Superconformal Bondi-Metzner-Sachs Algebra in Three Dimensions
TL;DR: An explicit canonical realization of the conformal extension of BMS_{3} is shown to emerge from the asymptotic structure of conformal gravity in three dimensions, endowed with a new set of boundary conditions.
Abstract: The conformal extension of the ${\mathrm{BMS}}_{3}$ algebra is constructed. Apart from an infinite number of ``superdilatations,'' in order to incorporate superspecial conformal transformations, the commutator of the latter with supertranslations strictly requires the presence of nonlinear terms in the remaining generators. The algebra appears to be very rigid, in the sense that its central extensions as well as the coefficients of the nonlinear terms become determined by the central charge of the Virasoro subalgebra. The wedge algebra corresponds to the conformal group in three spacetime dimensions SO(3,2), so that the full algebra can also be interpreted as an infinite-dimensional nonlinear extension of the ${\mathrm{AdS}}_{4}$ algebra with nontrivial central charges. Moreover, since the Lorentz subalgebra [$sl(2,R)$] is nonprincipally embedded within the conformal (wedge) algebra, according to the conformal weight of the generators, the conformal extension of ${\mathrm{BMS}}_{3}$ can be further regarded as a ${W}_{(2,2,2,1)}$ algebra. An explicit canonical realization of the conformal extension of ${\mathrm{BMS}}_{3}$ is then shown to emerge from the asymptotic structure of conformal gravity in three dimensions, endowed with a new set of boundary conditions. The supersymmetric extension is also briefly addressed.
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TL;DR: The conformal symmetry algebra in 2D (Diff(S1)⊕Diff (S1)) is shown to be related to its ultra/non-relativistic version (BMS3≈GCA2) through a nonlinear map of the generators, without any sort of limiting process.
Abstract: The conformal symmetry algebra in 2D (Diff(S1)⊕Diff(S1)) is shown to be related to its ultra/non-relativistic version (BMS3≈GCA2) through a nonlinear map of the generators, without any sort of limiting process. For a generic classical CFT2, the BMS3 generators then emerge as composites built out from the chiral (holomorphic) components of the stress-energy tensor, T and $$ \overline{T} $$
, closing in the Poisson brackets at equal time slices. Nevertheless, supertranslation generators do not span Noetherian symmetries. BMS3 becomes a bona fide symmetry once the CFT2 is marginally deformed by the addition of a $$ \sqrt{T\overline{T}} $$
term to the Hamiltonian. The generic deformed theory is manifestly invariant under diffeomorphisms and local scalings, but it is no longer a CFT2 because its energy and momentum densities fulfill the BMS3 algebra. The deformation can also be described through the original CFT2 on a curved metric whose Beltrami differentials are determined by the variation of the deformed Hamiltonian with respect to T and $$ \overline{T} $$
. BMS3 symmetries then arise from deformed conformal Killing equations, corresponding to diffeomorphisms that preserve the deformed metric and stress-energy tensor up to local scalings. As an example, we briefly address the deformation of N free bosons, which coincides with ultra-relativistic limits only for N = 1. Furthermore, Cardy formula and the S-modular transformation of the torus become mapped to their corresponding BMS3 (or flat) versions.
17 citations
TL;DR: In this paper , it was shown that the on-shell conformal Carrollian scalar can be interpreted as the flat-space limit of the singleton representation of the conformal algebra.
9 citations
TL;DR: In this paper , the analysis of the asymptotic properties of gravity in higher spacetime dimensions D , with a particular emphasis on the case D = 5, is presented.
Abstract: A bstract We develop the analysis of the asymptotic properties of gravity in higher spacetime dimensions D , with a particular emphasis on the case D = 5. Our approach deals with spatial infinity and is Hamiltonian throughout. It is shown that the asymptotic symmetry algebra BMS 5 , which is realized non linearly, contains a four-fold family of angle- dependent supertranslations. The structure of this non-linear algebra is investigated and a presentation in which the Poincaré subalgebra is linearly realized is constructed. Invariance of the energy is studied. Concluding comments on higher dimensions D ≥ 6 are also given.
