A. Lewis Licht
We show that a rigorous path integral method of introducing gauge fields in the UnParticle lagrangian leads to somewhat different and more complicated vertexes than those currently used.
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We show that it is possible to couple gauge fields to unparticles without the use of path integrals in the unparticle effective action. This is done by treating the unparticle field as a vector in an abstract Hilbert space and the gauge field as an operator on that space.
We show that the requirement of gauge invariance is not enough to fix the form of interactions between unparticles and gauge fields, thus revealing a wide new class of gauged unparticle actions. Our approach also allows us to construct operators which create gauge invariant coloured unparticles. We discuss both their perturbative and non--perturbative properties.
We show that the path ordered Wilson line integral used in 0802.0313 to make a nonlocal action gauge invariant is mathematically inconsistent. We also show that it can lead to reasonable gauge field vertexes by the use of a second mathematically unjustifiable procedure.
The derivation of Feynman rules for unparticles carrying standard model quantum numbers is discussed. In particular, this note demonstrates that an application of Mandelstam's approach to constructing a gauge-invariant action reproduces for unparticles the vertices one obtains through the usual minimal coupling scheme; other non-trivial requirements are satisfied as well. This approach is compared to an alternative method 0801.0892 that has recently been constructed by A. L. Licht.
Modern theoretical models strongly suggest that new phenomena await discovery above the energy scale of the Standard Model (SM) of particle interactions. In this paper we argue that correct description of particle physics in the TeV energy scale needs to account for degrees of freedom obeying the conformal (or scale) invariance. In this respect, the existing of Georgi's unparticles is strongly argued. We present the gauge model of scalar unparticles. The ground state of scalar unparticles in the continuum is restricted by the vacuum expectation value of the SM Higgs boson and the scale dimensi…
We examine the correspondence between the anti-de Sitter (AdS) description of conformal field theories (CFTs) and the unparticle description of CFTs. We show how unparticle actions are equivalent to holographic boundary actions for fields in AdS, and how massive unparticles provide a new type of infrared cutoff that can be simply implemented in AdS by a soft breaking of conformal symmetry. We also show that processes involving scalar unparticles with dimensions d_s<2 or fermion unparticles with dimensions d_f<5/2 are insensitive to ultraviolet cutoff effects. Finally we show that gauge interac…
We consider the unparticle action that is made gauge invariant by inclusion of an open Wilson line factor. In deriving vertexes from such an action it has been customary to use a form of differentiating the Wilson line originally proposed by Mandelstam. Using a simple example, we show that the Mandelstam derivative is mathematically inconsistent. We show that there are two ways to define differentiation of the Wilson line. The mathematically consistent method is to differentiate the explicit dependence of the line on the endpoint. The other method is a functional derivative and corresponds in …
The possibility of the presence of unparticle has been discussed recently adding a mass like term for gauge field with the Vector Schwinger model at the classical level \cite{GEOR1}. A one loop correction due to bosonization is taken into account and investigation is carried over to study the effect of it in connection with the unparticle scenario. It has been found that mass of the gauge boson acquires a generalized expression with the bare coupling constant and the parameters involved in the masslike terms added at the classical level term as well the terms entered in the model during the on…
We first quantize the action proposed by Casalbuoni and Gomis in [Phys. Rev. D \textbf{90}, 026001 (2014)], an action that describes two massless relativistic scalar particles interacting via a conformally invariant potential. The spectrum is a continuum of massive states that may be interpreted as unparticles. We then obtain in a similar way the mass operator for a deformed action in which two terms are introduced that break the conformal symmetry: a mass term and an extra position-dependent coupling constant. A simple Ansatz for the latter leads to a mass operator with linear confinement in …
We present the conformal windows of SU(N) supersymmetric and nonsupersymmetric gauge theories with vector-like matter transforming according to higher irreducible representations of the gauge group. We determine the fraction of asymptotically free theories expected to develop an infrared fixed point and find that it does not depend on the specific choice of the representation. This result is exact in supersymmetric theories while it is an approximate one in the nonsupersymmetric case. The analysis allows us to size the unparticle world related to the existence of underlying gauge theories deve…
We study interactions of unparticles ${\cal {U}}$ of dimension $d_{\cal {U}}$ due to Georgi with Standard Model (SM) fields through effective operators. The unparticles describe the low energy physics of a non-trivial scale invariant sector. Since unparticles come from beyond the SM physics, it is plausible that they transform as a singlet under the SM gauge group. This helps tremendously in limiting possible interactions. We analyze interactions of scalar ${\cal {U}}$, vector ${\cal {U}}$$^μ$ and spinor ${\cal {U}}$$^s$ unparticles with SM fields and derivatives up to dimension four. Using th…
Using the gauge-invariant but path-dependent variables formalism, we examine the effect of the space-time dimensionality on a physical observable in the unparticle scenario. We explicitly show that long-range forces between particles mediated by unparticles are still present whenever we go over into lower dimensions.
