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1.
We classify two-dimensional local conformal nets with parity symmetry and central charge less than 1, up to isomorphism. The maximal ones are in a bijective correspondence with the pairs of A-D-E Dynkin diagrams with the difference of their Coxeter numbers equal to 1. In our previous classification of one-dimensional local conformal nets, Dynkin diagrams D
2n +1
and E
7
do not appear, but now they do appear in this classification of two-dimensional local conformal nets. Such nets are also characterized as two-dimensional local conformal nets with -index equal to 1 and central charge less than 1. Our main tool, in addition to our previous classification results for one-dimensional nets, is 2-cohomology vanishing for certain tensor categories related to the Virasoro tensor categories with central charge less than 1.Supported in part by JSPS.Supported in part by GNAMPA and MIUR. 相似文献
2.
A conformal optical system refers to the one whose first optical surface conforms to both aerodynamic and imaging requirements. Appropriate correction is required because a conformal dome induces significant aberrations. This paper intends to explain that an effective solution to the easy-fabrication conic surface corrector compensates aberrations induced by a coaxial aspheric dome. A conformal optical system with an ellipsoid MgF2 conformal dome, which has a fineness ratio of 2.0, is designed as an example. The field of regard angle is pm 30 degrees with a pm 2 degree instantaneous field of view. The system's ultimate value of modulation transfer function is close to the diffraction limit, which indicates that the performance of the conic conformal optical system with a fixed conic corrector meets the imaging requirements. 相似文献
3.
In this paper we further develop the theory of α-induction for nets of subfactors, in particular in view of the system of
sectors obtained by mixing the two kinds of induction arising from the two choices of braiding. We construct a relative braiding
between the irreducible subsectors of the two “chiral” induced systems, providing a proper braiding on their intersection.
We also express the principal and dual principal graphs of the local subfactors in terms of the induced sector systems. This
extended theory is again applied to conformal or orbifold embeddings of SU(n WZW models. A simple formula for the corresponding modular invariant matrix is established in terms of the two inductions,
and we show that it holds if and only if the sets of irreducible subsectors of the two chiral induced systems intersect minimally
on the set of marked vertices, i.e. on the “physical spectrum” of the embedding theory,
or if and only if the canonical endomorphism sector of the conformal or orbifold inclusion subfactor is in the full induced
system. We can prove either condition for all simple current extensions of SU
(
n
) and many conformal inclusions, covering in particular all type I modular invariants of SU(2) and SU(3), and we conjecture that it holds also for any other conformal inclusion of SU
(
n
) as well. As a by-product of our calculations, the dual principal graph for the conformal inclusion SU(3)5⊂SU(6)1 is computed for the first time.
Received: 24 December 1998 / Accepted: 22 February 1999 相似文献
4.
Michael J. Markowitz 《General Relativity and Gravitation》1982,14(12):1095-1105
A space-timeM is said to be conformally hyperbolic if the intrinsic conformal Lorentz pseudodistanced
M
is a true distance. In this paper we first derive criteria which insure the conformal hyperbolicity of certain space-times which are generalizations of the Robertson-Walker spaces. Thend
M
is determined explicitly for Einstein-de Sitter space, and important cosmological model.Author partially supported by NSF Grant No. MCS 80-03573. 相似文献
5.
We investigate the propagation equations for the expansion, vorticity and shear for perfect fluid space-times which are geodesic.
It is assumed that space-time admits a conformal Killing vector which is inheriting so that fluid flow lines are mapped conformally.
Simple constraints on the electric and magnetic parts of the Weyl tensor are found for conformal symmetry. For homothetic
vectors the vorticity and shear are free; they vanish for nonhomothetic vectors. We prove a conjecture for conformal symmetries
in the special case of inheriting geodesic flows: there exist no proper conformal Killing vectors (ψ
;ab
≠ 0) for perfect fluids except for Robertson-Walker space-times. For a nonhomothetic vector field the propagation of the
quantity ln (R
ab
u
a
u
b
) along the integral curves of the symmetry vector is homogeneous. 相似文献
6.
