Constraints for anomalous dimensions of local light-cone operators in [ϕ 3]6 theory

Using the MS scheme, we derive in [? ³]₆ theory the collinear conformal Ward identity for the Green's functions of local light-cone operators of leading twist. The Ward identity for special collinear conformal transformations and renormalization group invariance give constraints for the off-diagonal part of the anomalous dimension matrix for the general case of β#0. We compute the anomaly of special conformal transformation in lowest loop order and obtain from the constraints the off-diagonal part of the anomalous dimension in 2-loop order.     

Higher-spin gauge and trace anomalies in two-dimensional backgrounds

Two-dimensional quantum fields in electric and gravitational backgrounds can be described by conformal field theories, and hence all the physical (covariant) quantities can be written in terms of the corresponding holomorphic quantities. In this paper, we first derive relations between covariant and holomorphic forms of higher-spin currents in these backgrounds, and then, by using these relations, obtain higher-spin generalizations of the trace and gauge (or gravitational) anomalies up to spin 4. These results are applied to derive higher-moments of Hawking fluxes in black holes in a separate paper [S. Iso, T. Morita, H. Umetsu, Hawking radiation via higher-spin gauge anomalies, arXiv: 0710.0456 [hep-th]].     

Partition functions and physical states in two-dimensional quantum gravity and supergravity

We review the Liouville theory calculation of the genus-one path integral for c 1 conformal models coupled to two-dimensional gravity. From the modular integrand we derive the existence of an infinite number of physical operators which are in one-to-one correspondence with the conformal primary fields and null states of the matter theory. We also calculate the torus path integral and find the spectrum of physical operators for superconformal models coupled to supergravity. The amplitude in the odd spin structure requires a special treatment and is found to be proportional to the Witten index of the matter theory.     

Chiral and conformal anomalies in lattice gauge theory

The continuum limit of the chiral and conformal (Weyl) Ward-Takahashi identities in the lattice Wilson action is studied. The Wilson term works for the chiral anomaly, but it gives rise to-15 times the conventional conformal anomaly for a smallr-parameter and a very sensitiver-dependence of the Λ-parameter. This shows that the strong symmetry breaking by the Wilson term by itself does not necessarily generate correct anomalies. In the lattice regularization the functional Jacobian factors becomec-numbers and do not contribute to anomalies, corresponding to the cut-off of short distance components; the naive continuum limit of lattice WT identities can thus behave differently from continuum ones. To reconstruct conventional identities from lattice relations, the lattice composite operators should be rewritten in terms of relevant continuum operators. In general, this identification of relevant operators is facilitated either by the procedure corresponding to Zimmermann's normal product algorithm or simply by the use of auxiliary regulators such as the dimensional regulator.     

Hard exclusive meson production and nonforward parton distributions

We present an analysis of twist-2, leading order QCD amplitudes for hard exclusive leptoproduction of mesons in terms of double/nonforward parton distribution functions. After reviewing some general features of nonforward nucleon matrix elements of twist-2 QCD string operators, we propose a phenomenological model for quark and gluon nonforward distribution functions. The corresponding QCD evolution equations are solved in the leading logarithmic approximation for flavor nonsinglet distributions. We derive explicit expressions for hard exclusive , , and neutral vector meson production amplitudes and discuss general features of the corresponding cross sections. Received: 12 November 1997 / Published online: 26 February 1998     

Light-cone distribution amplitudes of the ground state bottom baryons in HQET

We prove the existence of hidden symmetries in the general relativity theory defined by exact solutions with generic off-diagonal metrics, nonholonomic (non-integrable) constraints, and deformations of the frame and linear connection structure. A special role in characterization of such spacetimes is played by the corresponding nonholonomic generalizations of Stackel–Killing and Killing–Yano tensors. There are constructed new classes of black hole solutions and we study hidden symmetries for ellipsoidal and/or solitonic deformations of “prime” Kerr–Sen black holes into “target” off-diagonal metrics. In general, the classical conserved quantities (integrable and not-integrable) do not transfer to the quantized systems and produce quantum gravitational anomalies. We prove that such anomalies can be eliminated via corresponding nonholonomic deformations of fundamental geometric objects (connections and corresponding Riemannian and Ricci tensors) and by frame transforms.     