We analyze generalizations of the Schwinger model with more massless fermions and more vector fields. We focus on models with the gauge structure of ``diagonal color $SU(n)$'' but unlike previous investigators, we do not assume that all the gauge boson masses are the same. Unlike the Schwinger model, these are Banks-Zaks models with conformal sectors that survive at long distances. In addition to local operators that go to ``unparticle operators'' with non-zero anomalous dimensions at long distances, they contain local operators like the $\barψ_Lψ_R$ operator in the Schwinger model which go to…
We consider scale invariant theories of continuous mass fields, and show how interactions of these fields with the standard model can reproduce unparticle interactions. There is no fixed point or dimensional transmutation involved in this approach. We generalize interactions of the standard model to multiple unparticles in this formalism and explicitly work out some examples, in particular we show that the product of two scalar unparticles behaves as a normalized scalar unparticle with dimension equal to the sum of the two composite unparticle dimensions. Extending the formalism to scale invar…
A new type of scalar potential inspired by unparticles is proposed for the electroweak symmetry breaking. The interaction between the standard model fields and unparticle sector is described by the non-integral power of fields that originates from the nontrivial scaling dimension of the unparticle operator. We find that unlike the usual integral-power potential, the electroweak symmetry is broken at tree level. The scale invariance of unparticle sector is also broken simultaneously, resulting in a physical Higgs and a lighter scalar particle.
The unparticle field operator can be expanded in terms of creation and destruction operators corresponding to particles with a continuous mass spectrum. Hence, when the 4-momentum of an unparticle is measured, then the unparticle manifests as an ordinary particle with a definite (but arbitrary) mass.
We summarize basic features associated to dynamical breaking of the electroweak symmetry. The knowledge of the phase diagram of strongly coupled theories as function of the number of colors, flavors and matter representation plays a fundamental role when trying to construct viable extensions of the standard model (SM). Therefore we will report on the status of the phase diagram for SU(N) gauge theories with fermionic matter transforming according to arbitrary representations of the underlying gauge group. We will discuss how the phase diagram can be used to construct unparticle models. We will…
We examine a dark energy model where a scalar unparticle degree of freedom plays the role of quintessence. In particular, we study a model where the unparticle degree of freedom has a standard kinetic term and a simple mass potential, the evolution is slowly rolling and the field value is of the order of the unparticle energy scale ($λ_u$). We study how the evolution of $w$ depends on the parameters $B$ (a function of the unparticle scaling dimension $d_u$), the initial value of the field $ϕ_i$ (or equivalently, $λ_u$) and the present matter density $Ω_{m0}$. We use observational data from Typ…
Strongly Coupled Sectors in Inflation: Gapped Theories of Unparticles
本文研究了通胀期间强耦合观测子领域的新场景，通过高维共形场理论（无粒子）并紧致化额外维度，推导出无粒子的二点函数，并计算了四点关联函数，揭示了无粒子与重标量子的区分策略及干涉图案。
Searching for Unparticles with the Cosmic Microwave Background
研究通过宇宙微波背景数据分析无粒子模型，利用神经网络因子化方案和最优CMB估计器，将非可分离模板压缩为可分离形式，发现无粒子信号与单场自相互作用难以区分，但Δ接近半整数时形状不同。
We use gauge/gravity duality to study the thermodynamics of a field theory with asymptotic freedom in the ultraviolet and a fixed point in the infrared. We find a high temperature quark-gluon phase and a low T conformal unparticle phase. The phase transition between the phases is of first order or continuous, depending on the ratio of the radii of asymptotic AdS5 spaces at T=0 and T=infinity. This is a prediction from a model of gauge/gravity duality, not yet verified on the field theory side.
