Search

We demonstrate within the quantum field theoretical framework that an asymptotic particle falling into the black hole implants soft graviton hair on the horizon, conforming with the classical proposal of Hawking, Perry and Strominger. A key ingredient to this result is the construction of gravitational Wilson line dressings of an infalling scalar field, carrying a definite horizon supertranslation charge. It is shown that a typical Schwarzschild state is degenerate, and can be labeled by different soft supertranslation hairs parametrized for radial trajectories by the mass and energy of the infalling particle and its asymptotic point of contact with the horizon. The supertranslation zero modes are also obtained in terms of zero-frequency graviton operators, and are shown to be the expected canonical partners of the linearized horizon charge that enlarge the horizon Hilbert space., Comment: 40 pages, 2 figures

Recently it has been shown that infrared divergences in the conventional S-matrix elements of gauge and gravitational theories arise from a violation of the conservation laws associated with large gauge symmetries. These infrared divergences can be cured by using the Faddeev-Kulish (FK) asymptotic states as the basis for S-matrix elements. Motivated by this connection, we study the action of BMS supertranslations on the FK asymptotic states of perturbative quantum gravity. We compute the BMS charge of the FK states and show that it characterizes the superselection sector to which the state belongs. Conservation of the BMS charge then implies that there is no transition between different superselection sectors, hence showing that the FK graviton clouds implement the necessary vacuum transition induced by the scattering process., Comment: 39 pages

We present a covariant formulation of the Kinoshita-Lee-Nauenberg (KLN) theorem for processes involving the radiation of soft particles. The role of the disconnected diagrams is explored and a rearrangement of the perturbation theory is performed such that the purely disconnected diagrams are factored out. The remaining effect of the disconnected diagrams results in a simple modification of the usual Feynman rules for the S-matrix elements. As an application, we show that, when combined with the Low theorem, this leads to a proof of the absence of the 1/Q corrections to inclusive processes (such as the Drell-Yan process). In this paper the Abelian case is discussed to all orders in the coupling. {copyright} {ital 1997} {ital The American Physical Society}

The infrared behavior of perturbative quantum gravity is studied using the method developed for QED by Faddeev and Kulish. The operator describing the asymptotic dynamics is derived and used to construct an IR-finite S matrix and space of asymptotic states. All-orders cancellation of IR divergences is shown explicitly at the level of matrix elements for the example case of gravitational potential scattering. As a practical application of the formalism, the soft part of a scalar scattering amplitude is related to the gravitational Wilson line and computed to all orders., Comment: 34 pages, 8 figures

Numerical simulations are performed of a test scalar field in a spacetime undergoing gravitational collapse. The behavior of the scalar field near the singularity is examined and implications for generic singularities are discussed. In particular, our example is the first confirmation of the BKL conjecture for an asymptotically flat spacetime., Comment: 10 pages, 11 figures, references added

A chiral invariant background field method is introduced in order to study the structure of higher order terms in chiral perturbation theory. Explicit one-loop calculations are presented together with the construction of the most general O (p6) chiral lagrangian relevant for anomalous processes. The non-renormalization of the coefficient of the Wess-Zumino term in both two and four dimensions is discussed in general.

We investigate decoupling of heavy Kaluza-Klein modes in an Abelian Higgs model with space-time topologies $\mathbb{R}^{3,1} \times S^{1}$ and $\mathbb{R}^{3,1} \times S^{1}/\mathbb{Z}_{2}$. After integrating out heavy KK modes we find the effective action for the zero mode fields. We find that in the $\mathbb{R}^{3,1} \times S^{1}$ topology the heavy modes do not decouple in the effective action, due to the zero mode of the 5-th component of the 5-d gauge field $A_{5}$. Because $A_{5}$ is a scalar under 4-d Lorentz transformations, there is no gauge symmetry protecting it from getting mass and $A_{5}^{4}$ interaction terms after loop corrections. In addition, after symmetry breaking, we find new divergences in the $A_{5}$ mass that did not appear in the symmetric phase. The new divergences are traced back to the gauge-goldstone mixing that occurs after symmetry breaking. The relevance of these new divergences to Symanzik's theorem is discussed. In order to get a more sensible theory we investigate the $S^{1}/\mathbb{Z}_{2}$ compactification. With this kind of compact topology, the $A_{5}$ zero mode disappears. With no $A_{5}$, there are no new divergences and the heavy modes decouple. We also discuss the dependence of the couplings and masses on the compactification scale. We derive a set of RG-like equations for the running of the effective couplings with respect to the compactification scale. It is found that magnitudes of both couplings decrease as the scale $M$ increases. The effective masses are also shown to decrease with increasing compactification scale. All of this opens up the possibility of placing constraints on the size of extra dimensions., 35 pages, 6 figures

