Joaquim Gomis, Giorgio Longhi
We study the canonical realization of BMS symmetry for a massive scalar field introduced in reference \cite{LM}. We will construct an invariant scalar product for the generalized momenta. As a consequence we will introduce a quadratic Casimir with the supertranslations.
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We construct a free field realization of an extension of the BMS algebra in $2+1$ dimensional space-time. Besides the supertranslations and superrotations, the extension contains an infinite set of superdilatations. We also comment the difficulties that appear when trying to extend the algebra to that of the full conformal group.
A canonical realization of the BMS (Bondi-Metzner-Sachs) algebra is given on the phase space of the classical real Klein-Gordon field . By assuming the finiteness of the generators of the Poincaré group, it is shown that a countable set of conserved quantities exists (supertranslations); this set transforms under a particular Lorentz representation, which is uniquely determined by the requirement of having an invariant four-dimensional subspace, which corresponds to the Poincaré translations. This Lorentz representation is infinite-dimensional, non unitary, reducible and indecomposable. Its re…
Free field realization of the BMS Ising model
本文通过非齐次BMS自由费米子理论实现BMS Ising模型，发现其对称性增强为新型BMS-Kac-Moody代数，并利用费米子-玻色子对偶得到该模型，其底层代数为$W(2,2,1)$-代数。
Explicit boundary conditions are given at spatial infinity for four-dimensional supergravity, which provide a realization of the super-BMS algebra of Awada, Gibbons and Shaw. The results are then generalized to the $N$- extended super-BMS algebras.
Supersymmetric BMS$_4$ Algebras Revisited: Electric/Magnetic Superalgebras and Free Field Realization
本文系统分类了BMS$_4$代数的超对称扩展，揭示了电/磁超代数的构造及R-对称性在超对称扩展中的作用。
We express the nonlocal BMS charges of a free massless Klein-Gordon scalar field in 2+1 in terms of the Green functions of the polyharmonic operators. Using the properties of these Green functions, we are able to discuss the asymptotic behaviour of the fields that ensures the existence of the charges, and prove that one obtains a realization of the 2+1 BMS algebra in canonical phase space. We also discuss the transformations in configuration space, and show that in this case the algebra closes only up to skew-symmetric combinations of the equations of motion. The formulation of the charges, in…
We give an explicit quantum super field construction of the N=2 super Casimir WA(n)-algebras, which is obtained from supersymmetric Miura transformation for the Lie superalgebra A(n,n-1). And also we give an extension of this algebra including a super vertex operator which depends on simple root system of A(n,n-1).
In this work we present a BMS-like ansatz for a Chern-Simons theory based on the semi-simple enlargement of the Poincaré symmetry, also known as AdS-Lorentz algebra. We start by showing that this ansatz is general enough to contain all the relevant stationary solutions of this theory and provides with suitable boundary conditions for the corresponding gauge connection. We find an explicit realization of the asymptotic symmetry at null infinity, which defines a semi-simple enlargement of the $\mathfrak{bms}_3$ algebra and turns out to be isomorphic to three copies of the Virasoro algebra. The f…
Particle realization of Bondi-Metzner-Sachs symmetry in 2+1 space-time
在(2+1)时空中利用非线性实现框架构建了包含BMS超平移对称性的洛伦兹不变有质量粒子模型，分析了其相空间约束与规范变换，并证明消除规范自由度后的物理约化空间仍具有BMS残余对称性。
BMS$_3$ invariant field theories
该研究回顾并构建具BMS₃对称性的二维场论，分析边界贡献等，引入外部源推导通量平衡定律。在平坦空间全息框架下，简单自由电BMS₃模型可重现三维爱因斯坦引力单值分类，还研究AdS₃和dS₃平坦空间极限，为平坦空间全息提供互补实现。
A Celestial Kinematical Interpretation for an Extended BMS$_4$
本文基于光锥动量构造了含超旋转的无质量 BMS$_4$ 代数的运动学实现，并从 Klein-Gordon 场辛结构出发构造了动力学实现，通过 Mellin 变换与球谐函数建立了与已有工作的联系。
BMS-like algebras: canonical realisations and BRST quantisation
本文推广三维BMS代数至任意参数λ，给出Weyl λ-BMS代数的辛实现，构造其中心扩张及BRST复形，并证明上同调与N=2超共形手征环同构，同时指出共形推广需W-代数且其无BRST复形。
The Bondi-van der Burg-Metzner-Sachs (BMS) group is the asymptotic symmetry group of asymptotically flat gravity. Recently, Donnay et al. have derived an analogous symmetry group acting on black hole event horizons. For a certain choice of boundary conditions, it is a semidirect product of ${\rm Diff}(S^2)$, the smooth diffeomorphisms of the two-sphere, acting on $C^\infty(S^2)$, the smooth functions on the two-sphere. We observe that the same group appears in fluid dynamics as symmetries of the compressible Euler equations. We relate these two realizations of ${\rm Diff}(S^2)\ltimes C^\infty(…
We construct canonical realizations of the $\mathfrak{bms}_3$ algebra as symmetry algebras of a free Klein-Gordon (KG) field in $2+1$ dimensions, for both the massive and massless case. We consider two types of realizations, one on-shell, written in terms of the Fourier modes of the scalar field, and the other one off-shell with non-local transformations written in terms of the KG field and its momenta. These realizations contain both supertranslations and superrotations, for which we construct the corresponding Noether charges.