The Sommerfield model with a massive vector field coupled to a massless fermion in 1+1 dimensions is an exactly solvable analog of a Bank-Zaks model. The `physics' of the model comprises a massive boson and an unparticle sector that survives at low energy as a conformal field theory (Thirring model). I discuss the `Schwinger point' of the Sommerfield model in which the vector boson mass goes to zero. The limit is singular but gauge invariant quantities should be well-defined. I give a number of examples, both (trivially) with local operators and with nonlocal products connected by Wilson lines…
We derive model-independent, universal upper bounds on the Operator Product Expansion (OPE) coefficients in unitary 4-dimensional Conformal Field Theories. The method uses the conformal block decomposition and the crossing symmetry constraint of the 4-point function. In particular, the OPE coefficient of three identical dimension $d$ scalar primaries is found to be bounded by ~ 10(d-1) for 1<d<1.7. This puts strong limits on unparticle self-interaction cross sections at the LHC.
We investigate a nonrelativistic version of Georgi's "unparticle physics." We define the unnucleus as a field in a nonrelativistic conformal field theory. Such a field is characterized by a mass and a conformal dimension. We then consider the formal problem of scatterings to a final state consisting of a particle and an unnucleus and show that the differential cross section, as a function of the recoil energy received by the particle, has a power-law singularity near the maximal recoil energy, where the power is determined by the conformal dimension of the unnucleus. We argue that unlike the r…
We present a BRST symmetric gaugeon formalism for the two-form gauge fields. A set of vector gaugeon fields is introduced as a quantum gauge freedom. One of the gaugeon fields satisfies a higher derivative field equation; this property is necessary to change the gauge-fixing parameter of the two-form gauge field. A naive Lagrangian for the vector gaugeon fields is itself invariant under a gauge transformation for the vector gaugeon field. The Lagrangian of our theory includes the gauge-fixing terms for the gaugeon fields and corresponding Faddeev--Popov ghosts terms.
Quantization of 2D Abelian Gauge Theory without the Kinetic Term of Gauge Field as Anomalous Gauge Theory
不含规范场动力学项的无质量Schwinger模型存在规范反常。在最一般的规范条件下，我们把这个模型看作反常的规范理论。我们证明了由于规范反常，规范场成为一个动力学变量。
We examine the relation between Coulomb-gauge fields and the gauge-invariant fields constructed in the temporal gauge for two-color QCD by comparing a variety of properties, including their equal-time commutation rules and those of their conjugate chromoelectric fields. We also express the temporal-gauge Hamiltonian in terms of gauge-invariant fields and show that it can be interpreted as a sum of the Coulomb-gauge Hamiltonian and another part that is important for determining the equations of motion of temporal-gauge fields, but that can never affect the time evolution of ``physical'' state v…
Using a gauge symmetry derived by applying the Dirac constraint formalism to supergravity with cosmological term in 2+1 dimensions, we construct a gauge theory with many characteristics of Yang-Mills theory. The gauge transformation mixes two Bosonic fields and one Fermionic field.
