Impact factor for gluon production in multi-Regge kinematics in the next-to-leading order

The one-loop correction to the impact factor for gluon production upon the transition of a one-Reggeon state in the t channel to a two-Reggeon state is found. This impact factor is an element of multiparticle amplitudes in multi-Regge kinematics. The correction in question is necessary for developing the theory of Regge and multi-Regge processes. In particular, it is necessary for proving the multi-Regge form of the amplitude in the next-to-leading-logarithm approximation. This correction also makes it possible to complete the verification of the last of the unproven bootstrap conditions for gluon Reggeization and to prove, in this approximation, the validity of the multi-Regge form of the amplitude. All necessary calculations are presented, and an explicit expression for the impact factor in front of all possible color states in the t channel is given.     

Color-kinematics duality for Sudakov form factor in non-supersymmetric pure Yang–Mills theory

We study the duality between color and kinematics for the Sudakov form factors of $mathrm{tr}({F}^{2})$ in non-supersymmetric pure Yang-Mills theory. We construct the integrands that manifest the color-kinematics duality up to two loops. The resulting numerators are given in terms of Lorentz products of momenta and polarization vectors, which have the same powers of loop momenta as that from the Feynman rules. The integrands are checked by d-dimensional unitarity cuts and are valid in any dimension. We find that massless-bubble and tadpole topologies are needed at two loops to realize the color-kinematics duality. Interestingly, the two-loop solution contains a large number of free parameters suggesting the duality may hold at higher loop orders.     

Small x phenomenology on gluon evolution through the BFKL equation in light of a constraint in multi-Regge kinematics

We investigate the impact of so-called kinematic constraint on gluon evolution at small x.Implanting the constraint on the real emission term of the gluon ladder diagram, we obtain an integro-differential form of the Balitsky-Fadin-Kuraev-Lipatov(BFKL) equation. Later we solve the equation analytically using the method of characteristics. We sketch the Bjorken x and transverse momentum k_t~2 dependence of our solution of unintegrated gluon distributions f (x,k_t~2) in the kinematic constraint supplemented BFKL equation and contrasted the same with the original BFKL equation. Then we extract the integrated gluon density xg(x, Q~2) from unintegrated gluon distributions f (x,k_t~2) and compared our theoretical prediction with that of global data fits, namely NNPDF3.1 sx and CT14. Finally we illustrate the phenomenological implication of our solution for unintegrated gluon distribution f (x,k_T~2) towards exploring high precision HERA DIS data by the theoretical prediction of proton structure functions(F_2 and F_L).     

Equivalence of dimensional reduction and dimensional regularisation

For some years there has been uncertainty over whether regularisation by dimensional reduction (DRED) is viable for non-supersymmetric theories. We resolve this issue by showing that DRED is entirely equivalent to standard dimensional regularisation (DREG), to all orders in perturbation theory and for a general renormalisable theory. The two regularisation schemes are related by an analytic redefinition of the couplings, under which the -functions calculated using DRED transform into those computed in DREG. TheS-matrix calculated using DRED is numerically equal to the DREG version, ensuring that both schemes give the same physics.     

Stability and dimensional reduction

With the help of dynamical system methods the stability ofR×S ³×S ^D solutions (whereS ³ andS ^D are maximally symmetric spaces) with the static microspace and the energy-momentum tensor determined by unifying theories is investigated. The general stability criterion is given and the significance of certain particular cosmological solutions is discussed.     

Signature and unitary in the multi-Regge model

In a previous paper it was shown how factorisation and signature properties for production processes arose from a well-defined set of singularities in complex angular momentum and helicity. These arose for Feynman diagrams without crossed channel singularities. In this paper we show how the general case gives rise to a sum of terms of this form. We also show how these precise singularities are crucial to prevent the occurence of terms in inclusive pionisation cross sections which are much greater than the canonical pomeron terms.     

Dynamical dimensional reduction

We propose to call a dynamical dimensional reduction effective if the corresponding dynamical system possesses a single attracting critical point representing expanding physical space-time and static internal space. We show that theBV × T ^D multidimensional cosmological model with a hydrodynamic energy-momentum tensor provides an example of effective dimensional reduction. We also study the dynamics of the multidimensional cosmological model of typeBI × T ^D with an energy-momentum tensor representing low temperature quantum effects, monopole contribution and the cosmological constant. It turns out that anisotropy and the cosmological constant are crucial for the process of dimensional reduction to be effective. We argue that this is the general property of homogeneous multidimensional cosmological models.     

