Beltrami Gauge Symmetry and 2D Induced Gravity

We introduce the Beltrami gauge symmetry related to the Beltrami parametrization of the metrics and the Beltrami equations. We explore its role in 2d induced gravity and show that Polynkov's. SL(R) and KPZ's residual symmetries are subsymmetries of the Beltrami gnuge symmetry in the light-cone gauge. We also find that the 2d induced gravity with or without matter can be reformulated as Beltrami-Liouville field theories on Riemann surfaces of higher genus.     

Migdal renormalization group approach to deconfinement phase transition

The Migdal renormalization group approach is applied to a finite temperature lattice gauge theory. Imposing the periodic boundary condition in the timelike orientation, the phase structure of the finite temperature lattice gauge system with a gauge groupG in (d+1)-dimensional space is determined by two kinds of recursion equations, describing spacelike and timelike correlations, respectively. One is the recursion equation for ad-dimensional gauge system with the gauge groupG, and the other corresponds to ad-dimensional spin system for which the effective theory is described by the nearest neighbor interaction of the Wilson lines. Detailed phase structure is investigated for theSU(2) gauge theory in (3+1)-dimensional space. Deconfinement phase transition is obtained. Using the recursion equation for the three dimensional spin system of the Wilson lines, it is shown that the flow of the renormalization group trajectories leads to a phase transition of the three dimensional Ising model.     

Supergravity in (2 + 1) dimensionsfrom (3 + 1)-dimensional supergravity

In the context of the formalism proposed by Stelle-West and Grignani-Nardelli, it is shown that Chern-Simons supergravity can be consistently obtained as a dimensional reduction of (3 + 1)-dimensional supergravity, when written as a gauge theory of the Poincaré group. The dimensional reductions are consistent with the gauge symmetries, mapping (3 + 1)-dimensional Poincaré supergroup gauge transformations onto (2 + 1)-dimensional Poincaré supergroup ones.     

Gauge coupling renormalization in AdS5

We present the relation of the 4-dimensional low energy gauge coupling and the 5-dimensional fundamental gauge coupling of bulk gauge boson in a slice of AdS₅, which is orbifolded byZ ₂ ×Z′₂. We calculate the full 1-loop corrections for the case of generic 5-dimensional scalar, Dirac fermion, and vector fields with arbitraryZ ₂×Z′₂. For the supersymmetric case, we obtain the result more easily by using the 4-dimensional effective supergravity approach.     

Beltrami-de Sitter时空和de Sitter不变的狭义相对论

分析了在相对论体系中狭义相对性原理和宇宙学原理之间的关系以及Beltrami-de Sitter -陆启铿疑难.指出可以把狭义相对性原理推广到非零常曲率时空，在具有Beltrami度规 的de Sitter/反de Sitter时空中建立狭义相对论的运动学和粒子动力学. 在这类狭义相对 论中,相对于Beltrami坐标同时性，Beltrami坐标系就是惯性坐标系，相应的观测者为惯 性观测者; 对于自由粒子和光讯号, 惯性定律成立;可以定义可观测量,它们不但守恒而且还 满足推广的爱因斯坦关系.除了Beltrami坐标时同时性之外，对于共动观测, 还可以取固 有时同时性;此时，Beltrami度规成为Robertson-Walker型的度规，其3维空间是闭的,对 于平坦的偏离为宇宙学常数的量级.这表明,在这类狭义相对论中,相对性原理与“完美”宇 宙学原理之间存在内在联系,并不存在那些问题.进而,基于最新观测事实，重述了Mach原 理；指出对于Beltrami-de Sitter/反de Sitter时空，宇宙学常数恰恰给出惯性运动的起 源. 关键词： 狭义相对性原理 宇宙学原理 de Sitter不变的狭义相对论 Beltrami-de Sitter时空 同时性 Mach原理     

