Anton Ilderton
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.
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If scale invariance is exact, unparticles are unlikely to be probed in colliders since there are stringent constraints from astrophysics and cosmology. However these constraints are inapplicable if scale invariance is broken at a scale mu >~ 1 GeV. The case 1 GeV <~ mu < M_Z is particularly interesting since it allows unparticles to be probed at and below the Z pole. We show that mu can naturally be in this range if only vector unparticles exist, and briefly remark on implications for Higgs phenomenology. We then obtain constraints on unparticle parameters from e+ e- -> mu+ mu- cross-section a…
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 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 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 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.
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 show that the unparticle action that is made gauge invariant by the inclusion of an open Wilson line factor can be transformed into the integral-differential operator action that avoids the use of the Wilson line factor. The two forms of the action should therefore give the same Feynman diagrams. We also show that it is relatively easy to construct Feynman diagrams using the operator action.
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 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 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.
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 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 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 …
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…
Rigid gauge invariance comprises the symmetry content for physical quantities in a local gauge theory. Its derivation from BRS invariance is thus crucial for determining the physical consequences of the symmetry.
For gauge theory, the matrix element for any physical process is independent of the gauge used. Since this is a formal statement and examples are known where gauge invariance is violated, for any specific process this gauge invariance needs to be checked by explicit calculation. In this paper, gauge invariance is found to hold for a large non-trivial class of processes described by tree diagrams in the standard model -- tree diagrams with two external $W$ bosons and any number of external Higgs bosons. This verification of gauge invariance is quite complicated, and is based on a direct study o…
We discuss the problem of large gauge invariance at finite temperature.
A simple general proof of gauge invariance in QED is given in the framework of causal perturbation theory. It illustrates a method which can also be used in non-abelian gauge theories.
The inconsistence of Dirac-Weyl field equations with the universal U(1) gauge invariance of neutrinos in quantum mechanics led to generalize the special relativity to the generic relativity, which was composed of the special relativity and its three analogues with different signatures of metrics. The combination of the universal U(1) gauge invariance and the generic relativity naturally deduced the strong gauge symmetries $% SU(3)$ and the electroweak ones $SU(2)\times U(1)$ in the Standard Model. The universal U(1) gauge invariance of elementary fermions is attributed to its nature of complex…
Appreciating the classical understanding of the elementary particle the "dynamical" Poincare algebra is developed. It is shown that the "dynamical" Poincare algebra and the equations of motion of particles with arbitrary spin are gauge invariant and that gauge invariance and relativistic invariance stand on equal footings. A "dynamical" non-minimal interaction is constructed explicitly and the Rarita-Schwinger equation is considered in the framework of this "dynamical" interaction.
Certain (3+1)-dimensional chiral non-Abelian gauge theories have been shown to exhibit a new type of global gauge anomaly, which in the Hamiltonian formulation is due to the fermion zero-modes of a Z-string-like configuration of the gauge potential and the corresponding spectral flow. Here, we clarify the relation between this Z-string global gauge anomaly and other anomalies in both 3+1 and 2+1 dimensions. We then point out a possible trade-off between the (3+1)-dimensional Z-string global gauge anomaly and the violation of CPT and Lorentz invariance.
We describe higher-dimensional theories whose low-energy 4D descriptions contain larger gauge or global symmetry groups. As an example, we construct a Higgsless SU(2) x U(1) model of electroweak symmetry breaking. The 5D SU(2) gauge invariance contains both the weak SU(2) gauge group and a custodial symmetry that protects the rho parameter. Fermions obtain isospin-violating masses while maintaining universal gauge couplings among all three generations. As a further example, we construct a model of chiral color based on a single SU(3).
Gauge invariance and soft limits can be enough to determine the analytic structure of scattering amplitudes in certain theories. This prompts the question of how gauge invariance is connected to analytic structure in more general theories. Here we focus on QED in background plane waves. We show that imposing gauge invariance introduces new virtuality poles into internal momenta on which amplitudes factorise into a series of terms. Each term is gauge invariant, has a different analytic structure in external momenta, and exhibits a hard/soft factorisation. The introduced poles are dictated by in…
It is shown that space-time dependent gauge couplings do not completely break gauge invariance. We demonstrate this in various gauge theories.
A recently proposed formulation of chiral lattice gauge theories is reviewed, in which the locality and gauge invariance of the theory can be preserved if the fermion representation of the gauge group is anomaly-free.
We motivate the concept of emergent gauge symmetry and discuss ways that this concept can be tested. The key idea is that if a symmetry is emergent, one should look for small violations of this symmetry because the underlying fundamental theory does not contain the symmetry. We describe our recent work implementing this idea in the gravity sector. We also describe the reasons why violations of gauge symmetry may well be linked to violations of Lorentz invariance.