8 citations
13 Nov 2022
TL;DR: In this article , the authors study the inhomogeneous BMS free fermion theory and show that it gives a free field realization of the BMS Ising model, which is not a minimal model with respect to BMS$_3$ since the minimal model construction based on BMS Kac determinant always leads to chiral Virasoro minimal models.
Abstract: In this work, we study the inhomogeneous BMS free fermion theory, and show that it gives a free field realization of the BMS Ising model. We find that besides the BMS symmetry there exists an anisotropic scaling symmetry in BMS free fermion theory. As a result, the symmetry of the theory gets enhanced to an infinite dimensional symmetry generated by a BMS-Kac-Moody algebra, similar to the one in the BMS free scalar model. Different from the BMS free scalar case, the Kac-Moody level in the algebra is nonvanishing now such that the corresponding modules are further enlarged to BMS-Kac-Moody staggered modules. We show that there exists an underlying $W(2,2,1)$ structure in the operator product expansion of the currents, and the BMS-Kac-Moody staggered modules can be viewed as highest-weight modules of this $W$-algebra. Moreover we obtain the BMS Ising model by a fermion-boson duality. This BMS Ising model is not a minimal model with respect to BMS$_3$, since the minimal model construction based on BMS Kac determinant always leads to chiral Virasoro minimal models. Instead, the underlying algebra of the BMS Ising model is the $W(2,2,1)$-algebra, which can be understood as a quantum conformal BMS$_3$ algebra.
7 citations
TL;DR: In this article, a consistent way of coupling three-dimensional hyper-Maxwell-Chern-Simons gravity theory with massless spin-$\frac{5}{2}$ gauge fields was presented.
Abstract: We present a consistent way of coupling three-dimensional Maxwell-Chern-Simons gravity theory with massless spin-$\frac{5}{2}$ gauge fields. We first introduce the simplest hyper-Maxwell-Chern-Simons gravity generically containing two massless spin-2 fields coupled with a massless Majorana fermion of spin $\frac{5}{2}$ whose novel underlying superalgebra is explicitly constructed. We then present three alternative hypersymmetric extensions of the Maxwell algebra which are shown to emerge from the In\"on\"u-Wigner contraction procedure of precise combinations of the $\mathfrak{o}\mathfrak{s}\mathfrak{p}(1|4)$ and the $\mathfrak{s}\mathfrak{p}(4)$ algebras. This allows us to construct distinct types of hyper-Maxwell-Chern-Simons theories that extend to include generically interacting nonpropagating spin-4 fields accompanied by one or two spin-$\frac{5}{2}$ gauge fields.
5 citations
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Book•
13 Dec 1996
TL;DR: This paper developed conformal field theory from first principles and provided a self-contained, pedagogical, and exhaustive treatment, including a great deal of background material on quantum field theory, statistical mechanics, Lie algebras and affine Lie algesas.
Abstract: Filling an important gap in the literature, this comprehensive text develops conformal field theory from first principles. The treatment is self-contained, pedagogical, and exhaustive, and includes a great deal of background material on quantum field theory, statistical mechanics, Lie algebras and affine Lie algebras. The many exercises, with a wide spectrum of difficulty and subjects, complement and in many cases extend the text. The text is thus not only an excellent tool for classroom teaching but also for individual study. Intended primarily for graduate students and researchers in theoretical high-energy physics, mathematical physics, condensed matter theory, statistical physics, the book will also be of interest in other areas of theoretical physics and mathematics. It will prepare the reader for original research in this very active field of theoretical and mathematical physics.
3,440 citations
"Superconformal Bondi-Metzner-Sachs ..." refers background in this paper
...Conformal field theories, formulated in terms of these enhanced symmetries, have spanned a wealth impressive results in a wide variety of contexts [3–7]....
