arXiv subjects

George Savvidy

Publications and source records attributed to George Savvidy.

At least 55 records · Page 3Linked to original sources

arXiv2015

Generalisation of the Yang-Mills Theory

We suggest an extension of the gauge principle which includes tensor gauge fields. In this extension of the Yang-Mills theory the vector gauge boson becomes a member of a bigger family of gauge bosons of arbitrary large integer spins. The proposed extension is essentially based on the extension of the Poincaré algebra and the existence of an appropriate transversal representations. The invariant Lagrangian is expressed in terms of new higher-rank field strength tensors. It does not contain higher derivatives of tensor gauge fields and all interactions take place through three- and four-particle exchanges with a dimensionless coupling constant. We calculated the scattering amplitudes of non-Abelian tensor gauge bosons at tree level, as well as their one-loop contribution into the Callan-Symanzik beta function. This contribution is negative and corresponds to the asymptotically free theory. Considering the contribution of tensorgluons of all spins into the beta function we found that it is leading to the theory which is conformally invariant at very high energies. The proposed extension may lead to a natural inclusion of the standard theory of fundamental forces into a larger theory in which vector gauge bosons, leptons and quarks represent a low-spin subgroup. We consider a possibility that inside the proton and, more generally, inside hadrons there are additional partons - tensorgluons, which can carry a part of the proton momentum. The extension of QCD influences the unification scale at which the coupling constants of the Standard Model merge, shifting its value to lower energies.

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arXiv2015

Proton Spin and Tensorgluons

Recently it was suggested that inside the hadrons there are additional partons - tensorgluons - which carry the same charges as the gluons, but have larger spin. The nonzero density of tensorgluons can be created inside a nucleon by radiation of tensorgluons by gluons. Tensorgluons can carry a part of nucleon momentum together with gluons. Because tensorgluons have a larger spin, they can influence the spin structure of the nucleon. We analyse a possible contribution of polarised tensorgluon density to the spin of the nucleon. This contribution appears in the next to leading order, compared to the gluons and can provide a substantial screening effect due to the larger spin of tensorgluons.

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arXiv2014

Tensor gluons and proton structure

In a recent article we were considering a possibility that inside a proton and, more generally, inside hadrons there could be additional partons - tensor-gluons, which carry a part of the proton momentum. Tensor-gluons have zero electric charge, like gluons, but have a larger spin. Therefore we call them tensor-gluons. The nonzero density of tensor-gluons can be generated by the emission of tensor-gluons by gluons. Tensor-gluons can further split into the pairs of tensor-gluons through a different channels. To describe all these processes one should know the general splitting probabilities for tensor-gluons. These probabilities should fulfill very general symmetry relations, which we were able to resolve by introducing a splitting index. This approach allows to find out the general form of the splitting functions, to derive corresponding DGLAP evolution equations and to calculate the one-loop Callan-Simanzik beta function for tensor-gluons of a given spin. Our results provide a nontrivial consistency check of the theory and of the Callan-Simanzik beta function calculations, because the theory has a unique coupling constant and its high energy behavior should be universal for all particles of the spectrum. We argue that the contribution of all spins into the beta function vanishes leading to a conformal invariant theory at very high energies.

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arXiv2014

Proton structure and tensor gluons

We consider a possibility that inside the proton and, more generally, inside the hadrons there are additional partons - tensor-gluons, which can carry a part of the proton momentum. The tensor-gluons have zero electric charge, like gluons, but have a larger spin. Inside the proton a nonzero density of the tensor-gluons can be generated by the emission of tensor-gluons by gluons. The last mechanism is typical for non-Abelian tensor gauge theories, in which there exists a gluon-tensor-tensor vertex of order g. Therefore the number of gluons changes not only because a quark may radiate a gluon or because a gluon may split into a quark-antiquark pair or into two gluons, but also because a gluon can split into two tensor-gluons. The process of gluon splitting suggests that part of the proton momentum which was carried by neutral partons is shared between vector and tensor gluons. We derive evolution equations for the parton distribution functions which take into account these new processes. The momentum sum rule allows to find the tensor-gluons contribution to the Callan-Simanzik beta function and to calculate the corresponding anomalous dimensions. This contribution changes the behavior of the structure functions, and the logarithmic correction to the Bjorken scaling becomes more mild. This also influences the unification scale at which the coupling constants of the Standard Model merge, shifting its value to lower energies of order of 40 TeV.