It is shown that anti-BRST invariance in quantum gauge theories can be considered as the quantized version of the symmetry of classical gauge theories with respect to different gauge fixing mechanisms.
It is shown that the creation of a monopole is a gauge invariant statement, based on topology. Creating a monopole is independent on the abelian projection in which it is created. This is fundamental in defining an order parameter for detecting dual superconductivity of the QCD vacuum.
A recent construction of the electroweak theory, based on perturbative quantum gauge invariance alone, is extended to the case of more generations of fermions with arbitrary mixing. The conditions implied by second order gauge invariance lead to an isolated solution for the fermionic couplings in agreement with the standard model. Third order gauge invariance determines the Higgs potential. The resulting massive gauge theory is manifestly gauge invariant, after construction.
We show that any BRST invariant quantum action with open or closed gauge algebra has a corresponding local background gauge invariance. If the BRST symmetry is anomalous, but the anomaly can be removed in the antifield formalism, then the effective action possesses a local background gauge invariance. The presence of antifields (BRST sources) is necessary. As an example we analyze chiral $W_3$ gravity.
The role of the gauge invariance in noncommutative field theory is discussed. A basic introduction to noncommutative geometry and noncommutative field theory is given. Background invariant formulation of Wilson lines is proposed. Duality symmetries relating various noncommutative gauge models are being discussed.
We check whether the SU(5) model, originally suggested by Georgi and Glashow, is compatible with perturbative quantum gauge invariance in first and second order for massive asymptotic gauge fields. We see that this is not the case: the SU(5) grand unified model does not meet with our restrictions from second order gauge invariance.
We study noncommutative deformations of Yang-Mills theories and show that these theories admit a infinite, continuous family of twisted star-gauge invariances. This family interpolates continuously between star-gauge and twisted gauge transformations. The possible physical role of these start-twisted invariances is discussed.
A new analysis of the gauge invariances and their unity with diffeomorphism invariances in second order metric gravity is presented which strictly follows Dirac's constrained Hamiltonian approach.
It is proved that classical BRS-invariance of the Lagrangian implies perturbative gauge invariance for tree diagrams to all orders. The proof applies in particular to the Einstein Hilbert Largrangian of gravity.
In this talk, I summarize the status of our understanding of the puzzle of large gauge invariance at finite temperature.
We show for the case of interacting massless vector bosons, how the structure of Yang-Mills theories emerges automatically from a more fundamental concept, namely perturbative quantum gauge invariance. It turns out that the coupling in a non-abelian gauge theory is necessarily of Yang-Mills type plus divergence- and coboundary couplings. The extension of the method to massive gauge theories is briefly discussed.
We address the study of gauge invariance in the Standard Model Extension which encompasses all Lorentz-violating terms originated by spontaneous symmetry breaking at the Planck scale. In particular, we fully evaluate Ward identities involving two and three point functions and derive the conditions which assure gauge invariance of the electromagnetic sector of the Standard Model Extension at one-loop. We show that momentum routing invariance is sufficient to fix arbitrary and regularization dependent parameters intrinsic to perturbation theory in the diagrams involved. A scheme which judiciousl…
We show how the widely used concept of spontaneous symmetry breaking can be explained in causal perturbation theory by introducing a perturbative version of quantum gauge invariance. Perturbative gauge invariance, formulated exclusively by means of asymptotic fields, is discussed for the simple example of Abelian U(1) gauge theory (Abelian Higgs model). Our findings are relevant for the electroweak theory, as pointed out elsewhere.
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 conjecture that the leading two-derivative tree-level amplitudes for gluons and gravitons can be derived from gauge invariance together with mild assumptions on their singularity structure. Assuming locality (that the singularities are associated with the poles of cubic graphs), we prove that gauge-invariance in just (n-1) particles together with minimal power-counting uniquely fixes the amplitude. Unitarity in the form of factorization then follows from locality and gauge invariance. We also give evidence for a stronger conjecture: assuming only that singularities occur when the sum of a s…
Quantum theory of the gauge models in the causal approach leads to some cohomology problems. We investigate these problems in detail.
We study the gauge invariance of the massive modes in the compactification of gauge theories from D=5 to D=4. We deal with Abelian gauge theories of rank one and two, and with non-Abelian ones of rank one. We show that Stückelberg fields naturally appear in the compactification mechanism, contrarily to what usually occurs in literature where they are introduced by hand, as a trick, to render gauge invariance for massive theories. We also show that in the non-Abelian case they appear in a very different way when compared with their usual implementation in the non-Abelian Proca model.