We investigate the decoupling of heavy Kaluza-Klein modes in $\phi^{4}$ theory and scalar QED with space-time topology $\mathbb{R}^{3,1} \times S^{1}$. We calculate the effective action due to integrating out heavy KK modes. We construct generalized RGE's for the couplings with respect to the compactification scale $M$. With the solutions to the RGE's we find the $M$-scale dependence of the effective theory due to higher dimensional quantum effects. We find that the heavy modes decouple in $\phi^{4}$ theory, but do not decouple in scalar QED. This is due to the zero mode of the 5-th component $A_{5}$ of the 5-d gauge field. Because $A_{5}$ is a scalar under 4-d Lorentz transformations, there is no gauge symmetry protecting it from getting mass and $A_{5}^{4}$ interaction terms after loop corrections. In light of these unpleasant features, we explore $S^{1}/\mathbb{Z}_{2}$ compactifications, which eliminate $A_{5}$, allowing for the heavy modes to decouple at low energies. We also explore the possibility of decoupling by including higher dimensional operators. It is found that this is possible, but a high degree of fine tuning is required., Comment: 9 pages, no figures; sign error on equations 20, 36, 37; Added additional references

We consider perturbative expansions in theories with an infrared cutoff $\lambda$. The infrared sensitive pieces are defined as terms nonanalytic in the infinitesimal $\lambda^2$ and powers of this cutoff characterize the strength of these infrared contributions. It is argued that the sum over the initial and final degenerate ( as $\lambda \to 0$) states which is required by the Kinoshita - Lee - Nauenberg theorem eliminates terms of order $\lambda^0$ and $\lambda^1$. However, the quadratic and higher order terms in general do not cancel. This is investigated in simple examples of KLN cancellations, of relevance to the inclusive decay rate of a heavy particle, at the one loop level., Comment: 20 pages, LaTeX

Fermionic solitons are defined in terms of localized self-consistent solutions of the classical equations of motion for bosons and Dirac fields. The one-loop quantum-mechanical correction to the mass of such a state is given by the diagonal S-matrix element in a self-consistent interaction picture. The various contributions to the energy shift are discussed, and the gauge invariance of our result is verified explicitly. Our operator formulation for fermionic solitons is shown to be equivalent to a Feynman path-integral prescription proposed by Dashen, Hasslacher, and Neveu.

The Bogomolny equation for linear perturbations of the Prasad-Sommerfield monopole is solved exactly. Explicit expressions for all the normalizable and unnormalizable nongauge modes are obtained, and previous results of Mottola on the normalizable modes are confirmed. A new choice of gauge facilitates the solution. Open questions and possible applications are mentioned.

We study the limit when the $\ensuremath{\sigma}$ mass is very large compared to other scales in the renormalized light-particle-irreducible Green's functions of the linear $\ensuremath{\sigma}$ model with $\mathrm{SO}(N+1)$ symmetry. This is a strong-coupling limit. The resulting theory is summarized by an effective Lagrangian, from which Green's functions, not just the $S$-matrix elements, can be reproduced to $O(1)$. At the one-loop level, the effective Lagrangian is explicitly constructed and the relationship between the infinities of the nonlinear model and the heavy-mass effects is clarified. We then discuss the construction of the effective Lagrangian to all orders via the method of oversubtraction. This investigation can either be looked upon as a systematic way of organizing the heavy-Higgs-boson effects or it may be interpreted as a method of defining a renormalization program for the nonlinear $\ensuremath{\sigma}$ model.

I discuss the phase structure of massive gauge invariant QCD (the gauged non-linear sigma model) using an operator formalism proposed by 't Hooft. The dual variables for this system are determined and the 't Hooft loop operator is constructed from these dual field variables. Its equal time commutation relations with the Wilson loop operator is explicitly verified. The system possesses two possible phases. In the semi-classical approximation (weak coupling), magnetic confinement as indicated by an area law for the expectation value of 't Hooft loops is observed. If above a certain critical coupling a condensate of vortices is formed, then the expectation value of the 't Hooft loop in the dilute vortex approximation shows a perimeter law indicating electric confinement.

We point out that neither a softly broken Peccei-Quinn symmetry nor a softly broken supersymmetry per se suffices to insure the finiteness of θ QCD renormalization. This is due to a logarithmic divergence that in general occurs in the higher loop corrections to the gluino mass.

We impose the constraint of the unitarity of the S -matrix on the theory of a closed bosonic string propagating in a background of some of its modes. The equations of motion for not only the massless but also for some of the massive modes of the string are thus consistently obtained in a weak field expansion. To a given order in the weak field expansion, they contain contributions to all orders in α′. We also show that conformal invariance guarantees that the S -matrix be unitary.

We investigate the behaviour of the regulated Witten index, Δ=Tr(−1)F e−βH, in a class of exactly soluble models. We demonstrate that when the spectrum of the theory contains discrete states as well as a continuum, the index is, in general, β-dependent. If the spectrum is a purely continuous one extending to zero, the index is ill-defined and may have fractional values. The subtleties involved are discussed in detail and a possible remedy is suggested.