Starting from the well-known quantum Miura-like transformation for the non simply-laced Lie algebras B(3),we give an explicit construction of the Casimir WB(3) algebras.We reserve the notation WB(N) for the Casimir W algebras of type W(2,4,6,...,2N,N+1/2) which contains one fermionic field. It is seen that WB(3) algebra is closed an associative for all values of the central element c.
This thesis is devoted to the study of the deformation and rigidity of infinite dimensional Lie algebras which are not subject to the Hochschild-Serre factorization theorem. In particular, we consider $bms_{3}$, Virasoro-Kac-Moody and $bms_{4}$ algebras and their central extensions which are respectively obtained as asymptotic and/or near horizon symmetry algebras for Einstein gravity on $3d$ flat, AdS$_{3}$ and $4d$ flat spacetimes. We also explore possible deformations of the Maxwell-BMS algebra, which is obtained as asymptotic symmetry algebra of the Chern-Simons gravity theory invariant un…
We present a new method to compute quantum energies in presence of a background field. The method is based on the string-inspired worldline approach to quantum field theory and its numerical realization with Monte-Carlo techniques. Our procedure is applied to the study of the Casimir force between rigid bodies induced by a fluctuating real scalar field. We test our method with the classic parallel-plate configuration and study curvature effects quantitatively for the sphere-plate configuration. The numerical estimates are compared with the ``proximity force approximation''. Sizable curvature e…
On the realization of infinite (continuous) spin field representations in AdS${}_{\mathbf{4}}$ space
本文研究AdS4空间中无限自旋场的对称性，证明其定义条件具有SO(2,3)不变性，且Casimir算子由约束算子固定，该场由SO(2,3)群的最退化表示描述。
Recently, we have demonstrated that for a certain class of Casimir-type systems ("devices") the energy of zero-point vacuum fluctuations reaches its global minimum when the device rotates about a certain axis rather than remains static. This rotational vacuum effect may lead to the emergence of permanently rotating objects provided the negative rotational energy of zero-point fluctuations cancels the positive rotational energy of the device itself. In this paper, we show that for massless electrically charged particles the rotational vacuum effect should be drastically (astronomically) enhance…
Casimir energy is calculated for the 5D electromagnetism and 5D scalar theory in the {\it warped} geometry. It is compared with the flat case. A new regularization, called {\it sphere lattice regularization}, is taken. In the integration over the 5D space, we introduce two boundary curves (IR-surface and UV-surface) based on the {\it minimal area principle}. It is a {\it direct} realization of the geometrical approach to the {\it renormalization group}. The regularized configuration is {\it closed-string like}. We do {\it not} take the KK-expansion approach. Instead, the position/momentum prop…
An exponentially large extra dimension can be naturally realized by the Casimir energy and the gaugino condensation in 5D supersymmetric theory. The model does not require any hierarchies among the 5D parameters. The key ingredient is an additional modulus other than the radion, which generically exists in 5D supergravity. SUSY is broken at the vacuum, which can be regarded as the Scherk-Schwarz SUSY breaking. We also analyze the mass spectrum and discuss some phenomenological aspects.
The complete structure of the Casimir ${\cal{W}\cal{A}}_{\it{N}}$ algebras are shown to exist in such a way that the Casimir ${\cal{W}\cal{A}}_{\it{N}}$ algebra is a kind of truncated type of $\cal{W}_{\infty}$ algebra both in the primary and in the quadratic basis, first using the associativity conditions in the basis of primary fields and second using the Miura basis coming from the free field realization as a different basis. Finally one can say that the Casimir ${\cal{W}\cal{A}}_{\it{N}}$ algebra is a kind of truncated type of $\cal{W}_{\infty}$algebra,so it is clear from any construction …
We construct the free field representation of the affine currents, energy-momentum tensor and screening currents of the first kind of the current superalgebra $gl(m|n)_k$ uniformly for $m=n$ and $m\neq n$. The energy-momentum tensor is given by a linear combination of two Sugawara tensors associated with the two independent quadratic Casimir elements of $gl(m|n)$.