Phase transitions and dimensional reduction

Using field theoretic methods a formalism is presented within which the critical behaviour of a system undergoing a dimensional reduction may be investigated. As a paradigm we study an Ising-like system on S¹ × R^3−ε. If the size of the system is L, and the correlation length ξ, then as L/ξ varies it is possible to get critical behaviour associated with two different fixed points. By exploiting a set of renormalization schemes which lead to manifest dimensional reduction in the loop expansion, and utilizing the renormalization group and an expansion about the fixed point of the finite system, we quantitatively investigate such crossover behaviour in its entirety. In particular, effective susceptibility and correlation length exponents are defined and computed. These exponents interpolate between those associated with a (4 − ε)-dimensional and a (3 − ε)-dimensional Ising model.     

Spontaneous compactification and dimensional reduction

A connection between dimensional reduction and spontaneous compactification is studied. It is shown that the methods of the coset-space dimensional-reduction scheme can be effectively used for constructing solutions of multidimensional Einstein-Yang-Mills equations and for interpreting from the viewpoint of the four-dimensional theory.     

Non-abelian isometries and dimensional reduction

Dimensional reduction is carried out for space-times, with or without torsion, which possess non-abelian isometries. The spectra and the equations of motion of the dimensionally reduced theory are obtained directly from the higher dimensional theory. The spectra of the reduced theories are naturally given in terms of scalar fields and antisymmetric tensor field strengths. A method of studying the dependence on the extra dimensions is suggested.     

Remarks on duality of 1 dimensional quantum spin models

We present some results on duality maps and ground states of 1 dimensional quantum spin models. We also give some applications to Kramers Wannier duality and the nonlocal transformation that Kennedy and Tasaki discovered in their study of Haldane phase of quantum antiferromagnetic spin models.     

Fermions and parity violation in dimensional reduction schemes

Dimensional reduction, previously applied to Yang-Mills theories, is extended to gauge theories with spinor fields. It is shown that a fairly realistic model in Minkowski space can be obtained from the simplest initial lagrangian, defined in a space-time with extra, compact dimensions. Left-right asymmetry in the fermion sector in four dimensions is possible, and its occurrence is related to a non-vanishing Atiyah-Singer index.     

Chirality index and dimensional reduction of fermions

The number of four-dimensional chiral fermions obtained from dimensional reduction of models with spinor matter fields coupled to pure gravity in d > 4 dimensions is linked to topological properties of the internal d ? 4 dimensional space. This gives important restrictions on possible ground states of such models consistent with a realistic four-dimensional unified theory. Connections with spontaneous symmetry breaking and Yukawa couplings of fermions in unified theories are discussed.     

Symmetries of Einstein-Yang-Mills fields and dimensional reduction

LetE be a manifold on which a compact Lie groupS acts simply (all orbits of the same type);E can be written locally asM×S/I,M being the manifold of orbits (space-time) andI a typical isotropy group for theS action. We study the geometrical structure given by anS-invariant metric and anS-invariant Yang Mills field onE with gauge groupR. We show that there is a one to one correspondence between such structures and quadruplets of fields defined solely onM; _v is a metric onM,h are scalar fields characterizing the geometry of the orbits (internal spaces), ⁱ are other scalar fields (Higgs fields) characterizing theS invariance of the Lie(R)-valued Yang Mills field and is a Yang Mills field for the gauge groupN(I)|I×Z((I)),N(I) being the normalizer ofI inS, is a homomorphism ofI intoR associated to theS action, andZ((I)) is the centralizer of(I) inR. We express the Einstein-Yang-Mills Lagrangian ofE in terms of the component fields onM. Examples and model building recipes are given.     

Equivariant dimensional reduction and quiver gauge theories

We review recent applications of equivariant dimensional reduction techniques to the construction of Yang-Mills–Higgs–Dirac theories with dynamical mass generation and exactly massless chiral fermions.