共查询到20条相似文献,搜索用时 15 毫秒
1.
《Physics letters. [Part B]》1988,206(1):62-70
Particular examples and the general structure of extended conformal symmetries in coset conformal field theories are discussed. Discrete series of unitary representations, whose existence had been previously conjectured, are constructed for a class of extended conformal algebras introduced by Fateev and Zamolodchikov (FZ). The construction is a generalisation of the coset construction of the discrete series for the superconformal algebra using the coset spaces so(N) ⊕ su(N)/so(N), for fixed N. The N = 3 series is the FZ S3 algebra and the N = 4 series consists of two commuting copies of the superconformal algebra. A general method for analysing the extended conformal symmetries present in a particular coset theory and of constructing discrete series of representations of extended symmetry algebras is outlined. 相似文献
2.
P. Degiovanni 《Communications in Mathematical Physics》1990,127(1):71-99
We compute the modular properties of the possible genus-one characters of some Rational Conformal Field Theories starting from their fusion rules. We show that the possible choices ofS matrices are indexed by some automorphisms of the fusion algebra. We also classify the modular invariant partition functions of these theories. This gives the complete list of modular invariant partition functions of Rational Conformal Field Theories with respect to theA
N
(1)
level one algebra.Unité propre de Recherche du Centre National de la Recherche Scientifique, associée à l'Ècole Normale Supérieure et à l'Université de Paris-Sud 相似文献
3.
Governed by locality, we explore a connection between unitary braid group representations associated to a unitary R-matrix and to a simple object in a unitary braided fusion category. Unitary R-matrices, namely unitary solutions to the Yang-Baxter equation, afford explicitly local unitary representations of braid groups. Inspired by topological quantum computation, we study whether or not it is possible
to reassemble the irreducible summands appearing in the unitary braid group representations from a unitary braided fusion
category with possibly different positive multiplicities to get representations that are uniformly equivalent to the ones
from a unitary R-matrix. Such an equivalence will be called a localization of the unitary braid group representations. We show that the q = e
πi/6 specialization of the unitary Jones representation of the braid groups can be localized by a unitary 9 × 9 R-matrix. Actually this Jones representation is the first one in a family of theories (SO(N), 2) for an odd prime N > 1, which are conjectured to be localizable. We formulate several general conjectures and discuss possible connections to
physics and computer science. 相似文献
4.
Katsunori Kawamura 《Letters in Mathematical Physics》2009,87(3):199-207
We completely classify type III factor representations of Cuntz–Krieger algebras associated with quasi-free states up to unitary
equivalence. Furthermore, we realize these representations on concrete Hilbert spaces without using GNS construction. Free
groups and their type II1 factor representations are used in these realizations.
相似文献
5.
Roger E. Behrend Paul A. Pearce Valentina B. Petkova Jean-Bernard Zuber 《Nuclear Physics B》2000,570(3):525-589
We develop further the theory of Rational Conformal Field Theories (RCFTs) on a cylinder with specified boundary conditions emphasizing the role of a triplet of algebras: the Verlinde, graph fusion and Pasquier algebras. We show that solving Cardy's equation, expressing consistency of a RCFT on a cylinder, is equivalent to finding integer valued matrix representations of the Verlinde algebra. These matrices allow us to naturally associate a graph G to each RCFT such that the conformal boundary conditions are labelled by the nodes of G. This approach is carried to completion for sl(2) theories leading to complete sets of conformal boundary conditions, their associated cylinder partition functions and the A-D-E classification. We also review the current status for WZW sl(3) theories. Finally, a systematic generalisation of the formalism of Cardy–Lewellen is developed to allow for multiplicities arising from more general representations of the Verlinde algebra. We obtain information on the bulk–boundary coefficients and reproduce the relevant algebraic structures from the sewing constraints. 相似文献
6.