Why dilatation generators do not generate dilatations

We show that the Ward identities associated with broken scale invariance contain anomalies in renormalized perturbation theory. In low orders, these anomalies can be absorbed into a redefinition of the scale dimensions of the fields in the theory, but in higher orders this is not possible. Also, these anomalies cannot be removed by studying the Green's functions for objects other than canonical fields, e.g., currents. These results are established to first nontrivial order in perturbation theory by explicit Feynman calculations (which give us information at all momentum transfers), and in higher orders by the method of Callan and Symanzik (which gives information only at zero momentum transfer). The two approaches are consistent within their common domain of validity. Two appendices contain self-contained treatments of the formal canonical theory of scale and conformal transformations and of the derivation of Ward identities. In another appendix, we derive the Callan-Symanzik equations for Green's functions of currents, and show that no redefinition of scale dimension is necessary for these objects, although the other anomalies remain.     

Conformal Operators on Forms and Detour Complexes on Einstein Manifolds

For even dimensional conformal manifolds several new conformally invariant objects were found recently: invariant differential complexes related to, but distinct from, the de Rham complex (these are elliptic in the case of Riemannian signature); the cohomology spaces of these; conformally stable form spaces that we may view as spaces of conformal harmonics; operators that generalise Branson’s Q-curvature; global pairings between differential form bundles that descend to cohomology pairings. Here we show that these operators, spaces, and the theory underlying them, simplify significantly on conformally Einstein manifolds. We give explicit formulae for all the operators concerned. The null spaces for these, the conformal harmonics, and the cohomology spaces are expressed explicitly in terms of direct sums of subspaces of eigenspaces of the form Laplacian. For the case of non-Ricci flat spaces this applies in all signatures and without topological restrictions. In the case of Riemannian signature and compact manifolds, this leads to new results on the global invariant pairings, including for the integral of Q-curvature against the null space of the dimensional order conformal Laplacian of Graham et al.     

Long-range SL(2) Baxter equation in N=4 super-Yang–Mills theory

Relying on a few lowest order perturbative calculations of anomalous dimensions of gauge invariant operators built from holomorphic scalar fields and an arbitrary number of covariant derivatives in maximally supersymmetric gauge theory, we propose an all-loop generalization of the Baxter equation which determines their spectrum. The equation does not take into account wrapping effects and is thus asymptotic in character. We develop an asymptotic expansion of the deformed Baxter equation for large values of the conformal spin and derive an integral equation for the cusp anomalous dimension.     

SEMIDISCRETE INTEGRABLE NONLINEAR SYSTEMS GENERATED BY THE NEW FOURTH-ORDER SPECTRAL OPERATOR: LOCAL CONSERVATION LAWS

Starting with the semidiscrete integrable nonlinear Schrödinger system on a zigzag-runged ladder lattice we have presented the generalization and an essentially off-diagonal enlargement of its spectral operator which in the framework of zero-curvature equation allows to generate at least two new types of semidiscrete integrable nonlinear systems. The two types of evolutionary operators consistent with the extended spectral operator are proposed. In order to fix arbitrary sampling functions in each type of evolution operators we have to rely upon a restricted collection of lowest local conservation laws whose local densities are independent on the type of admissible evolution operators. For this purpose the modified procedure of seeking the infinite hierarchy of local conservation laws based upon several distinct generating functions has been developed and some lowest local conservation laws have been explicitly obtained.     

Quantum constraint algebra for a closed bosonic string in a gravitational and dilaton background

We derive the quantum constraint algebra for a closed bosonic string moving in a gravitational and dilaton background to first order in '. The hamiltonian approach is used to directly compute the quantum constraint commutators and calculate the c-and q-number anomalies that arise at the quantum level. The requirement that the algebra preserves the conformal invariance leads to the known background field equations.     

Classical and quantum conformal field theory

We define chiral vertex operators and duality matrices and review the fundamental identities they satisfy. In order to understand the meaning of these equations, and therefore of conformal field theory, we define the classical limit of a conformal field theory as a limit in which the conformal weights of all primary fields vanish. The classical limit of the equations for the duality matrices in rational field theory together with some results of category theory, suggest that (quantum) conformal field theory should be regarded as a generalization of group theory.On leave of absence from the Department of Physics, Weizmann Institute of Science, Rehovot 76100, Israel     

The second order spin-2 system in flat space near space-like and null-infinity

In previous work, the numerical solution of the linearized gravitational field equations near space-like and null-infinity was discussed in the form of the spin-2 zero-rest-mass equation for the perturbations of the conformal Weyl curvature. The motivation was to study the behavior of the field and properties of the numerical evolution of the system near infinity using Friedrich’s conformal representation of space-like infinity as a cylinder. It has been pointed out by H.O. Kreiss and others that the numerical evolution of a system using second order wave equations has several advantages compared to a system of first order equations. Therefore, in the present paper we derive a system of second order wave equations and prove that the solution spaces of the two systems are the same if appropriate initial and boundary data are given. We study the properties of this system of coupled wave equations in the same geometric setting and discuss the differences between the two approaches.     