We propose a systematic procedure for extracting gauge invariant and gauge fixed actions for various higher-spin gauge field theories from covariant bosonic open string field theory. By identifying minimal gauge invariant part for the original free string field theory action, we explicitly construct a class of covariantly gauge fixed actions with BRST and anti-BRST invariance. By expanding the actions with respect to the level N of string states, the actions for various massive fields including higher-spin fields are systematically obtained. As illustrating examples, we explicitly investigate …
The problem of gauge independent definition of the effective gauge field is considered. The Slavnov identities corresponding to a system of interacting quantum gauge and classical matter fields, playing the role of a measuring device, are obtained. With their help, in the case of power-counting renormalizable theories, gauge independence of the effective device action is proved in the low-energy limit, which allows to introduce the gauge independent notion of the effective gauge field.
We show that as in abelian gauge fields, nonabelian gauge fields are also trapped on a brane in the Randall-Sundrum model by applying a new mechanism based on topological Higgs mechanism. It is pointed out that although almost massless gauge fields are localized on the brane by the new mechanism, exactly massless gauge fields are not localized. This fact does not yield any problem to abelian gauge fields, but may give some problem to nonabelian gauge fields since it is known that there is a discontinuity between massless and massive gauge fields in the case of nonabelian gauge groups.
We review the procedure by which we implemented the non-Abelian Gauss's law and constructed gauge-invariant fields for QCD in the temporal (Weyl) gauge. We point out that the operator-valued transformation that transforms gauge-dependent temporal-gauge fields into gauge-invariant ones has the formal structure of a gauge transformation. We express the ``standard'' Hamiltonian for temporal-gauge QCD entirely in terms of gauge-invariant fields, calculate the commutation rules for these fields, and compare them to earlier work on Coulomb-gauge QCD. We also discuss multiplicities of gauge-invariant…
Inspired by the rich structure of covariant string field theory, we propose a minimal gauge invariant action for general massive integer spin n field. The action consists of four totally symmetric tensor fields of order respectively n, n-1, n-2 and n-3, and is invariant under the gauge transformation represented by two also totally symmetric fields of order n-1 and n-2. This action exactly has the same gauge structure as for the string field theory and we discuss general covariant gauge fixing procedure using the knowledge of string field theory. We explicitly construct the corresponding gauge…
We provide a gauge covariant formalism of the canonically quantized theory of spin-3/2 Rarita-Schwinger gauge field. The theory admits a quantum gauge transformation by which we can shift the gauge fixing parameter. The quantum gauge transformation does not change the BRST charge. Thus, the physical Hilbert space is trivially independent of the gauge fixing parameter.
Using generalized field strength tensors for non-Abelian tensor gauge fields one can explicitly construct all possible Lorentz invariant quadratic forms for rank-4 non-Abelian tensor gauge fields and demonstrate that there exist only two linear combinations of them which form a gauge invariant Lagrangian. Together with the previous construction of independent gauge invariant forms for rank-2 and rank-3 tensor gauge fields this construction proves the uniqueness of early proposed general Lagrangian up to rank-4 tensor fields. Expression for the coefficients of the general Lagrangian is presente…
The standard procedure for making a global phase symmetry local involves the introduction of a rank 1, vector field in the definition of the covariant derivative. Here it is shown that it is possible to gauge a phase symmetry using fields of various ranks. In contrast to other formulations of higher rank gauge fields we begin with the coupling of the gauge field to some matter field, and then derive the gauge invariant, field strength tensor. Some of these gauge theories are similar to general relativity in that their covariant derivatives involve derivatives of the rank n gauge field rather t…
We show that a-gauge, a class of covariant gauges developed for bosonic open string field theory, is consistently applied to the closed string field theory. A covariantly gauge-fixed action of massless fields can be systematically derived from a-gauge-fixed action of string field theory.
We discuss gravity-like formulations of massive Abelian and non-Abelian gauge field theories in four space-time dimensions with particular emphasis on the issue of gauge invariance. Alternative descriptions in terms of antisymmetric tensor fields and geometric variables, respectively, are analysed. In both approaches Stückelberg degrees of freedom factor out. We also demonstrate, in the Abelian case, that the massless limit for the gauge propagator, which does not exist in the vector potential formulation, is well-defined for the antisymmetric tensor fields.
