Quantization, group contraction and zero point energy

We study algebraic structures underlying 't Hooft's construction relating classical systems with the quantum harmonic oscillator. The role of group contraction is discussed. We propose the use of SU(1,1) for two reasons: because of the isomorphism between its representation Hilbert space and that of the harmonic oscillator and because zero point energy is implied by the representation structure. Finally, we also comment on the relation between dissipation and quantization.     

Dissipation and quantization for composite systems

In the framework of 't Hooft's quantization proposal, we show how to obtain from the composite system of two classical Bateman's oscillators a quantum isotonic oscillator. In a specific range of parameters, such a system can be interpreted as a particle in an effective magnetic field, interacting through a spin-orbit interaction term. In the limit of a large separation from the interaction region one can describe the system in terms of two irreducible elementary subsystems which correspond to two independent quantum harmonic oscillators.     

D(s0)+ (2317)-D0(2308) mass difference as evidence for tetraquarks

We argue that the anomalously small mass difference between the D(s0)+ (2317) and the recently observed D0(2308) (Belle) state is the first "smoking gun" experimental evidence of their tetraquark [cq(q q)] structure. The recently reported D(sJ)+ (2632) (SELEX) state completes the low-lying nonexotic tetraquark spectrum, as predicted by 't Hooft's instanton-induced effective quark interaction.     

On the unicity of the 't Hooft's magnetic monopole

We consider the most general rotationally invariant and stationary Yang-Mills potential generated by the SU(2)-gauge group. It is shown that the 't Hooft's substitution is unique up to a gauge if we impose the finite energy condition.     

LETTER: The Fermionic Entropy in Garfinkle-Horne Dilaton Black Hole Background

The expression of Fermionic entropy is derived in Garfinkle-Horne dilaton black hole background, by using 't Hooft's brick wall model and Newman-Penrose's spinor analysis approach.     

The Quantum Entropy in Horowitz-Strominger Black Hole Background

Using 't Hooft's brick wall model and Newman-Penrose's spinor analysis, the expression of the quantum entropy is derived in the Horowitz-Strominger black hole background. The calculations show us that the Fermionic entropy is 7/2 times the Bosonic entropy.     

How many gravitational't Hooft instantons are there past the first one?

Using the necessary and sufficient condition of Capovilla, Jacobson and Dell, it is shown that a result of Samuel for gravitational instantons does not extend to 't Hooft's instantons of winding numbers larger than one. A formula for the next instanton satisfying this condition is given.     

Anomaly matching conditions in supersymmetric gauge theories

Sufficient conditions are proven for 't Hooft's consistency conditions to hold at points in the moduli space of supersymmetric gauge theories. Known results for anomaly matching in supersymmetric QCD are rederived as a sample application of the results. The results can be used to show that the anomaly matching conditions hold for s-confining theories.     

Quantum aspects of GMS solutions of non-commutative field theory and large <Emphasis Type="Italic">N</Emphasis> limit of matrix models

We investigate quantum aspects of Gopakumar–Minwalla–Strominger (GMS) solutions of non-commutative field theory (NCFT) in the large non-commutativity limit, . Building upon a quantitative map between the operator formulation of 2- (respectively, (2+1)-) dimensional NCFTs and large-N matrix models of c=0 (respectively,c=1) non-critical strings, we show that GMS solutions are quantum mechanically sensible only if we make an appropriate joint scaling of and N. For 't Hooft's scaling, GMS solutions are replaced by large-N saddle-point solutions. GMS solutions are recovered from saddle-point solutions in the small 't Hooft coupling regime, but are destabilized in the large 't Hooft coupling regime by quantum effects. We make comparisons between these large-N effects and the recently studied infrared effects in NCFTs. We estimate the U(N) symmetry breaking effects of the gradient term and argue that they are suppressed only in the small 't Hooft coupling regime. Received: 2 January 2002 / Published online: 26 April 2002     

The Quantum Corrections to the Entropy of Stationary Axisymmetric Einstein-Maxwell-Dilaton-Axion Black Holes

By using 't Hooft's brick wall model, thecorrections for a massless quantum scalar field to theblack hole entropy are studied in a stationaryaxisymmetric Einstein-Maxwell-dilaton-axion black holespace-time. The free energy and entropy for this case arecalculated; in Hartle-Hawking states, the derivedquantum entropy is composed of the part that has ageometric feature and the part that is logarithmically divergent, and it turns out that thelogarithmic part is related to the characteristicquantities of a black hole.     