Sweeping from the superfluid to the Mott phase in the Bose-Hubbard model

We study the sweep through the quantum phase transition from the superfluid to the Mott state for the Bose-Hubbard model with a time-dependent tunneling rate J(t). In the experimentally relevant case of exponential decay J(t) proportional variant e -gamma t, an adapted mean-field expansion for large fillings n yields a scaling solution for the fluctuations. This enables us to analytically calculate the evolution of the number and phase variations (on-site) and correlations (off-site) for slow (gammamu) sweeps, where mu is the chemical potential. Finally, we derive the dynamical decay of the off-diagonal long-range order as well as the temporal shrinkage of the superfluid fraction in a persistent ring-current setup.     

Conformally and Projective Covariant Differential Operators

Motivated by the structure of conformal anomalies in two-dimensional gravity and its generalizations, the projective and conformal covariance properties of linear, bilinear and trilinear differential operators are investigated in some detail and the triviality of the covariant trilinear operators is demonstrated.     

Cosmological unparticle correlators

We introduce and study an extension of the correlator of unparticle matter operators in a cosmological environment. Starting from FRW spaces we specialize to a de Sitter space–time and derive its inflationary power spectrum which we find to be almost flat. We finally investigate some consequences of requiring the existence of a unitary boundary conformal field theory in the framework of the dS/CFT correspondence.     

Toward classification of conformal theories

By studying the representations of the mapping class groups which arise in 2D conformal theories we derive some restrictions on the value of the conformal dimension h_i of operators and the central charge c of the Virasoro algebra. As a simple application we show that when there are a finite number of operators in the conformal algebra, the h_i and c are all rational.     

Vertex Operators in 4D Quantum Gravity Formulated as CFT

We study vertex operators in 4D conformal field theory derived from quantized gravity, whose dynamics is governed by the Wess-Zumino action by Riegert and the Weyl action. Conformal symmetry is equal to diffeomorphism symmetry in the ultraviolet limit, which mixes positive-metric and negative-metric modes of the gravitational field and thus these modes cannot be treated separately in physical operators. In this paper, we construct gravitational vertex operators such as the Ricci scalar, defined as space-time volume integrals of them are invariant under conformal transformations. Short distance singularities of these operator products are computed and it is shown that their coefficients have physically correct signs. Furthermore, we show that conformal algebra holds even in the system perturbed by the cosmological constant vertex operator as in the case of the Liouville theory shown by Curtright and Thorn.     

Affine <Emphasis Type="Italic">SL</Emphasis>(2) Conformal Blocks from 4d Gauge Theories

We study Nekrasov’s instanton partition function of four-dimensional N=2{\mathcal{N}=2} gauge theories in the presence of surface operators. This can be computed order by order in the instanton expansion by using results available in the mathematical literature. Focusing in the case of SU(2) quiver gauge theories, we find that the results agree with a modified version of the conformal blocks of affine SL(2) algebra. These conformal blocks provide, in the critical limit, the eigenfunctions of the corresponding quantized Hitchin Hamiltonians.     

SO(4) Symmetry and Off-Diagonal Long-Range Order in the Hubbard Bilayer

Yang's η pairing operator is generalized to explore off-diagonal long-range order in the Hubbard bilayer with an arbitrary chemical potential. With this operator and a constraint condition on annihilation and creation operators, we construct explicitly eigenstates which possess simultaneously three kinds of off-diagonal long-range order, i.e., the intralayer one and the interlayer one for on-site pairing, and that for interlayer nearest-neighbor pairing. As in the simple Hubbard model there is also an SO(4) symmetry, with the generators properly defined. A sufficient condition leads to at least one of the above three kinds of off-diagonal long-range order. A constraint relation among different kinds of off-diagonal long-range order is also given. There exists a triplet of collective modes if the U(1) symmetry of a subgroup is spontaneously broken.