Light-like noncommutativity,light-front quantization and new light on UV/IR mixing

We revisit the problem of quantizing field theories on noncommutative Moyal space–time with light-like   noncommutativity. To tackle the issues arising from noncommuting and hence nonlocal time, we argue that for this case light-front quantization procedure should be employed. In this appropriate quantization scheme we perform the non-planar loop analysis for the light-like noncommutative field theories. One of the important and peculiar features of light-front quantization is that the UV cutoff of the light-cone Hamiltonian manifests itself as an IR cutoff for the light-cone momentum, p⁺$p^{+}$. Due to this feature, the naive results of covariant quantization for the light-like case allude to the absence of the UV/IR mixing in the light-front quantization. However, by a careful analysis of non-planar loop integrals we show that this is not the case and the UV/IR mixing persists. In addition, we argue in favour of the perturbative unitarity of light-like noncommutative field theories in the light-front quantization scheme.     

Cusped light-like Wilson loops in gauge theories

We propose and discuss a new approach to the analysis of the correlation functions which contain light-like Wilson lines or loops, the latter being cusped in addition. The objects of interest are therefore the light-like Wilson null-polygons, the soft factors of the parton distribution and fragmentation functions, high-energy scattering amplitudes in the eikonal approximation, gravitational Wilson lines, etc. Our method is based on a generalization of the universal quantum dynamical principle by J. Schwinger and allows one to take care of extra singularities emerging due to lightlike or semi-light-like cusps. We show that such Wilson loops obey a differential equation which connects the area variations and renormalization group behavior of those objects and discuss the possible relation between geometrical structure of the loop space and area evolution of the light-like cusped Wilson loops.     

Light-like Wilson line in QCD without path ordering

Unlike the Wilson line in QED the Wilson line in QCD contains path ordering. In this paper we get rid of the path ordering in the light-like Wilson line in QCD by simplifying all the infinite number of noncommuting terms in the SU(3) pure gauge. We prove that the light-like Wilson line in QCD naturally emerges when path integral formulation of QCD is used to prove factorization of soft and collinear divergences at all order in coupling constant in QCD processes at high energy colliders.     

Extremal Kähler metrics and Bach–Merkulov equations

In this paper, we study a coupled system of equations on oriented compact 4-manifolds which we call the Bach–Merkulov equations. These equations can be thought of as the conformally invariant version of the classical Einstein–Maxwell equations. Inspired by the work of C. LeBrun on Einstein–Maxwell equations on compact Kähler surfaces, we give a variational characterization of solutions to Bach–Merkulov equations as critical points of the Weyl functional. We also show that extremal Kähler metrics are solutions to these equations, although, contrary to the Einstein–Maxwell analogue, they are not necessarily minimizers of the Weyl functional. We illustrate this phenomenon by studying the Calabi action on Hirzebruch surfaces.     

On the Toroidal Surfaces of Revolution with Constant Mean Curvatures

It is shown that the surface with a constant mean curvature encloses the extremal volume among all toroidal surfaces of given area. The exact solution for the corresponding variational problem is derived, and its parametric analysis is performed in the limits of high and small mean curvatures. An absence of smooth torus with constant mean curvature is proved, and the extremal surface is demonstrated to have at least one edge located on the outer side of the torus.     

Null Wave Front and Ryu–Takayanagi Surface

The Ryu–Takayanagi formula provides the entanglement entropy of quantum field theory as an area of the minimal surface (Ryu–Takayanagi surface) in a corresponding gravity theory. There are some attempts to understand the formula as a flow rather than as a surface. In this paper, we consider null rays emitted from the AdS boundary and construct a flow representing the causal holographic information. We present a sufficient and necessary condition that the causal information surface coincides with Ryu–Takayanagi surface. In particular, we show that, in spherical symmetric static spacetimes with a negative cosmological constant, wave fronts of null geodesics from a point on the AdS boundary become extremal surfaces and therefore they can be regarded as the Ryu–Takayanagi surfaces. In addition, from the viewpoint of flow, we propose a wave optical formula to calculate the causal holographic information.     

Canonical formulation of pp-waves

We construct a Hamiltonian formulation for the class of plane-fronted gravitational waves with parallel rays (pp-waves). Because of the existence of a light-like Killing vector, the dynamics is effectively reduced to a 2+1 evolution with “time” chosen to be light-like. In spite of the vanishing action this allows us to geometrically identify a symplectic form as well as dynamical Hamiltonian, thus casting the system into canonical form.     

Gluon polarization in nucleons

In QCD the gauge-invariant gluon polarization in a nucleon can be defined either in a non-local way as the integral over the Ioffe-time distribution of polarized gluons, or in light-cone gauge as the forward matrix element of the local topological current. We have investigated both possibilities within the framework of QCD sum rules. Although the topological current is built from local fields, we have found that its matrix element retains sensitivity to large longitudinal distances. Because QCD sum rules produce artificial oscillations of the Ioffe-time distribution of polarized glue at moderate and large light-like distances, the calculation of the matrix element of the topological current results in a small value of . In a more consistent approach QCD sum rules are used to describe the polarized gluon distribution only at small light-like distances. Assuming that significant contributions to arise only from longitudinal length scales not larger than the nucleon size leads to . Received: 19 August 1997 / Published online: 20 February 1998     

Solutions of a bethe-salpeter equation

We study systematically and exhibit the Lorentz symmetry of the Bethe-Salpeter equation in the light-like case for two scalar quarks of different masses interacting via the exchange of a scalar photon. We develop a new approach for solving the eigenvalue problem of the equation for the general case (not only the light-like). Our method permits accurate analytic expressions for the spectrum and the wave functions.     