We study gauge transformations of the Hata-Kawano vector state on a D25-brane in the framework of vacuum string field theory. We show that among the infinite number of components of the polarization vector, all the components except one spacetime vector degree of freedom are gauge freedom, and give string field gauge transformations reproducing gauge transformations of the constant modes of the U(1) gauge field. These gauge transformations can be used to fix the normalization of the vector field. We also discuss a difficulty in obtaining a gauge invariant action of the vector field. Our argume…
Employing methods introduced by Schwinger in quantum electrodynamics, we compute the propagator for a non-Abelian gauge field in a plane wave background field. In the long distance limit a mass-like term for the gauge field is induced by this interaction.
Local quartic interaction of higher-spin gauge field with a scalar field is considered. In this special case, the nontrivial task of construction of interacting Lagrangian for the higher spin field in physical gauge was solved using the full power of Noether's procedure. As a result, the linear on-field gauge transformation is obtained and the corresponding commutator of transformation is analyzed. To understand the closure of this algebra the right-hand side of this commutator is classified in respect to gauge transformations coming from cubic interactions with different higher spin symmetric…
SU(3) gauge theory in the nonlinear gauge of the Curci--Ferrari type is studied. In the low-energy region, ghost condensation and subsequent gauge field condensation can happen. The latter condensation makes classical gauge fields massive. If the color electric potential with string is chosen as the classical gauge field, it produces the static potential with the linear potential. We apply this static potential to the three-quark system, and show, different from the $Y$-type potential, infrared divergence remains in the $Δ$-type potential. The color electric flux is also studied, and show that…
A local gauge invariant interaction Lagrangian for two gauge fields of spin $\ell$ and $\ell-2$ $(\ell>2)$ and the scalar field is defined. It gives rise to one-loop corrections to the gauge field propagator. The loop function contains the Goldstone boson propagator for gauge symmetry breaking. The proportionality factor in front of this propagator is the mass squared of the gauge boson.
We extend the construction of field operators in AdS as smeared single trace operators in the boundary CFT to gauge fields and gravity. Bulk field operators in a fixed gauge can be thought of as non-local gauge invariant observables. Non-local commutators result from the Gauss law constraint, which for gravity implies a perturbative notion of holography. We work out these commutators in a generalized Coulomb gauge and obtain leading order smearing functions in radial gauge.
Conformal low-spin anomalous currents and shadow fields in flat space-time of dimension greater than or equal to four are studied. Gauge invariant formulation for such currents and shadow fields is developed. Gauge symmetries are realized by involving Stueckelberg and auxiliary fields. Gauge invariant differential constraints for anomalous currents and shadow fields and realization of global conformal symmetries are obtained. Gauge invariant two-point vertices for anomalous shadow fields are also obtained. In Stueckelberg gauge frame, these gauge invariant vertices become the standard two-poin…
We review an alternative formulation of gauge field theories at finite temperature where unphysical degrees of freedom of gauge fields and the Faddeev-Popov ghosts are kept at zero temperature.
A single-parameter family of covariant gauge fixing conditions in bosonic string field theory is proposed. It is a natural string field counterpart of the covariant gauge in the conventional gauge theory, which includes the Landau gauge as well as the Feynman (Siegel) gauge as special cases. The action in the Landau gauge is largely simplified in such a way that numerous component fields have no derivatives in their kinetic terms and appear in at most quadratic in the vertex.
We suggest an extension of the gauge principle which includes tensor gauge fields. The extended non-Abelian gauge transformations of the tensor gauge fields form a new large group. On this group one can define field strength tensors, which are transforming homogeneously with respect to the extended gauge transformations. The invariant Lagrangian is quadratic in the field strength tensors and describes interaction of tensor gauge fields of arbitrary large integer spin $1,2,...$. It does not contain higher derivatives of the tensor gauge fields, and all interactions take place through three- and…
The development of nonabelian gauge fields for last 60 years is reviewed. The new method of quantization of gauge fields applicable beyond perturbation theory is proposed.