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arXiv2014

Extension of Chern-Simons forms

We investigate metric independent, gauge invariant and closed forms in the generalized YM theory. These forms are polynomial on the corresponding fields strength tensors - curvature forms and are analogous to the Pontryagin-Chern densities in the YM gauge theory. The corresponding secondary characteristic classes have been expressed in integral form in analogy with the Chern-Simons form. Because they are not unique, the secondary forms can be dramatically simplified by the addition of properly chosen differentials of one-step-lower-order forms. Their gauge variation can also be found yielding the potential anomalies in the gauge field theory.

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arXiv2013

Invariant scalar product on extended Poincare algebra

Two methods can be used to calculate explicitly the Killing form on the Lie algebras. The first one is a direct calculation of the traces of the generators in a matrix representation of the algebra, and the second one is the usage of the group invariance of the scalar product. We use both methods in our calculation of the scalar product on the extended Poincare algebra in order to have a cross check of our results. The algebra is infinite-dimensional and requires careful treatment of the infinities. The scalar product on the extended algebra found by both methods coincides and the important conclusion which follows is that Poincare generators are orthogonal to the gauge generators.

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arXiv2013

Non-Abelian tensor gauge fields and new topological invariants

In this article we shall consider the tensor gauge fields which are possible to embed into the existing framework of generalized YM theory and therefore allows to construct the gauge invariant and metric independent forms in 2n+4 and 2n+2 dimensions. These new forms are analogous to the Pontryagin-Chern-Simons densities in YM gauge theory and to the corresponding series of densities in 2n+3 dimensions constructed recently in arXiv:1205.0027.

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arXiv2013

Extension of Chern-Simons forms and new gauge anomalies

We present a general analysis of gauge invariant, exact and metric independent forms which can be constructed using higher rank field-strength tensors. The integrals of these forms over the corresponding space-time coordinates provides new topological Lagrangians. With these Lagrangians one can define gauge field theories which generalize the Chern-Simons quantum field theory. We also present explicit expressions for the potential gauge anomalies associated with the tensor gauge fields and classify all possible anomalies that can appear in lower dimensions. Of special interest are those which can be constructed in four, six, eight and ten dimensions.

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arXiv2012

Differential geometry construction of anomalies and topological invariants in various dimensions

In the model of extended non-Abelian tensor gauge fields we have found new metric-independent densities: the exact (2n+3)-forms and their secondary characteristics, the (2n+2)-forms as well as the exact 6n-forms and the corresponding secondary (6n-1)-forms. These forms are the analogs of the Pontryagin densities: the exact 2n-forms and Chern-Simons secondary characteristics, the (2n-1)-forms. The (2n+3)- and 6n-forms are gauge invariant densities, while the (2n+2)- and (6n-1)-forms transform non-trivially under gauge transformations, that we compare with the corresponding transformations of the Chern-Simons secondary characteristics. This construction allows to identify new potential gauge anomalies in various dimensions.

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arXiv2012

Conformal invariance of tensor bosons tree amplitudes

The BCFW recursion relation allows to find out the tree-level scattering amplitudes for gluons and tensor gauge bosons in generalized Yang-Mills theory. We demonstrate that the corresponding MHV amplitudes for the tensor gauge bosons of spin-s and n gluons are invariant under conformal group transformations. We discuss and compare the tree-level scattering amplitudes for the charged tensor bosons with the corresponding scattering amplitudes for gravitons, stressing their differences and similarities.

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arXiv2011

Production of non-Abelian tensor gauge bosons. Tree amplitudes in generalized Yang-Mills theory and BCFW recursion relation

The BCFW recursion relation allows to calculate tree-level scattering amplitudes in generalized Yang-Mills theory and, in particular, four-particle amplitudes for the production rate of non-Abelian tensor gauge bosons of arbitrary high spin in the fusion of two gluons. The consistency of the calculations in different kinematical channels is fulfilled when all dimensionless cubic coupling constants between vector bosons (gluons) and high spin non-Abelian tensor gauge bosons are equal to the Yang-Mills coupling constant. There are no high derivative cubic vertices in the generalized Yang-Mills theory. The amplitudes vanish as complex deformation parameter tends to infinity, so that there is no contribution from the contour at infinity. We derive a generalization of the Parke-Taylor formula in the case of production of two tensor gauge bosons of spin-s and N gluons (jets). The expression is holomorhic in the spinor variables of the scattered particles, exactly as the MHV gluon amplitude is, and reduces to the gluonic MHV amplitude when s=1. In generalized Yang-Mills theory the tree level n-particle scattering amplitudes with all positive helicities vanish, but tree amplitudes with one negative helicity particle are already nonzero.