On the stochastic confinement in SU(2) lattice gauge theory

We extend the Olesen approach to confinement, originally proposed for SU(∞) gauge theory, to the SU(2) group. We perform Monte Carlo calculations of the spectral density, which describes the distribution of eigenvalues of the Wilson loop in the SU(2) lattice gauge theory (LGT), for square loops up to size 4 × 4. Our results indicate the onset of disorder in the 4-dimensional LGT so that at weak coupling confinement is due to non-abelian fluctuations of the gauge field. We describe the Monte Carlo data by formulae of the 2-dimensional LGT with some effective coupling constant. We formulate how this effective coupling constant should depend on the size of the loop in order that the Olesen hypothesis about the dimensional reduction (i.e. approximate reduction of the 4-dimensional LGT to the effective 2-dimensional LGT in the confinement region) would be held. Using the strong-coupling expansion where the Olesen hypothesis holds in fourteen orders, we perform quantitative estimates. The density of simple vortices up to size 4 × 4 is calculated. A connection between the definitions of spectral densities for the SU(∞) and SU(2) groups is considered. Explicit formulae for the spectral density in the 2-dimensional SU(2) LGT are derived.     

Center flux correlation in SU(2) Yang-Mills theory

By using the method of center projection, the center vortex part of the gauge field is isolated and its propagator is evaluated in the center Landau gauge, which minimizes the open 3-dimensional Dirac volumes of nontrivial center links bounded by the closed 2-dimensional center vortex surfaces. The center field propagator is found to dominate the gluon propagator (in the Landau gauge) in the low momentum regime and to give rise to a power-law correction proportional to p(-2.9(1)) at high momentum. The screening mass of the center vortex field vanishes above the critical temperature of the deconfinement phase transition, which naturally explains the second order nature of this transition consistent with the vortex picture. Finally, the ghost propagator of the maximal center gauge is found to be infrared finite and, thus, shows that the coset fields play no role for confinement.     

First-order phase transitions in large entropy lattice models

We show the existence of a first-order phase transition in thev-dimensional Potts model forv≧2, when the number of states of a single spin is big enough. Low-temperature pure phases are proved to survive up to the critical temperature. Also the existence of a first-order transition in thev-dimensional Potts gauge model,v≧3, is obtained if the underlying gauge group is finite but large.     

Dirac and Pauli form factors of nucleons using nonlocal chiral effective Lagrangian

Dirac and Pauli form factors are investigated in the relativistic chiral effective Lagrangian.The octet and decuplet intermediate states are included in the one-loop calculation.The 4-dimensional regulator is introduced to deal with the divergence.Different from the non-relativistic case,this 4-dimensional regulator is generated from the nonlocal Lagrangian with the gauge link,which guarantees local gauge invariance.As a result,additional diagrams appear which ensure electric charge 1 and 0 for proton and neutron respectively.The obtained Dirac and Pauli form factors of the nucleons are all reasonable up to relatively large Q~2.     

Gauge Invariance of det (iD)2+1 and the Influence

The gauge invariance of det (iD) in (2+l)-dimensional spacetime is argued in two approaches.Unlike the (3 + 1)-dimensional case, det (iD) does not carry any topological information.Some brief discussions are presented.     

Abelian 3-form gauge theory: Superfield approach

We discuss a D-dimensional Abelian 3-form gauge theory within the framework of Bonora-Tonin’s superfield formalism and derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for this theory. To pay our homage to Victor I. Ogievetsky (1928–1996), who was one of the inventors of Abelian 2-form (antisymmetric tensor) gauge field, we go a step further and discuss the above D-dimensional Abelian 3-form gauge theory within the framework of BRST formalism and establish that the existence of the (anti-)BRST invariant Curci-Ferrari (CF) type of restrictions is the hallmark of any arbitrary p-form gauge theory (discussed within the framework of BRST formalism).     

Superspace,dimensional reduction,and stochastic quantization

The equivalence between a 6-dimensional stochastic classical scalar field theory and the corresponding 4-dimensional quantum field theory has been shown to stem from a hidden supersymmetry of the former. This has led to a formulation of quantum field theory in a superspace of 6 commuting and 2 anticommuting dimensions. We study gauge and spinor field theories defined on this superspace, showing that the dimensional reduction is a consequence of the geometry of the superspace, and that the stochastic formalism for gauge theories is a natural consequence of the structure of the superspace theory. This allows us to extend the stochastic formalism to include spinors.     

