Using the recently developed notion of a fractional Virasoro algebra, we explore the implied operator product expansions in nonlocal conformal field theories and their geometric meaning. We probe the interplay between classical nonlocality in the functional-analytic sense and quantization in a two-dimensional setting and find that nonlocal quantum dynamics realize this fractional Virasoro algebra exclusively with a state dependent central charge. Notably, we prove that the widely studied free Gaussian fixed points with a fractional Laplacian kinetic term does not fit this criterion but that the RG flow associated non-Gaussian fixed points do.
We study the symmetry of the class of nonlocal models which includes the nonlocal extension of the Pais-Uhlenbeck oscillator. As a consequence, we obtain an infinite dimensional symmetry algebra, containing the Virasoro algebra, which can be considered as a generalization of the non-relativistic conformal symmetries to the infinite order. Moreover, this nonlocal extension resembles to some extent the string model and on the quantum level it leads to the centrally extended Virasoro algebra.
We construct Euclidean Liouville conformal field theories in odd number of dimensions. The theories are nonlocal and non-unitary with a log-correlated Liouville field, a ${\cal Q}$-curvature background, and an exponential Liouville-type potential. We study the classical and quantum properties of these theories including the finite entanglement entropy part of the sphere partition function $F$, the boundary conformal anomaly and vertex operators' correlation functions. We derive the analogue of the even-dimensional DOZZ formula and its semi-classical approximation.
We study two nonlinear extensions of the nonlocal $R\,\Box^{-2}R$ gravity theory. We extend this theory in two different ways suggested by conformal symmetry, either replacing $\Box^{-2}$ with $(-\Box + R/6)^{-2}$, which is the operator that enters the action for a conformally-coupled scalar field, or replacing $\Box^{-2}$ with the inverse of the Paneitz operator, which is a four-derivative operator that enters in the effective action induced by the conformal anomaly. We show that the former modification gives an interesting and viable cosmological model, with a dark energy equation of state t…
We investigate the gravitational backreaction, generated by coupling a general conformal sector to external, classical gravity, as described by a conformal anomaly effective action. We address the issues raised by the regularization of the topological Gauss-Bonnet and Weyl terms in these actions and the use of dimensional regularization (DR). We discuss both their local and nonlocal expressions, as possible IR and UV descriptions of conformal theories, below and above the conformal breaking scale. Our discussion overlaps with several recent studies of dilaton gravities - obtained via a certain…
We consider CFT states defined by adding nonlocal multi-trace sources to the Euclidean path integral defining the vacuum state. For holographic theories, we argue that these states correspond to states in the gravitational theory with a good semiclassical description but with a more general structure of bulk entanglement than states defined from single-trace sources. We show that at leading order in large N, the entanglement entropies for any such state are precisely the same as those of another state defined by appropriate single-trace effective sources; thus, if the leading order entanglemen…
The general solution of the conformal Ward identities (CWI's) in momentum space, and their matching to perturbation theory, allows to uncover some specific characteristics of the breaking of conformal symmetry, induced by the anomaly. It allows to compare perturbative features of the 1-particle irreducible (1PI, nonlocal) anomaly action with the prediction of a similar (but exact) nonlocal action identified by the CWI's. The two predictions can be exactly matched at the level of 3-point functions. The analysis of the $TJJ$ and $TTT$ shows that both approaches - based either on 1PI or on the ex…
We show that a class of previously defined maps, called self-dual and causal morphisms, form classical symmetries of Yang-Mills fields in four complex dimensions. These maps generalize conformal transformations, and admit a nonlocal pullback connection that preserves the equations of the theory. First it is shown that self-dual morphisms form symmetries of the anti-self-dual Yang-Mills equations under this pullback. Then a supersymmetric generalization of causal morphisms is defined, which preserves solutions of the field equations for N=3 supersymmetric Yang-Mills theory. As a special case, t…
在c=-1玻色子鬼系统和c=2复标量理论之间建立了一个“正则映射”，在c=-2费米子鬼系统和c=1狄拉克理论之间建立了一个类似的映射。这种映射的存在是由各自理论的特征的同一性所暗示的。各个c <0 and c>0理论共享相同的状态空间，而共形场的空间是不同的。在c<0对应物的这种映射上，（c>0）复标量和狄拉克理论继承了隐藏的非定域sl（2）对称性。
We argue that every CFT contains light-ray operators labeled by a continuous spin J. When J is a positive integer, light-ray operators become integrals of local operators over a null line. However for non-integer J, light-ray operators are genuinely nonlocal and give the analytic continuation of CFT data in spin described by Caron-Huot. A key role in our construction is played by a novel set of intrinsically Lorentzian integral transforms that generalize the shadow transform. Matrix elements of light-ray operators can be computed via the integral of a double-commutator against a conformal bloc…
We compute the gravitational effective action by integrating out quantum matter fields in a weak gravitational field, using the Schwinger-Keldysh (in-in) formalism. We pay particular attention to the role of the initial quantum state in the structure of the nonlocal terms in the effective action, with an eye to nonlinear completions of the theory that may be relevant in astrophysics and cosmology. In this first paper we consider a quantum scalar field in thermal equilibrium, in a stationary gravitational field. We obtain a covariant expression for the nonlocal effective action, that can be exp…