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arXiv2011

Extensions of the Poincare group

We construct an extension of the Poincare group which involves a mixture of internal and space-time supersymmetries. The resulting group is an extension of the superPoincare group with infinitely many generators which carry internal and space-time indices. It is a closed algebra since all Jacobi identities are satisfied and it has therefore explicit matrix representations. We investigate the massless case and construct the irreducible representations of the extended symmetry. They are divided into two sets, longitudinal and transversal representations. The transversal representations involve an infinite series of integer and half-integer helicities. Finally we suggest an extension of the conformal group along the same line.

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arXiv2011

Large spin behavior of anomalous dimensions and short-long strings duality

We are considering the semi-classical string soliton solution of Gubser, Klebanov and Polyakov which represents highly excited states on the leading Regge trajectory, with large spin in $AdS_5$. A prescription relates this soliton solution with the corresponding field theory operators with many covariant derivatives, whose anomalous scaling dimension grows logarithmically with the space-time spin. We explicitly derive the dependence of anomalous dimension on spin for all leading and next-to-leading orders at strong coupling. We develop an iteration procedure which, in principle, allows to derive all terms in the large spin expansion of the anomalous scaling dimension of twist two operators. Our string theory results are consistent with the conjectured "reciprocity" relation, which has been verified to hold in perturbation theory up to five loops in N=4 SYM. We also derive a duality relation between long and short strings.

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arXiv2010

Extension of the Poincaré Group and Non-Abelian Tensor Gauge Fields

In the recently proposed generalization of the Yang-Mills theory the group of gauge transformation gets essentially enlarged. This enlargement involves an elegant mixture of the internal and space-time symmetries. The resulting group is an extension of the Poincaré group with infinitely many generators which carry internal and space-time indices. This is similar to the super-symmetric extension of the Poincaré group, where instead of an anti-commuting spinor variable one should introduce a new vector variable. The construction of irreducible representations of the extended Poincaré algebra identifies a vector variable with the derivative of the Pauli-Lubanski vector over its length. As a result of this identification the generators of the gauge group have nonzero components only in the plane transversal to the momentum and are projecting out non-Abelian tensor gauge fields into the transversal plane, keeping only their positively definite space-like components.

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arXiv2010

Non-Abelian Tensor Gauge Fields

Recently proposed extension of Yang-Mills theory contains non-Abelian tensor gauge fields. The Lagrangian has quadratic kinetic terms, as well as cubic and quartic terms describing non-linear interaction of tensor gauge fields with the dimensionless coupling constant. We analyze particle content of non-Abelian tensor gauge fields. In four-dimensional space-time the rank-2 gauge field describes propagating modes of helicity 2 and 0. We introduce interaction of the non-Abelian tensor gauge field with fermions and demonstrate that the free equation of motion for the spin-vector field correctly describes the propagation of massless modes of helicity 3/2. We have found a new metric-independent gauge invariant density which is a four-dimensional analog of the Chern-Simons density. The Lagrangian augmented by this Chern-Simons-like invariant describes massive Yang-Mills boson, providing a gauge-invariant mass gap for a four-dimensional gauge field theory.

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arXiv2010

Particle spectrum of Non-Abelian tensor gauge fields

We present a brief review of the non-Abelian tensor gauge field theory and analyze its free field equations for lower rank gauge fields when the interaction coupling constant tends to zero. The free field equations are written in terms of the first order derivatives of extended field strength tensors similar to the electrodynamics and non-Abelian gauge theories. We determine the particle content of the free field equations and count the propagating modes which they describe. In four-dimensional space-time the rank-2 gauge field describes propagating modes of helicity two and zero. We show that the rank-3 gauge field describes propagating modes of helicity-three and a doublet of helicity-one gauge bosons. Only four-dimensional space-time is physically acceptable, because in five- and higher-dimensional space-time the equation has solutions with negative norm states. We discuss the structure of the particle spectrum for higher rank gauge fields.

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arXiv2009

Production of charged spin-two gauge bosons in gluon-gluon scattering

We consider the production of charged spin-two gauge bosons in the gluon-gluon scattering and calculate polarized cross sections for each set of helicity orientations of initial and final particles. The angular dependence of this cross section is compared with the gluon-gluon scattering cross section in QCD .

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arXiv2009

Connection between non-Abelian tensor gauge fields and open strings

We compare the structure of the tree level scattering amplitudes in non-Abelian tensor gauge field theory and in open string theory with Chan-Paton charges. We limit ourselves considering only lower rank tensor fields in both theories. We identify the symmetric and antisymmetric components of the second rank tensor gauge field with the string excitations on the third and forth levels. In the process of this identification we have been selecting only those parts of the tree level scattering amplitudes in the open string theory which have dimensionless coupling constants in four dimensions. It seems that this subclass of tree level scattering amplitudes may provide important information about the structure of the open string theory and most probably it is equivalent to the non-Abelian tensor gauge field theory.

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