'The one-loop effective action (EA) with an accuracy up to linear curvature terms ind=4R
2-gravity, conformal gravity, andN=1,d=4 conformal supergravity on the backgroundR
4×T4–k,k=1, 2, 3 is calculated. (Here,R
k is thek-dimensional curved space, Tn is then-dimensional torus). The one-loop EA in multidimensionalR
2-gravity and ind=10 conformal supergravity on the backgroundR
4 ×T
d–4 is also obtained. The mechanism of inducing the Einstein gravity from the EA of considered theories of higher derivative (super)gravity is presented.We are grateful to I. L. Bukhbinder for the numerous discussions of considered questions. 相似文献
7.
We investigate quantum deformation of conformal algebras by constructing the quantum space forsl
q
(4). The differential calculus on the quantum space and the action of the quantum generators are studied. We derive deformedsu(2,2) algebra from the deformedsl(4) algebra using the quantum 4-spinor and its conjugate spinor. The quantum 6-vector inso
q
(4,2) is constructed as a tensor product of two sets of 4-spinors. We obtain theq-deformed conformal algebra with the suitable assignment of the generators which satisfy the reality condition. The deformed Poincaré algebra is derived through a contraction procedure.Work partially supported by the Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture (#030083) 相似文献
8.
In this paper we construct a newN = 6 superconformal algebra which extends the Virasoro algebra by theSO
6 current algebra, by 6 odd primary fields of conformal weight 3/2 and by 10 odd primary fields of conformal weight 1/2. The
commutation relations of this algebra, which we will refer to asCK
6, are represented by short distance operator product expansions (OPE). We constructCK
6, as a subalgebra of theSO(6) superconformal algebra K6, thus giving it a natural representation as first order differential operators on the circle withN = 6 extended symmetry. We show thatCK
6 has no nontrivial central extensions.
Partially supported by NSC grant 85-2121-M-006-019 of the ROC.
Partially supported by NSF grant DMS-9622870. 相似文献
9.
《Nuclear Physics B》1999,539(3):643-670
The conformal anomaly for 4D gravity-matter theories, which are non-minimally coupled with the dilaton, is systematically studied. Special care is taken of rescaling of fields, treatment of total derivatives, hermiticity of the system operator and the choice of measure. Scalar, spinor and vector fields are taken as the matter quantum fields and their explicit conformal anomalies in the gravity-dilaton background are found. The cohomology analysis is carried out and some new conformal invariants and trivial terms, involving the dilaton, are obtained. The symmetry of the constant shift of the dilaton field plays an important role. The general structure of the conformal anomaly is examined. It is shown that the dilaton affects the conformal anomaly characteristically for each case: (1) [Scalar] The dilaton changes the conformal anomaly only by a new conformal invariant, I4; (2) [Spinor] The dilaton does not change the conformal anomaly; (3) [Vector] The dilaton changes the conformal anomaly by three new (generalized) conformal invariants, I4, I2, I1. We present some new anomaly formulae which are useful for practical calculations. Finally, the anomaly induced action is calculated for the dilatonic Wess-Zumino model. We point out that the coefficient of the total derivative term in the conformal anomaly for the 2D scalar coupled to a dilaton is ambiguous. This resolves the disagreement between earlier calculations and the result of Hawking and Bousso. 相似文献
10.
Simonetta Frittelli Carlos Kozameh Ezra T. Newman 《Communications in Mathematical Physics》2001,223(2):383-408
We first show how, from the general 3rd order ODE of the form , one can construct a natural Lorentzian conformal metric on the four-dimensional space . When the function satisfies a special differential condition the conformal metric possesses a conformal Killing field, , which in turn, allows the conformal metric to be mapped into a three dimensional Lorentzian metric on the space ) or equivalently, on the space of solutions of the original differential equation. This construction is then generalized
to the pair of differential equations, z
ss
=S(z,z
s
,z
t
,z
st
,s,t) and z
tt
=T(z,z
s
,z
t
,z
st
,s,t), with z
s
and z
t
the derivatives of z with respect to s and t. In this case, from S and T, one can again, in a natural manner, construct a Lorentzian conformal metric on the six dimensional space (z,z
s
,z
t
,z
st
,s,t). When the S and T satisfy differential conditions analogous to those of the 3rd order ode, the 6-space then possesses a pair of conformal Killing fields, and which allows, via the mapping to the four-space of (z,z
s
,z
t
,z
st
) and a choice of conformal factor, the construction of a four-dimensional Lorentzian metric. In fact all four-dimensional
Lorentzian metrics can be constructed in this manner. This construction, with further conditions on S and T, thus includes all (local) solutions of the Einstein equations.