We give a general bosonic construction of oscillator-like unitary irreducible representations (UIR) of non-compact groups whose coset spaces with respect to their maximal compact subgroups are Hermitian symmetric. With the exception of E7(7), they include all the non-compact invariance groups of extended supergravity theories in four dimensions. These representations have the remarkable property that each UIR is uniquely determined by an irreducible representation of the maximal compact subgroup. We study the connection between our construction, the Hermitian symmetric spaces and the Tits-Koecher construction of the Lie algebras of corresponding groups. We then give the bosonic construction of the Lie algebra ofE
7(7) in SU(8), SO(8) and U(7) bases and study its properties. Application of our method toE
7(7) leads to reducible unitary representations.Dedicated to Feza Gürsey on the occasion of his 60th birthdayAlexander von Humboldt Fellow, on leave from Physics Dept., Bogaziçi University, Istanbul/Turkey: work supported in part by TBTAK, The National Science and Technology Council of Turkey 相似文献
7.
Unitary representations of some infinite-dimensional Lie algebras motivated by string theory on AdS3
《Nuclear Physics B》1999,561(3):413-432
We consider some unitary representations of infinite-dimensional Lie algebras motivated by string theory on AdS3. These include examples of two kinds: the A,D,E type affine Lie algebras and the N=4 superconformal algebra. The first presents a new construction for free field representations of affine Lie algebras. The second is of a particular physical interest because it provides some hints that a hybrid of the NSR and GS formulations for string theory on AdS3 exists. 相似文献
8.
Detlev Buchholz Claudio D’Antoni Roberto Longo 《Communications in Mathematical Physics》2007,270(1):267-293
We introduce a new type of spectral density condition, that we call L
2- nuclearity. One formulation concerns lowest weight unitary representations of and turns out to be equivalent to the existence of characters. A second formulation concerns inclusions of local observable
von Neumann algebras in Quantum Field Theory. We show the two formulations to agree in chiral Conformal QFT and, starting
from the trace class condition for the conformal Hamiltonian L
0, we infer and naturally estimate the Buchholz-Wichmann nuclearity condition and the (distal) split property. As a corollary,
if L
0 is log-elliptic, the Buchholz-Junglas set up is realized and so there exists a β-KMS state for the translation dynamics on
the net of C*-algebras for every inverse temperature β > 0. We include further discussions on higher dimensional spacetimes. In particular,
we verify that L
2-nuclearity is satisfied for the scalar, massless Klein-Gordon field.
Dedicated to László Zsidó on the occasion of his sixtieth birthday
Supported by MIUR, GNAMPA-INDAM and EU network “Quantum Spaces–Non Commutative Geometry” HPRN-CT-2002-00280 相似文献
9.
T. A. Larsson 《Communications in Mathematical Physics》2000,214(2):469-491
Let the DRO (Diffeomorphism, Reparametrization, Observer) algebra?DRO(N) be the extension of diff(N)⊕ diff(1) by its four inequivalent Virasoro-like cocycles. Here diff(N) is the diffeomorphism algebra in N-dimensional spacetime and diff(1) describes reparametrizations of trajectories in the space of tensor-valued p-jets. DRO(N) has a Fock module for each p and each representation of gl(N). Analogous representations for gauge algebras (higher-dimensional Kac–Moody algebras) are also given. The reparametrization
symmetry can be eliminated by a gauge fixing procedure, resulting in previously discovered modules. In this process, two DRO(N) cocycles transmute into anisotropic cocycles for diff(N). Thus the Fock modules of toroidal Lie algebras and their derivation algebras are geometrically explained.
Received: 29 October 1998 / Accepted: 2 May 2000 相似文献
10.
In two earlier articles we constructed algebraic-geometric families of genus one (i.e. elliptic) Lie algebras of Krichever–Novikov
type. The considered algebras are vector fields, current and affine Lie algebras. These families deform the Witt algebra,
the Virasoro algebra, the classical current, and the affine Kac–Moody Lie algebras respectively. The constructed families
are not equivalent (not even locally) to the trivial families, despite the fact that the classical algebras are formally rigid.
