An algebraic framework for quantization in presence of arbitrary number of point-like defects on the line is developed. We consider a scalar field which interacts with the defects and freely propagates away of them. As an application we compute the Casimir force both at zero and finite temperature. We derive also the charge density in the Gibbs state of a complex scalar field with defects. The example of two delta-defects is treated in detail.
We comment on the recent work [1], and on its relations with our papers [2,3] cited therein. In particular we show that, contrarily to what stated in [1], the Casimir energy density determined therein in the case of a single delta-like singularity coincides with the energy density obtained previously in our paper [2] using a different approach.
In this paper, an explicit expression for the Casimir operator (or the Casimir invariant) of the inhomogeneous group ISL(n,R) in its enveloping algebra is proposed, which using contractions of the tenso- rial indices of the generating operators P^{rho} and E^{nu}{mu} may be presented in the following (slightly more comprehensible as equation (1)) form. The Casimir is obtained by symmetrizing this expression. This tensor form is useful in the classification of particles in affine gravitational gauge theories; such as that based on ISL(4,R). It is also proven that the Casimir of ISL(n,R) can be …
We discuss consequences of the breaking of conformal symmetry by a flat or spherical extended operator. We adapt the embedding formalism to the study of correlation functions of symmetric traceless tensors in the presence of the defect. Two-point functions of a bulk and a defect primary are fixed by conformal invariance up to a set of OPE coefficients, and we identify the allowed tensor structures. A correlator of two bulk primaries depends on two cross-ratios, and we study its conformal block decomposition in the case of external scalars. The Casimir equation in the defect channel reduces to …
We evaluate quantum effects due to a $2$-component Dirac field in $2+1$ space-time dimensions, coupled to domain-wall like defects with a smooth shape. We show that those effects induce non trivial contributions to the (shape-dependent) energy of the domain walls. For a single defect, we study the divergences in the corresponding self-energy, and also consider the role of the massless zero mode, corresponding to the Callan-Harvey mechanism, by coupling the Dirac field to an external gauge field. For two defects, we show that the Dirac field induces a non trivial, Casimir-like effect between th…
We study half-BPS line defects in $\mathcal{N}=2$ superconformal theories using the bootstrap approach. We concentrate on local excitations constrained to the defect, which means the system is a $1d$ defect CFT with $\mathfrak{osp}(4^*|2)$ symmetry. In order to study correlation functions we construct a suitable superspace, and then use the Casimir approach to calculate a collection of new superconformal blocks. Special emphasis is given to the displacement operator, which controls deformations orthogonal to the defect and is always present in a defect CFT. After setting up the crossing equati…
In this paper we present a complete and detailed analysis of the calculation of both the Wightman function and the vacuum expectation value of the energy-momentum tensor that arise from quantum vacuum fluctuations of massive and massless scalar fields in the cosmic dispiration spacetime, which is formed by the combination of two topological defects: a cosmic string and a screw dislocation. This spacetime is obtained in the framework of the Einstein-Cartan theory of gravity and is considered to be a chiral space-like cosmic string. For completeness we perform the calculation in a high-dimension…
Sigma models effectively describe ordered phases of systems with spontaneously broken symmetries. At low energies, field configurations fall into solitonic sectors, which are homotopically distinct classes of maps. Depending on context, these solitons are known as textures or defect sectors. In this paper, we address the problem of enumerating and describing the solitonic sectors of sigma models. We approach this problem via an algebraic topological method -- combinatorial homotopy, in which one models both spacetime and the target space with algebraic objects which are higher categorical gene…
Paramagnetic spin systems with spontaneously broken spatial symmetries, such as valence bond solid (VBS) phases, can host topological defects carrying non-trivial quantum numbers, which enables the paradigm of deconfined quantum criticality. In this work, we study the properties of topological defects in valence plaquette solid (VPS) phases on square and cubic lattices. We show that the defects of the VPS order parameter, in addition to possessing non-trivial quantum numbers, have fracton mobility constraints deep in the VPS phase, which has been overlooked previously. The spinon inside a sing…
Excess free energy and Casimir forces in systems with long-range interactions of van-der-Waals type: General considerations and exact spherical-model results
Line Defects in Liouville Conformal Field Theory: Localized Cosmological Constants and Decohered Hyperbolic Geometries
Leinweber Institute for Theoretical Physics and Department of Physics, University of California, Berkeley（加州大学伯克利分校雷恩韦伯理论物理研究所与物理系）；Center for Cosmology and Particle Physics, New York University（纽约大学宇宙学与粒子物理中心）
The Coulomb and Higgs indices of the 3d $\mathcal{N}=4$ $U(N)$ ADHM theories can be decorated by line defect operators as the line defect correlators. We obtain exact closed-form expressions and various non-trivial algebraic relations for the correlators of the Wilson lines in the fundamental and (anti)symmetric representations by means of the Hall-Littlewood expansion, the Fermi-gas method and the residue calculation. From the large $N$ limit of the correlators we obtain the single particle gravity indices which are expected to encode the spectra of fluctuation modes on the gravity duals of l…