't Hooft黑洞量子态理论的一个推论

从't Hooft将黑洞作为高度简并的量子态的理论出发, 考虑黑洞的量子效应, 由于海森堡测不准原理, 导出视界面上的时空坐标是非对易的.利用非对易场论的办法, 研究了大的远离极端情况的Reissner-Nordstrom黑洞,成功的同时推导出黑洞的温度和熵. 而且预言了场的动力学自由度的数目, 该数目支持了最小超对称标准模型.     

Entropy of the Quantum Electromagnetic Field in Static, Spherically Symmetric Dilaton Black Holes

The quantum correction to the entropy of four-dimensional nonextreme static,spherically symmetric dilaton black holes arising from electromagnetic fields isinvestigated by 't Hooft's brick wall model. The Garfinkle-Horowitz-Strominger,Gibbons-Maeda, and Garfinkle-Horne dilaton black holes areconsidered. It is shown that the one-loop quantum correction arising from theelectromagnetic fields is exactly twice that due to a massless scalar field. Theresult agrees with that of the Schwarzschild and Reissner-Nordström blackholes.     

The light-baryon spectrum in a relativistic quark model with instanton-induced quark forces

This is the second of a series of three papers treating light-baryon resonances up to 3 GeV within a relativistically covariant quark model based on the three-fermion Bethe-Salpeter equation with instantaneous two- and three-body forces. In this paper we apply the covariant Salpeter framework (which we developed in the first paper, U. L?ring, K. Kretzschmar, B.Ch. Metsch, H.R. Petry, Eur. Phys. J. A 10, 309 (2001)) to specific quark model calculations. Quark confinement is realized by a linearly rising three-body string potential with appropriate spinorial structures in Dirac space. To describe the hyperfine structure of the baryon spectrum we adopt 't Hooft's residual interaction based on QCD-instanton effects and demonstrate that the alternative one-gluon exchange is disfavored on phenomenological grounds. Our fully relativistic framework allows to investigate the effects of the full Dirac structures of residual and confinement forces on the structure of the mass spectrum. In the present paper we present a detailed analysis of the complete non-strange-baryon spectrum and show that several prominent features of the nucleon spectrum such as, e.g., the Roper resonance and approximate “parity doublets” can be uniformly explained due to a specific interplay of relativistic effects, the confinement potential and 't Hooft's force. The results for the spectrum of strange baryons will be discussed in a subsequent paper, see U. L?ring, B.Ch. Metsch, H.R. Petry, this issue, p. 447. Received: 27 March 2001 / Accepted: 17 April 2001     

't Hooft loop in SU(2) Yang-Mills theory

We study the behavior of the spatial and temporal 't Hooft loop at zero and finite temperature in the 4D SU(2) Yang-Mills theory, using a new numerical method. In the deconfined phase T > T(c), the spatial 't Hooft loop exhibits a dual string tension, which vanishes at T(c) with a 3D Ising-like critical exponent.     

Black hole thermodynamics from calculations in strongly coupled gauge theory

We develop an approximation scheme for the quantum mechanics of N D0-branes at finite temperature in the 't Hooft large- N limit. The entropy of the quantum mechanics calculated using this approximation agrees well with the Bekenstein-Hawking entropy of a ten-dimensional nonextremal black hole with 0-brane charge. This result is in accordance with the duality conjectured by Itzhaki, Maldacena, Sonnenschein, and Yankielowicz [Phys. Rev. D 58, 046004 (1998)]. Our approximation scheme provides a model for the density matrix which describes a black hole in the strongly coupled quantum mechanics.     