We continue McCartor and Robertson's recent demonstration of the indispensability of ghost fields in the light-cone gauge quantization of gauge fields. It is shown that the ghost fields are indispensable in deriving well-defined antiderivatives and in regularizing the most singular component of gauge field propagator. To this end it is sufficient to confine ourselves to noninteracting abelian fields. Furthermore to circumvent dealing with constrained systems, we construct the temporal gauge canonical formulation of the free electromagnetic field in auxiliary coordinates $x^μ=(x^-,x^+,x^1,x^2)$…
We obtain static gauge field configurations for SU(2) Yang-Mills gauge theory in the absence of chromo-magnetic field. We also present a systematic way to obtain such configurations for SU(3) and SU(4) YM gauge theories by realizing their Lie algebras in terms of SU(2). Generalization of our method to SU(N) gauge theory with N>2 is straight forward. The gauge fields thus obtained are complex. We investigated the issue of uniform as well as real chromo-electric field with these configurations. Furthermore, we investigated the possible class of vacuum solutions for the gauge fields and found tha…
The cohomological approach to the problem of consistent interactions between fields with a gauge freedom is reviewed. The role played by the BRST symmetry is explained. Applications to massless vector fields and 2-form gauge fields are surveyed.
Field-Antifield formalism for Anomalous Gauge Theories
本文推广了场-反场形式，用一个封闭的、不可约的经典规范代数来处理反常规范理论。引入额外的自由度，我们构造了这些新场的规范变换，Wess-Zumino项和相应的测度。
We study gauge invariant quantities in the open superstring field theory proposed by Berkovits, extending the precedent discussion in bosonic string field theory. Our gauge invariants are ``on-shell''. As its applications, we define quantities which are expected to be related to the U(1) field strength -- a RR coupling and a ``component'' of the string field equation of motion, and consider their naive extensions to off-shell. Order by order calculations show that the field strength extracted from the RR coupling is not gauge invariant, while from the component of the equation of motion we obt…
Self-Dual Gauge Fields from Superstring Field Theory
该研究通过超弦场论推导出自对偶规范场的行动，并揭示了其与背景度量和两个耦合度量之间的非线性关系。
We study the problem of axial and gauge anomalies in a reducible theory involving vector and tensor gauge fields coupled in a topological way. We consider that vector and axial fermionic currents couple with the tensor field in the same topological manner as the vector gauge one. This kind of coupling leads to an anomalous axial current, contrarily to the results found in literature involving other tensor couplings, where no anomaly is obtained.
Using Poincare parametrization of AdS space, we study totally symmetric arbitrary spin massless fields in AdS space of dimension greater than or equal to four. CFT adapted gauge invariant formulation for such fields is developed. Gauge symmetries are realized similarly to the ones of Stueckelberg formulation of massive fields. We demonstrate that the curvature and radial coordinate contributions to the gauge transformation and Lagrangian of the AdS fields can be expressed in terms of ladder operators. Realization of the global AdS symmetries in the conformal algebra basis is obtained. Modified…
Gauge Field Theories on Riemann Surfaces
本文将任意亏格的黎曼曲面上的自由规范场理论量子化为协变规范场。导出了规范场的传播子，并详细分析了它们的性质。作为应用，计算了具有规范群$SU(N)$的Yang-Mills场论的最低阶关联函数.
In this ultra short note, gauge field propagation in D-brane configuration of M theory in the BFSS matrix formulation is considered. Noncommutativity of the space plays a key role for appearance of gauge fields as physical degrees of freedom.
In the framework of gauge invariant Stueckelberg approach, totally symmetric arbitrary spin shadow fields in flat space-time of dimension greater than or equal to four are studied. Gauge invariant two-point vertices for such shadow fields are obtained. We demonstrate that, in Stueckelberg gauge frame, these gauge invariant vertices become the standard two-point vertices of CFT. Light-cone gauge two-point vertices of the shadow fields are also obtained. AdS/CFT correspondence for the shadow fields and the non-normalizable solutions of free massless totally symmetric arbitrary spin AdS fields is…
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