Received: 10 October 2000 / Accepted: 26 June 2001 相似文献
11.
Bo-wei Xu 《Foundations of Physics》1993,23(2):329-339
In this article we present a brief review of the conformal symmetry and the two-dimensional conformal quantum field theories. As concrete applications of the conformal theories to the critical phenomena in statistical systems, we calculate the value of central charge and the anomalous scale dimensions of the Z
2
symmetric quantum chain with boundary condition. The results are compatible with the prediction of the conformal field theories. 相似文献
12.
Starting from an abelian rigid braided monoidal category C{\mathcal{C}} we define an abelian rigid monoidal category CF{\mathcal{C}_F} which captures some aspects of perturbed conformal defects in two-dimensional conformal field theory. Namely, for V a rational vertex operator algebra we consider the charge-conjugation CFT constructed from V (the Cardy case). Then C = Rep(V){\mathcal{C} = {\rm Rep}(V)} and an object in CF{\mathcal{C}_F} corresponds to a conformal defect condition together with a direction of perturbation. We assign to each object in CF{\mathcal{C}_F} an operator on the space of states of the CFT, the perturbed defect operator, and show that the assignment factors through
the Grothendieck ring of CF{\mathcal{C}_F}. This allows one to find functional relations between perturbed defect operators. Such relations are interesting because
they contain information about the integrable structure of the CFT. 相似文献
13.
A. L. Kataev 《JETP Letters》2012,94(11):789-794
The generalized Crewther relations in the channels of the non-singlet and vector quark currents are considered. These relations
follow from the double application of the operator product expansion approach to the same axial vector-vector-vector triangle
amplitude in two regions, adjoining to the angle sides (x, y) (or p
2, q
2). We assume that the generalized Crewther relations in these two kinematic regimes result in the existence of the same perturbation
expression for two products of the coefficient functions of annihilation and deepinelastic scattering processes in the non-singlet
and vector channels. This feature explains the conformal symmetry motivated cancellations between the singlet α
s
3 corrections to the Gross-Llewellyn Smith sum rule S
GLS of νN deep inelastic scattering and the singlet α
s
3 correction to the e
+
e
−-annihilation Adler function D
A
V
in the product of the corresponding perturbative series. Taking into account the Baikov-Chetyrkin-Kuhn fourth order result
for S
GLS and the perturbative effects of the violation of the conformal symmetry in the generalized Crewther relation, we obtain the
analytical contribution to the singlet α
s
4 correction to the D
A
V
function. Its a-posteriori comparison with the recent result of direct diagram-by-diagram evaluation of the singlet fourth
order corrections to D
A
V
function demonstrates the coincidence of the predicted and obtained ζ32-contributions to the singlet term. They can be obtained in the conformal invariant limit from the original Crewther relation.
Therefore, on the contrary to previous belief, the appearance of ζ3-terms in the perturbative series in quantum field theory gauge models does not contradict to the property of the conformal
symmetry and can be considered as regular feature. The Banks-Zaks motivated relation between our predicted and the obtained
directly fourth order corrections is mentioned. It confirms the expectation, previously made by Baikov-Chetykin-Kuhn, that
at the 5-loop level the generalized Crewther relation in the channel of vector currents may receive additional singlet contribution,
which in this order of perturbation theory is proportional to the first coefficient of the QCD β function. 相似文献
14.
Vl. S. Dotsenko 《Journal of statistical physics》1984,34(5-6):781-791
The conformal algebra for operators of theZ
3 model at the phase transition point is built. Critical exponents are found in this approach as solutions of simple algebraic equations, which are consistency conditions of the algebra. Multipoint correlation functions obey linear differential equations. Some solutions are given for the four-point correlation functions of theZ
3 model at the phase transition point. 相似文献
15.