Energy loss of an infinitely massive half-Bogomol'nyi-Prasad-Sommerfeld particle by radiation to all orders in 1/N

We use the AdS/CFT correspondence to compute the energy radiated by an infinitely massive half-Bogomol'nyi-Prasad-Sommerfeld particle charged under N=4 super Yang-Mills theory, transforming in the symmetric or antisymmetric representation of the gauge group, and moving in the vacuum, to all orders in 1/N and for large 't Hooft coupling. For the antisymmetric case we consider D5-branes reaching the boundary of five-dimensional anti-de Sitter space (AdS(5)) at arbitrary timelike trajectories, while for the symmetric case, we consider a D3-brane in AdS(5) that reaches the boundary at a hyperbola. We compare our results to the one obtained for the fundamental representation, deduced by considering a string in AdS(5).     

Effective two-dimensional description from critical phenomena in black holes

We study the occurrence of critical phenomena in four-dimensional, rotating and charged black holes, derive the critical exponents and show that they fulfill the scaling laws. Correlation function critical exponents and Renormalization Group considerations assign an effective (spatial) dimension,d=2, to the system. The two-dimensional Gaussian approximation to critical systems is shown to reproduce all the black hole's critical exponents. Higher order corrections (which are always relevant) are discussed. Identifying the two-dimensional surface with the event horizon and noting that generalization of scaling leads to conformal invariance and then to string theory, we arrive at 't Hooft's string interpretation of black holes. From this, a model for dealing with a coarse grained black hole quantization is proposed. We also give simple arguments that lead to a rough quantization of the black hole mass in units of the Planck mass, i.e.M(1/2)M _Pll with anl positive integer and then, from this result, to the proportionality between quantum entropy and area.This essay received the fifth award from the Gravity Research Foundation, 1994—Ed.     

Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity

We study some aspects of Maldacena's large-N correspondence between superconformal gauge theory on the D3-brane and maximal supergravity on AdS by introducing macroscopic strings as heavy (anti-) quark probes. The macroscopic strings are semi-infinite Type IIB strings ending on a D3-brane world-volume. We first study deformation and fluctuation of D3-branes when a macroscopic BPS string is attached. We find that both dynamics and boundary conditions agree with those for the macroscopic string in anti-de Sitter supergravity. As a by-product we clarify how Polchinski's Dirichlet and Neumann open string boundary conditions arise dynamically. We then study the non-BPS macroscopic string–anti-string pair configuration as a physical realization of a heavy quark Wilson loop. We obtain the static potential from the supergravity side and find that the potential exhibits non-analyticity of the square-root branch cut in the 't Hooft coupling parameter. We put forward non-analyticity as a prediction for large-N gauge theory in the strong 't Hooft coupling limit. By turning on the Ramond–Ramond zero-form potential, we also study the vacuum angle dependence of the static potential. We finally discuss the possible dynamical realization of the heavy N-prong string junction and of the large-N loop equation via a local electric field and string recoil thereof. Throughout comparisons of the AdS–CFT correspondence, we find that a crucial role is played by “geometric duality” between the UV and IR scales in directions perpendicular to the D3-brane and parallel ones, explaining how the AdS spacetime geometry emerges out of four-dimensional gauge theory at strong coupling. Received: 21 September 2001 / Published online: 12 November 2001     

Generalized path-integral solution and coherent states of the harmonic oscillator in D-dimensions

We construct a general form of propagator in arbitrary dimensions and give an exact wavefunction of a time- dependent forced harmonic oscillator in D（D ≥ 1） dimensions. The coherent states, defined as the eigenstates of annihilation operator, of the D-dimensional harmonic oscillator are derived. These coherent states correspond to the minimum uncertainty states and the relation between them is investigated.     

A note on anomaly matching for finite density QCD

We note that the QCD phases at large finite density respect 't Hooft anomaly matching conditions. Specifically the spectrum of the light excitations possesses the correct quantum numbers required to obey global anomaly constraints. We argue that 't Hooft constraints can be used at finite density along with non perturbative methods to help selecting the correct phase.