Gauge and gravitational anomalies and Hawking radiation of rotating BTZ black holes

In this paper we obtain the flux of Hawking radiation from rotating BTZ black holes from the gauge and gravitational anomalies point of view. Then we show that the gauge and gravitational anomaly in BTZ spacetime is cancelled by the total flux of a 2-dimensional blackbody at the Hawking temperature of the spacetime.     

Finite matrix models with continuous local gauge invariance

We construct a hamiltonian lattice gauge theory which possesses local SU (2) gauge invariance and yet is defined on a Hilbert space of 5-dimensional real vectors for every link. This construction does not allow for generalization to arbitrary SU(N), but a small variation of it can be generalized to an SU(N) × U(1) local gauge invariant model. The latter is solvable in simple gauge sectors leading to trivial spectra. We display these by studying a U(1) local gauge invariant model with similar characteristics.     

β FUNCTION FOR SU(2)×SU(2) CHIRAL MODEL ON 2-DIMENSIONAL RANDOM TRIANGLE LATTICE

The β function behavior for SU(2)×SU(2) chiral model on 2-dimensional random triangle lattice has been studied with Monte Carlo renormalization group method.Its behavior is similar to that of the 4-dimensional SU(2) gauge theory.However,it is smoother from weak to strong coupling regions.There is no nonperturbative peak structure.The asymptotic scaling starts beyond β=1.6.     

Independent Plaquette Trial Action for 4-Dimensional Lattice Gauge Theory

Based on the explicit expressions of the plaquette formulations, the independent plaquette trial action for 4-dimensional lattice gauge theory is introduced. As an example, the mean plaquette energy EP for the SU(2) lattice gauge theory is calculated by using action variational approach with the independent trial action. The results are in good agreement with the Monte Carlo results in the strong coupling and the crossover region, and the curve is smooth in the whole region, which show that 4-dimensional SU(2) theory has only a single, confining phase. The unwanted discontinuity of EP given by the single link trial action, which is used in the earlier variational calculations has been avoided.     

Gaupta-Bleuler triplet for massless spin-3/2 field in de Sitter space

Physicists have been interested in quantization of spinor and vector free fields in 4-dimensional de Sitter space-time,in ambient space notation.The Gupta-Bleuler formalism has been extensively applied to the quantization of gauge invariant theories.The field equation of the massless spin-3/2 fields is gauge invariant in de Sitter space.In this paper,we study the quantization of massless spin-3/2 gauge fields in de Sitter space-time by the Gupta-Bleuler formalism.This triplet carries an indecomposable representation of the de Sitter group.     

Calculation of Vacuum Wavefunction and Mass .Gap from Improved (2+l)-Dimensional SU(2) Lattice Gauge Field Hamiltonian

The truncated eigenvalue equation of SU(N) lattice gauge theory is studied by using improved lattice gauge Hamiltonian with a proper truncation scheme that preserves the continuum limit. The calculations of vacuum state wavefunction and glueball mass of (2+1)-dimensional SU(2) theory up to third order are carried out, the results show the improvement of scaling behavior in deep weak coupling region.     

On free 4D Abelian 2-form and anomalous 2D Abelian 1-form gauge theories

We demonstrate a few striking similarities and some glaring differences between (i) the free four- (3+1)-dimensional (4D) Abelian 2-form gauge theory, and (ii) the anomalous two- (1+1)-dimensional (2D) Abelian 1-form gauge theory, within the framework of Becchi–Rouet–Stora–Tyutin (BRST) formalism. We demonstrate that the Lagrangian densities of the above two theories transform in a similar fashion under a set of symmetry transformations even though they are endowed with a drastically different variety of constraint structures. With the help of our understanding of the 4D Abelian 2-form gauge theory, we prove that the gauge-invariant version of the anomalous 2D Abelian 1-form gauge theory is a new field-theoretic model for the Hodge theory where all the de Rham cohomological operators of differential geometry find their physical realizations in the language of proper symmetry transformations. The corresponding conserved charges obey an algebra that is reminiscent of the algebra of the cohomological operators. We briefly comment on the consistency of the 2D anomalous 1-form gauge theory in the language of restrictions on the harmonic state of the (anti-) BRST and (anti-) co-BRST invariant version of the above 2D theory.