Reparametrization invariance being treated as a gauge symmetry shows some specific peculiarities. We study these peculiarities both from a general point of view and on concrete examples. We consider the canonical treatment of reparametrization invariant systems in which one fixes the gauge on the classical level by means of time-dependent gauge conditions. In such an approach one can interpret different gauges as different reference frames. We discuss the relations between different gauges and the problem of gauge invariance in this case. Finally, we establish a general structure of reparametr…
The concept of perturbative gauge invariance formulated exclusively by means of asymptotic fields is generalized to massive gauge fields. Applying it to the electroweak theory leads to a complete fixing of couplings of scalar and ghost fields and of the coupling to leptons, in agreement with the standard theory. The W/Z mass ratio is also determined, as well as the chiral character of the fermions. We start directly with massive gauge fields and leptons and, nevertheless, obtain a theory which satisfies perturbative gauge invariance.
The possibility of having a gauge fixing term in the effective Lagrangian that is not a quadratic expression has been explored in spin-two theories so as to have a propagator that is both traceless and transverse. We first show how this same approach can be used in spontaneously broken gauge theories as an alternate to the 't Hooft gauge fixing which avoids terms quadratic in the scalar fields. This "non-quadratic" gauge fixing in the effective action results in there being two complex Fermionic and one real Bosonic ghost fields. A global gauge invariance involving a Fermionic gauge parameter,…
Gauge independence of dimension two condensate in Yang-Mills theory is demonstrated by using a noncommutative theory technique.
The scale invariance of the coupling constant in the induced gauge theory due to its compositeness condition is demonstrated in the renormalization group flow of the finite-cutoff gauge theory at the leading order in 1/N, where N is the number of the matter fermion species.
We present an elegant method to prove the invariance of the Chern-Simons part of the non-Abelian action for N coinciding D-branes under the R-R and NS-NS gauge transformations, by carefully defining what is meant by a background gauge transformation in the non-Abelian world volume action. We study as well the invariance under massive gauge transformations of the massive Type IIA supergravity and show that no massive dielectric couplings are necessary to achieve this invariance.
In the Coulomb gauge, the Hamiltonian of QCD contains terms of order h^2, identified by Christ and Lee, which are non-local but instantaneous. The question is addressed how these terms fit in with BRST invariance. Our discussion is confined to the simplest, O(g^4), example.
We show explicitly that the question of gauge invariance of the effective potential in standard scalar electrodynamics remains unchanged despite the introduction of the Chern-Simons term. The result does not depend on the presence of the Maxwell term in the Chern-Simons territory.
We point out a critical defect in the calculation of the functional determinant of the gluon loop in the Savvidy-Nielsen-Olesen (SNO) effective action. We prove that the gauge invariance naturally exclude the unstable tachyonic modes from the gluon loop integral. This guarantees the stability of the magnetic condensation in QCD.
A possibility to represent the standard model of fundamental particles covariant derivatives by means of approximate generalized fractional Riemann-Liouville derivatives of multifractal time and space model is shown.
In this paper we will discuss the effect of a having a boundary on the supersymmetric invariance and gauge invariance of the Bagger-Lambert-Gustavsson (BLG) Theory. We will show that even though the supersymmetry and gauge invariance of the original BLG theory is broken due to the presence of a boundary, it restored by the addition of suitable boundary terms. In fact, to achieve the gauge invariance of this theory, we will have to introduce new boundary degrees of freedom. The boundary theory obeyed by these new boundary degrees of freedom will be shown to be a generalization of the gauged Wes…
We study the 0+1 dimensional Chern-Simons theory at finite temperature within the framework of derivative expansion. We obtain various interesting relations, solve the theory within this framework and argue that the derivative expansion is not a suitable formalism for a study of the question of large gauge invariance.
The topological non-Abelian Chern-Simons theory with a boundary is shown to require a scalar field companion in order to preserve overall gauge-invariance both in the 3 dimensional manifold, as well as on its boundary. This scalar field, originally being a pure-gauge Chern-Simons excitation that indicates the most general topological gauge structure in the bulk, is found to be crucial for dynamic scalar excitation on the 2 dimensional generic boundary manifold, the latter naturally representing a conformal mode. This gauge/CFT correspondence is general, for a compact gauge group.
We comment on a recent puzzle regarding renormalization group invariance of exact results in SUSY theories, and argue that a purported renormalization of the dynamical scale Λdoes not in fact occur.
We present an extremely simple solution to the renormalization of quantum electrodynamics based on Epstein-Glaser approach to renormalization theory.
Recursion relations are succinctly obtained for $(++... +)$ and $(-++... +)$ amplitudes in the context of the space-cone gauge in QCD. We rely on the helicity symmetry of the problems to dictate our choices of reference twistors and the momentum shifts to complexify the amplitudes. Of great importance is the power of gauge Lorentz invariance, which is enough to determine the soft factors in the latter cases.
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