R. K. Kaul 《Communications in Mathematical Physics》1994,162(2):289-319
A method to obtain explicit and complete topological solution of SU(2) Chern-Simons theory onS
3 is developed. To this effect the necessary aspects of the theory of coloured-oriented braids and duality properties of conformal blocks for the correlators ofSU(2)
k
Wess-Zumino conformal field theory are presented. A large class of representations of the generators of the groupoid of coloured-oriented braids are obtained. These provide a whole lot of new link invariants of which Jones polynomials are the simplest examples. These new invariants are explicity calculated as illustrations for knots up to eight crossings and twocomponent multicoloured links up to seven crossings. 相似文献
16.
Height Fluctuations in the Honeycomb Dimer Model 总被引:1,自引:0,他引:1
Richard Kenyon 《Communications in Mathematical Physics》2008,281(3):675-709
We study a model of random surfaces arising in the dimer model on the honeycomb lattice. For a fixed “wire frame” boundary
condition, as the lattice spacing ϵ → 0, Cohn, Kenyon and Propp [3] showed the almost sure convergence of a random surface to a non-random limit shape Σ0. In [12], Okounkov and the author showed how to parametrize the limit shapes in terms of analytic functions, in particular
constructing a natural conformal structure on them. We show here that when Σ0 has no facets, for a family of boundary conditions approximating the wire frame, the large-scale surface fluctuations (height
fluctuations) about Σ0 converge as ϵ → 0 to a Gaussian free field for the above conformal structure. We also show that the local statistics of the fluctuations
near a given point x are, as conjectured in [3], given by the unique ergodic Gibbs measure (on plane configurations) whose slope is the slope
of the tangent plane of Σ0 at x. 相似文献
17.
《Fortschritte der Physik》2017,65(5)
According to the dS/CFT correspondence, correlators of fields generated during a primordial de Sitter phase are constrained by three‐dimensional conformal invariance. Using the properties of radially quantized conformal field theories and the operator‐state correspondence, we glean information on some points. The Higuchi bound on the masses of spin‐s states in de Sitter is a direct consequence of reflection positivity in radially quantized CFT3 and the fact that scaling dimensions of operators are energies of states. The partial massless states appearing in de Sitter correspond from the boundary CFT3 perspective to boundary states with highest weight for the conformal group. Finally, we discuss the inflationary consistency relations and the role of asymptotic symmetries which transform asymptotic vacua to new physically inequivalent vacua by generating long perturbation modes. We show that on the CFT3 side, asymptotic symmetries have a nice quantum mechanics interpretation. For instance, acting with the asymptotic dilation symmetry corresponds to evolving states forward (or backward) in “time” and the charge generating the asymptotic symmetry transformation is the Hamiltonian itself. 相似文献
18.
We propose a procedure for computing the boundary stress tensor associated with a gravitating system in asymptotically anti-de
Sitter space. Our definition is free of ambiguities encountered by previous attempts, and correctly reproduces the masses
and angular momenta of various spacetimes. Via the AdS/CFT correspondence, our classical result is interpretable as the expectation
value of the stress tensor in a quantum conformal field theory. We demonstrate that the conformal anomalies in two and four
dimensions are recovered. The two dimensional stress tensor transforms with a Schwarzian derivative and the expected central
charge. We also find a nonzero ground state energy for global AdS5, and show that it exactly matches the Casimir energy of the dual super Yang–Mills theory on S
3×R.
Received: 20 April 1999 / Accepted: 8 July 1999 相似文献
19.
Feng Xu 《Communications in Mathematical Physics》1998,192(2):349-403
Various puzzles about subfactors and integrable lattice models associated with conformal inclusions are resolved in the framework
of constructive quantum field theory in two dimensions. In particular, a new class of braided endomorphisms are obtained for
a general class of conformal inclusions and their properties are analyzed. The existence of subfactors with principal graphs
E
6 or E
8 follows from a rather simple argument in our construction. The fusion graphs of many new examples are given.
Received: 12 September 1996 / Accepted: 3 July 1997 相似文献
20.
O. Babelon 《Communications in Mathematical Physics》1991,139(3):619-643
We derive a universal formula for the exchange algebra in the Bloch wave basis. The main tool we use is a lattice version of the Coulomb gas picture of conformal field theory, making its quantum group structure explicit from the very beginning. Calulations are then reduced to a factorization problem inU
q
(sl
2). 相似文献