Free mixed-symmetry continuous-spin fields propagating in AdS(5) space and flat R(4,1) space are studied. In the framework of a light-cone gauge formulation of relativistic dynamics, we build simple actions for such fields. Realization of relativistic symmetries on space of light-cone gauge mixed-symmetry continuous-spin fields is also found. Interrelations between constant parameters entering the light-cone gauge actions and eigenvalues of the Casimir operators of space-time symmetry algebras are obtained. Using these interrelations and requiring that the field dynamics in AdS(5) be irreducib…
We develop a method to compute the Casimir effect for arbitrary geometries. The method is based on the string-inspired worldline approach to quantum field theory and its numerical realization with Monte-Carlo techniques. Concentrating on Casimir forces between rigid bodies induced by a fluctuating scalar field, we test our method with the parallel-plate configuration. For the experimentally relevant sphere-plate configuration, we study curvature effects quantitatively and perform a comparison with the ``proximity force approximation'', which is the standard approximation technique. Sizable cur…
Asymptotic Higher Spin Symmetries: Noether Realization & Algebraic Structure in Einstein-Yang-Mills Theory
本文研究渐近高自旋对称性的相空间实现，揭示其在爱因斯坦-杨-米尔斯理论中的代数结构及守恒荷的构建方法。
Dirac/Weyl-node-induced oscillating Casimir effect
该研究理论证明Dirac/Weyl半金属中相对论电子场存在卡西米尔效应，其能量随薄膜厚度振荡，源于动量空间中的Dirac/Weyl节点，并可在Cd3As2和Na3Bi等材料薄膜中实验观测。
General Junction Condition and Casimir Effect for (1+1)-Dimensional Scalar Network CFT
研究(1+1)维自由标量场在网络上最一般的连接条件，由O(p)群刻画，并推导网络Casimir能量的上下界。
Casimir-Induced Quintessence in Dark Dimension
研究通过暗维度中的Casimir效应诱导quintessence场，利用五维框架中标准模型限制在四维膜上，推导radion有效作用量，并通过扩展模型实现正真空能，与DESI BAO测量一致。
Free Field Realization of $\mathcal{W}$-Algebra Associated with Exceptional Lie Algebras
本文通过递归构造，利用自由玻色子与屏蔽电荷，实现了与例外李代数相关的W-代数，并验证了不同构造的等价性，计算了生成元的W-荷。
We investigate the massless scalar particle dynamics on $AdS_{N+1} ~ (N>1)$ by the method of Hamiltonian reduction. Using the dynamical integrals of the conformal symmetry we construct the physical phase space of the system as a $SO(2,N+1)$ orbit in the space of symmetry generators. The symmetry generators themselves are represented in terms of $(N+1)$-dimensional oscillator variables. The physical phase space establishes a correspondence between the $AdS_{N+1}$ null-geodesics and the dynamics at the boundary of $AdS_{N+2}$. The quantum theory is described by a UIR of $SO(2,N+1)$ obtained at t…
We investigate the asymptotic structure of the free Rarita-Schwinger theory in four spacetime dimensions at spatial infinity in the Hamiltonian formalism. We impose boundary conditions for the spin-3/2 field that are invariant under an infinite-dimensional (abelian) algebra of non-trivial asymptotic fermionic symmetries. The compatibility of this set of boundary conditions with the invariance of the theory under Lorentz boosts requires the introduction of boundary degrees of freedom in the Hamiltonian action, along the lines of electromagnetism. These boundary degrees of freedom modify the sym…
Construction of superintegrable systems based on Lie algebras have been introduced over the years. However, these approaches depend on explicit realisations, for instance as a differential operators, of the underlying Lie algebra. This is also the case for the construction of their related symmetry algebra which take usually the form of a finitely generated quadratic algebra. These algebras often display structure constants which depend on the central elements and in particular on the Hamiltonian. In this paper, we develop a new approach reexamining the case of the generic superintegrable syst…
We analyze the phenomenon of fermion pairing into an effective boson associated with anomalies and the anomalous commutators of currents bilinear in the fermion fields. In two spacetime dimensions the chiral bosonization of the Schwinger model is determined by the axial current anomaly of massless Dirac fermions. A similar bosonized description applies to the 2D conformal trace anomaly of the fermion stress tensor. For both the chiral and conformal anomalies, correlation functions involving anomalous currents, $j^μ_5$ or $T^{μν}$ of massless fermions exhibit a massless boson $1/k^2$ pole, and …
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