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TL;DR: In this paper, the authors constructed three dimensional Chern-Simons-matter theories with gauge groups U(N) × U(n) and SU(N), SU(2) × SU (2) which have explicit = 6 superconformal symmetry.
Abstract: We construct three dimensional Chern-Simons-matter theories with gauge groups U(N) × U(N) and SU(N) × SU(N) which have explicit = 6 superconformal symmetry. Using brane constructions we argue that the U(N) × U(N) theory at level k describes the low energy limit of N M2-branes probing a C4/Zk singularity. At large N the theory is then dual to M-theory on AdS4 × S7/Zk. The theory also has a 't Hooft limit (of large N with a fixed ratio N/k) which is dual to type IIA string theory on AdS4 × CP3. For k = 1 the theory is conjectured to describe N M2-branes in flat space, although our construction realizes explicitly only six of the eight supersymmetries. We give some evidence for this conjecture, which is similar to the evidence for mirror symmetry in d = 3 gauge theories. When the gauge group is SU(2) × SU(2) our theory has extra symmetries and becomes identical to the Bagger-Lambert theory.
3,091 citations
"Superconformal Bondi-Metzner-Sachs ..." refers background in this paper
...It is also worth pointing out that the superconformal extension of the BMS3 algebra can be interpreted as an infinite-dimensional centrally-extended nonlinear extension of the super AdS4 algebra (osp (1|4)), suggesting the possibility of a different version of the AdS4/CFT3 correspondence [74], presumably topological and with enhanced symmetries....
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TL;DR: In this paper, a short introduction to N = 1 supersymmetry and supergravity and review the attempts to construct models in which the breakdown scale of the weak interactions is related to supersymmetric breaking is given.
3,056 citations
"Superconformal Bondi-Metzner-Sachs ..." refers background in this paper
...Besides, extensions of the Poincaré algebra that contain additional fermionic generators of spin 1/2, known as super-Poincaré algebras, provide the building blocks for most of supersymmetric field theories, enjoying a prominent and complementary source of exciting developments [8–14]....
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TL;DR: A survey of methods by which supersymmetry could be observed in experiments at present and future accelerators can be found in this paper, with considerable emphasis on pedagogical completeness.
2,841 citations
"Superconformal Bondi-Metzner-Sachs ..." refers background in this paper
...Besides, extensions of the Poincaré algebra that contain additional fermionic generators of spin 1/2, known as super-Poincaré algebras, provide the building blocks for most of supersymmetric field theories, enjoying a prominent and complementary source of exciting developments [8–14]....
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TL;DR: In this paper, it is shown that the flow of information to infinity is controlled by a single function of two variables called the news function, together with initial conditions specified on a light cone, which fully defines the behaviour of the system.
Abstract: This paper is divided into four parts. In part A, some general considerations about gravitational radiation are followed by a treatment of the scalar wave equation in the manner later to be applied to Einstein’s field equations. In part B, a co-ordinate system is specified which is suitable for investigation of outgoing gravitational waves from an isolated axi-symmetric reflexion-symmetric system . The metric is expanded in negative powers of a suitably defined radial co-ordinate r , and the vacuum field equations are investigated in detail. It is shown that the flow of information to infinity is controlled by a single function of two variables called the news function. Together with initial conditions specified on a light cone, this function fully defines the behaviour of the system . No constraints of any kind are encountered. In part C, the transformations leaving the metric in the chosen form are determined. An investigation of the corresponding transformations in Minkowski space suggests that no generality is lost by assuming that the transformations, like the metric, may be expanded in negative powers of r . In part D, the mass of the system is defined in a way which in static metrics agrees with the usual definition. The principal result of the paper is then deduced, namely, that the mass of a system is constant if and only if there is no news; if there is news, the mass decreases monotonically so long as it continues. The linear approximation is next discussed, chiefly for its heuristic value, and employed in the analysis of a receiver for gravitational waves. Sandwich waves are constructed, and certain non-radiative but non-static solutions are discussed. This part concludes with a tentative classification of time-dependent solutions of the types considered.
2,324 citations