This effect is due to the fact that the algebras are infinite dimensional. In this article the results are reviewed and developed
further. The constructions are induced by the geometric process of degenerating the elliptic curves to singular cubics. The
algebras are of relevance in the global operator approach to the Wess–Zumino–Witten–Novikov models appearing in the quantization
of Conformal Field Theory. 相似文献
11.
Eric?Harrelson Alexander?A.?Voronov J.?Javier?Zú?iga 《Letters in Mathematical Physics》2010,94(1):1-26
We set up a Batalin–Vilkovisky Quantum Master Equation (QME) for open-closed string theory and show that the corresponding
moduli spaces give rise to a solution, a generating function for their fundamental chains. The equation encodes the topological
structure of the compactification of the moduli space of bordered Riemann surfaces. The moduli spaces of bordered J-holomorphic curves are expected to satisfy the same equation, and from this viewpoint, our paper treats the case of the target
space equal to a point. We also introduce the notion of a symmetric Open-Closed Topological Conformal Field Theory (OC TCFT)
and study the L
∞ and A
∞ algebraic structures associated to it. 相似文献
12.
We establish a dynamical equivalence between the bosonic part of pure type I supergravity in D = 10 and a D = 1 non-linear σ-model on the Kac–Moody coset space DE
10/K(DE
10) if both theories are suitably truncated. To this end we make use of a decomposition of DE
10 under its regular SO(9,9) subgroup. Our analysis also deals partly with the fermionic fields of the supergravity theory and we define corresponding representations of the generalised spatial Lorentz group K(DE
10). 相似文献
13.
We construct unitary representations of (1,0) and (2,0) superconformal algebras in six dimensions by using superfields defined on harmonic superspaces with coset manifolds USp(2n)/[U(1)]n, n=1, 2. In the spirit of the AdS7/CFT6 correspondence, massless conformal fields correspond to supersingletons in AdS7. By tensoring them we produce all short representations corresponding to 1/2 and 1/4 BPS anti-de Sitter bulk states of which massless bulk representations are particular cases. 相似文献
14.
A new form of superselection sectors of topological origin is developed. By that it is meant a new investigation that includes
several extensions of the traditional framework of Doplicher, Haag and Roberts in local quantum theories. At first we generalize
the notion of representations of nets of C*–algebras, then we provide a brand new view on selection criteria by adopting one with a strong topological flavour. We prove
that it is coherent with the older point of view, hence a clue to a genuine extension. In this light, we extend Roberts’ cohomological
analysis to the case where 1–cocycles bear non-trivial unitary representations of the fundamental group of the spacetime,
equivalently of its Cauchy surface in the case of global hyperbolicity. A crucial tool is a notion of group von Neumann algebras
generated by the 1–cocycles evaluated on loops over fixed regions. One proves that these group von Neumann algebras are localized
at the bounded region where loops start and end and to be factorial of finite type I. All that amounts to a new invariant, in a topological sense, which can be defined as the dimension of the factor. We prove
that any 1–cocycle can be factorized into a part that contains only the charge content and another where only the topological
information is stored. This second part much resembles what in literature is known as geometric phases. Indeed, by the very
geometrical origin of the 1–cocycles that we discuss in the paper, they are essential tools in the theory of net bundles,
and the topological part is related to their holonomy content. At the end we prove the existence of net representations.
Dedicated to Klaus Fredenhagen on the occasion of his sixtieth birthday 相似文献
15.
Paul de Medeiros José Figueroa-O’Farrill Elena Méndez-Escobar Patricia Ritter 《Communications in Mathematical Physics》2009,290(3):871-902
Since the pioneering work of Bagger–Lambert and Gustavsson, there has been a proliferation of three-dimensional superconformal
Chern–Simons theories whose main ingredient is a metric 3-algebra. On the other hand, many of these theories have been shown
to allow for a reformulation in terms of standard gauge theory coupled to matter, where the 3-algebra does not appear explicitly.