Integrable Structures in Classical Off-Shell 10D Supersymmetric Yang–Mills Theory

The field equations of supersymmetric Yang–Mills theory in ten dimensions may be formulated as vanishing curvature conditions on light-like rays in superspace. In this article, we investigate the physical content of the modified SO(7) covariant superspace constraints put forward earlier [11]. To this end, group-algebraic methods are developed which allow to derive the set of physical fields and their equations of motion from the superfield expansion of the supercurl, systematically. A set of integrable superspace constraints is identified which drastically reduces the field content of the unconstrained superfield but leaves the spectrum including the original Yang–Mills vector field completely off-shell. A weaker set of constraints gives rise to additional fields obeying first order differential equations. Geometrically, the SO(7) covariant superspace constraints descend from a truncation of Witten's original linear system to particular one-parameter families of light-like rays. Received: 20 April 2000 / Accepted: 10 September 2000     

Hamiltonian evolution and quantization for extremal black holes

We present and contrast two distinct ways of including extremal black holes in a Lorentzian Hamiltonian quantization of spherically symmetric Einstein-Maxwell theory. First, we formulate the classical Hamiltonian dynamics with boundary conditions appropriate for extremal black holes only. The Hamiltonian contains no surface term at the internal infinity, for reasons related to the vanishing of the extremal hole surface gravity, and quantization yields a vanishing black hole entropy. Second, we give a Hamiltonian quantization that incorporates extremal black holes as a limiting case of nonextremal ones, and examine the classical limit in terms of wave packets. The spreading of the packets, even the ones centered about extremal black holes, is consistent with continuity of the entropy in the extremal limit, and thus with the Bekenstein-Hawking entropy even for the extremal holes. The discussion takes place throughout within Lorentz-signature spacetimes.     

A Metric for an Evans-Vigier Field

In this paper we present an example of a specific metric which geometrizes explicitly a light-like four-vector potential field (Evans-Vigier field). We define the concepts of semilocal and complete geometrization and show that a light-like vector field has the same geometrical structure as a gravitational Kerr field. With this background in mind we discuss a theoretical proposition that a rotating body generates, besides a special gravitational field, a magnetic-type gauge field which might be identified with a geometrized Evans-Vigier field. We finally present a discussion which inform us that a classical Evans-Vigier field represents a novel type of field because we cannot identify it with any of the known electromagnetic fields.     

The Dynamics of Relativistic Strings Moving in the Minkowski Space $$\mathbb{R}^{1+n}$$

In this paper we investigate the dynamics of relativistic (in particular, closed) strings moving in the Minkowski space . We first derive a system with n nonlinear wave equations of Born-Infeld type which governs the motion of the string. This system can also be used to describe the extremal surfaces in . We then show that this system enjoys some interesting geometric properties. Based on this, we give a sufficient and necessary condition for the global existence of extremal surfaces without space-like point in with given initial data. This result corresponds to the global propagation of nonlinear waves for the system describing the motion of the string in . We also present an explicit exact representation of the general solution for such a system. Moreover, a great deal of numerical analyses are investigated, and the numerical results show that, in phase space, various topological singularities develop in finite time in the motion of the string. Finally, some important discussions related to the theory of extremal surfaces of mixed type in are given.     

Circular orbits in extremal Reissner-Nordstrom spacetime

Circular null geodesic orbits, in extremal Reissner-Nordstrom spacetime, are examined with regard to their stability, and compared with similar orbits in the near-extremal situation. Extremization of the effective potential for null circular orbits shows the existence of a stable circular geodesic in the extremal spacetime, precisely on the event horizon which coincides with the null geodesic generator. Such a null orbit on the horizon is also indicated by the global minimum of the effective potential for circular timelike orbits. This type of geodesic is of course absent in the corresponding near-extremal spacetime, as we show here, testifying to differences between the extremal limit of a generic RN spacetime and the exactly extremal geometry.     

Two remarks on extremal equilibrium states

First it is shown that each extremal equilibrium state is representable as limit of Gibbs states in finite volumes, and that an analogous statement holds for extremal invariant equilibrium states. Secondly we prove that for negative pair interactions only one equilibrium state exists which minimizes (resp. maximizes) the particle density, but that in general there are more than two extremal invariant equilibrium states with the same particle density. In this context, periodic interactions are studied.     

Inelastic diffractive scattering in nonperturbative QCD

We examine diffractive proton-proton scattering and photo- and electroproduction of mesons , where X denotes a proton or a final state, into which the proton can go by diffractive dissociation. Using a functional integral approach we derive the scattering amplitudes, which are governed by the expectation values of light-like Wegner-Wilson loops, which are then evaluated using the model of the stochastic vacuum. For the proton, we assume a quark-diquark structure. From the scattering amplitudes we calculate total and differential cross sections for high centre of mass energy and small momentum transfer and compare with experiments. Furthermore we calculate isovector form factors for the proton and the pion within the same model. Received: 30 January 2001 / Revised version: 29 June 2001 / Published online: 3 August 2001     

Superplane integrability and three dimensional supergravity

The requirement of integrability in all light-like superplanes yields the proper kinematical constraints for the three-dimensional supergravity theory formulated in superspace. The theory with the Breitenlohner set of auxiliary fields is obtained.