Anomaly-mediated Scalar Gravitational Interactions and the Coupling of Conformal Sectors
Dipartimento di Matematica e Fisica, Università del Salento（萨伦托大学数学与物理系）；INFN Sezione di Lecce（意大利国家核物理研究所莱切分部）；National Center for HPC, Big Data and Quantum Computing（高性能计算、大数据与量子计算国家中心）；CNR-nanotec, Lecce（国家研究委员会纳米技术研究所莱切分部）
We present a comprehensive discussion of renormalisation of 3-point functions of scalar operators in conformal field theories in general dimension. We have previously shown that conformal symmetry uniquely determines the momentum-space 3-point functions in terms of certain integrals involving a product of three Bessel functions (triple-K integrals). The triple-K integrals diverge when the dimensions of operators satisfy certain relations and we discuss how to obtain renormalised 3-point functions in all cases. There are three different types of divergences: ultralocal, semilocal and nonlocal, …
We give a solution to the long-standing problem of constructing the generators of hidden symmetries of the quantum Higgs oscillator, a particle on a d-sphere moving in a central potential varying as the inverse cosine-squared of the polar angle. This superintegrable system is known to possess a rich algebraic structure, including a hidden SU(d) symmetry that can be deduced from classical conserved quantities and degeneracies of the quantum spectrum. The quantum generators of this SU(d) have not been constructed thus far, except at d=2, and naive quantization of classical conserved quantities l…
Indian Institute of Science Education and Research（印度科学教育与研究机构）；Indian Institute of Technology Indore（印多尔印度理工学院）；Indian Institute of Technology, Hyderabad（海得拉巴印度理工学院）
Recently, entropy corrections on nonorientable manifolds such as the Klein bottle are proposed as a universal characterization of critical systems with an emergent conformal field theory (CFT). We show that entropy correction on the Klein bottle can be interpreted as a boundary effect via transforming the Klein bottle into an orientable manifold with nonlocal boundary interactions. The interpretation reveals the conceptual connection of the Klein bottle entropy with the celebrated Affleck-Ludwig entropy in boundary CFT. We propose a generic scheme to extract these universal boundary entropies …
The effective action in gauge theories is known to depend on a choice of gauge fixing conditions. This dependence is such that any change of gauge conditions is equivalent to a field redefinition in the effective action. In this sense, the quantum deformation of conformal symmetry in the N = 4 super Yang-Mills theory, which was computed in 't Hooft gauge in hep-th/9808039 and hep-th/0203236, is gauge dependent. The deformation is an intrinsic property of the theory in that it cannot be eliminated by a local choice of gauge (although we sketch a field redefinition induced by a nonlocal gauge wh…
We consider a nonlocal scalar field theory inspired by the tachyon action in open string field theory. The Lorentz-covariant action is characterized by a parameter $ξ^2$ that quantifies the amount of nonlocality. Restricting to purely time-dependent configurations, we show that a field redefinition perturbative in $ξ^2$ reduces the action to a local two-derivative theory with a $ξ^2$-dependent potential. This picture is supported by evidence that the redefinition maps the wildly oscillating rolling tachyon solutions of the nonlocal theory to conventional rolling in the new scalar potential. Fo…
We briefly review the current status of nonlocal gravity (NLG), which is a classical nonlocal generalization of Einstein's theory of gravitation based on a certain analogy with the nonlocal electrodynamics of media. Nonlocal gravity thus involves integro-differential field equations and a causal constitutive kernel that should ultimately be determined from observational data. We consider the stationary gravitational field of an isolated rotating astronomical source in the linear approximation of nonlocal gravity. In this weak-field and slow-motion approximation of NLG, we describe the gravitom…
在不假设任何kappa规范固定的情况下，构造了AdS 5 × S 5共形规范空间中IIB超弦的无穷多个守恒非定域荷，并证明了它们满足超Yangian代数.所得的代数与我们以前的工作相同，其中假设一个特殊的规范，使得Noether流满足平坦性条件。然而，AdS空间上超弦的Noether流的平坦性条件一般是不成立的。我们发现，反常的贡献被吸收到当前的费米子约束起着至关重要的作用，和由此产生的保守的非局域电荷有不同的表达式满足相同的超杨代数。
The invariance of physical observables like particle's mass under a local field redefinition is a well-known and important property of quantum field theory. In this paper, on the other hand, we investigate nonlocal field redefinitions eliminating a physical observable from a theory. Indeed, by giving explicit examples, we present invertible nonlocal field redefinitions reducing a massive theory to the massless one, and vice versa. The studied examples are: classical harmonic oscillator, the scalar field theory, and the Dirac field theory.
We prove in two ways that, for a special class of nonlocal field theories consistent with linear and non-linear stability at the classical level, and with unitarity and super-renormalizability or finiteness at the quantum level, the $n$-point tree-level scattering amplitudes are the same as those of the underlying local theory. In particular, the $n$-point amplitudes of nonlocal gravity, with or without coupling to matter, are the same as for Einstein's general relativity.
In this paper, we study the Casimir force for a class of Lorentzian nonlocal field theories. These theories include a continuum of massive excitations. In this regard, the effect of continuum massive modes on Casimir force is of interest. We focus on the simplest case of two absorbing parallel planes in 1+1 dimensions, and we show that unlike local field theories, the thickness of the absorbing "walls" changes the value of Casimir force.