In this paper we reconcile these two sets of results by pointing out the Lie-algebraic origin of some metric 3-algebras, including
those which have already appeared in three-dimensional superconformal Chern–Simons theories. More precisely, we show that
the real 3-algebras of Cherkis–S?mann, which include the metric Lie 3-algebras as a special case, and the hermitian 3-algebras
of Bagger–Lambert can be constructed from pairs consisting of a metric real Lie algebra and a faithful (real or complex, respectively)
unitary representation. This construction generalises and we will see how to construct many kinds of metric 3-algebras from
pairs consisting of a real metric Lie algebra and a faithful (real, complex or quaternionic) unitary representation. In the
real case, these 3-algebras are precisely the Cherkis–S?mann algebras, which are then completely characterised in terms of
this data. In the complex and quaternionic cases, they constitute generalisations of the Bagger–Lambert hermitian 3-algebras
and anti-Lie triple systems, respectively, which underlie N = 6 and N = 5 superconformal Chern–Simons theories, respectively. In the process we rederive the relation between certain types of
complex 3-algebras and metric Lie superalgebras. 相似文献
16.
Using the duality equations of Moore and Seiberg we define for every primary field in a Rational Conformal Field Theory a
proper Markov trace and hence a knot invariant. Next we define two nested algebras and show, using results of Ocneanu, how
the position of the smaller algebra in the larger one reproduces part of the duality data. A new method for constructing Rational
Conformal Field Theories is proposed. 相似文献
17.
We show that the duality properties of Rational Conformal Field Theories follow from the defining relations and the representation theory of quantum groups. The fusion and braiding matrices are q-analogues of the 6j-symbols and the modular transformation matrices are obtained from the properties of the co-multiplication. We study in detail the Wess-Zumino-Witten models and the rational gaussian models as examples, but carry out the arguments in general. We point out the connections with the Chern-Simons approach. We give general arguments of why the general solution to the polynomial equations of Moore and Seiberg describing the duality properties of Rational Conformal Field Theories defines a Quantum Group acting on the space of conformal blocks. A direct connection between Rational Theories and knot invariants is also presented along the lines of Jones' original work. 相似文献
18.
We analyze the polynomial part of the Iwasawa realization of the coset representative of non compact symmetric Riemannian spaces. We start by studying the role of Kostant's principal SU(2)P subalgebra of simple Lie algebras, and how it determines the structure of the nilpotent subalgebras. This allows us to compute the maximal degree of the polynomials for all faithful representations of Lie algebras. In particular the metric coefficients are related to the scalar kinetic terms while the representation of electric and magnetic charges is related to the coupling of scalars to vector field strengths as they appear in the Lagrangian. We consider symmetric scalar manifolds in ‐extended supergravity in various space‐time dimensions, elucidating various relations with the underlying Jordan algebras and normed Hurwitz algebras. For magic supergravity theories, our results are consistent with the Tits‐Satake projection of symmetric spaces and the nilpotency degree turns out to depend only on the space‐time dimension of the theory. These results should be helpful within a deeper investigation of the corresponding supergravity theory, e.g. in studying ultraviolet properties of maximal supergravity in various dimensions. 相似文献
19.
The mass spectrum of pure Yang–Mills theory in 3+1 dimensions is discussed for an arbitrary simple gauge algebra within a
quasigluon picture. The general structure of the low-lying gluelump and two-quasigluon glueball spectrum is shown to be common
to all algebras, while the lightest C=− three-quasigluon glueballs only exist when the gauge algebra is A
r≥2, that is, in particular,
\mathfraksu(N 3 3)\mathfrak{su}(N\geq3). Higher-lying C=− glueballs are shown to exist only for the A
r≥2, Dodd−r≥4 and E6 gauge algebras. The shape of the static energy between adjoint sources is also discussed assuming the Casimir scaling hypothesis
and a funnel form; it appears to be gauge-algebra dependent when at least three sources are considered. As a main result,
the present framework’s predictions are shown to be consistent with available lattice data in the particular case of an
\mathfraksu(N)\mathfrak{su}(N) gauge algebra within ’t Hooft’s large-N limit. 相似文献
20.