boundary Conditions ◽  
Conformal Boundary ◽  
Fusion Rules

scholarly journals BOUNDARY S MATRIX FOR THE TRICRITICAL ISING MODEL

1996 ◽  
Vol 11 (25) ◽  
pp. 4491-4512 ◽  
Author(s):  
LEUNG CHIM
Keyword(s):  
Ising Model ◽  
Boundary Conditions ◽  
Half Plane ◽  
Scattering Theory ◽  
Energy Operator ◽  
Conformal Boundary ◽  
Different Boundary Conditions ◽  
S Matrix

The tricritical Ising model perturbed by the subleading energy operator [Formula: see text] was known to be an integrable scattering theory of massive kinks,14 and in fact it preserves supersymmetry. We consider here the model defined on the half-plane with a boundary and compute the associated factorizable boundary S matrix. The conformal boundary conditions of this model are identified and the corresponding S matrices are found. We also show how some of these S matrices can be perturbed and generate “flows” between different boundary conditions.

scholarly journals Modelling of free-form conformal metasurfaces

2018 ◽  
Vol 9 (1) ◽  
Author(s):  
Kedi Wu ◽  
Philippe Coquet ◽  
Qi Jie Wang ◽  
Patrice Genevet
Keyword(s):  
Boundary Conditions ◽  
Electromagnetic Fields ◽  
Photonic Devices ◽  
Free Form ◽  
Computationally Efficient ◽  
Conformal Boundary ◽  
Artificial Boundary Conditions ◽  
Theoretical Predictions ◽  
Control Light ◽  
Computationally Efficient Algorithms

Abstract Artificial electromagnetic surfaces, metasurfaces, control light in the desired manner through the introduction of abrupt changes of electromagnetic fields at interfaces. Current modelling of metasurfaces successfully exploits generalised sheet transition conditions (GSTCs), a set of boundary conditions that account for electric and magnetic metasurface-induced optical responses. GSTCs are powerful theoretical tools but they are not readily applicable for arbitrarily shaped metasurfaces. Accurate and computationally efficient algorithms capable of implementing artificial boundary conditions are highly desired for designing free-form photonic devices. To address this challenge, we propose a numerical method based on conformal boundary optics with a modified finite difference time-domain (FDTD) approach which accurately calculates the electromagnetic fields across conformal metasurfaces. Illustrative examples of curved meta-optics are presented, showing results in good agreement with theoretical predictions. This method can become a powerful tool for designing and predicting optical functionalities of conformal metasurfaces for new lightweight, flexible and wearable photonic devices.

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