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Register a new userOn the Strong Coupling Scaling Dimension of High Spin Operators
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We give an exact analytic solution of the strong coupling limit of the integral equation which was recently proposed to describe the universal scaling function of high spin operators in N = 4 gauge theory. The solution agrees with the prediction from string theory, confirms the earlier numerical analysis and provides a basis for developing a systematic perturbation theory around strong coupling.
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In this paper we study the one-loop evolution equation of the Higgs quartic coupling $lambda$ in the minimal Universal Extra Dimension model, and find that there are certain bounds on the extra dimension due to the singularity and vacuum stability conditions of the Higgs sector. In the range $250GeV sim {R^{- 1}} sim 80TeV$ of the compactification radius, we notice that for a given initial value $lambda ({M_Z})$, there is an upper limit on ${R^{- 1}}$ for a Higgs mass of $183GeV sim {m_H}({M_Z}) sim 187GeV$; where any other compactification scales beyond that have been ruled out for theories where the evolution of $lambda$ does not develop a Landau pole and become divergent in the whole range (that is, from the electroweak scale to the unification scale). Likewise, in the range of the Higgs mass $152GeV sim {m_H}({M_Z}) sim 157GeV$, for an initial value $lambda ({M_Z})$, we are led to a lower limit on ${R^{- 1}}$; any other compactification scales below that will be ruled out for theories where the evolution of $lambda$ does not become negative and destabilize the vacuum between the electroweak scale and the unification scale. For a Higgs mass in the range $157GeV < {m_H}({M_Z}) < 183GeV$, the evolution of $lambda$ is finite and the theory is valid in the whole range (from the electroweak scale to the unification scale) for $250GeV sim {R^{- 1}} sim 80TeV$.
The Asymptotic Safety hypothesis states that the high-energy completion of gravity is provided by an interacting renormalization group fixed point. This implies non-trivial quantum corrections to the scaling dimensions of operators and correlation functions which are characteristic for the corresponding universality class. We use the composite operator formalism for the effective average action to derive an analytic expression for the scaling dimension of an infinite family of geometric operators $int d^dx sqrt{g} R^n$. We demonstrate that the anomalous dimensions interpolate continuously between their fixed point value and zero when evaluated along renormalization group trajectories approximating classical general relativity at low energy. Thus classical geometry emerges when quantum fluctuations are integrated out. We also compare our results to the stability properties of the interacting renormalization group fixed point projected to $f(R)$-gravity, showing that the composite operator formalism in the single-operator approximation cannot be used to reliably determine the number of relevant parameters of the theory.
We examine the Brown-Rho scaling for meson masses in the strong coupling limit of lattice QCD with one species of staggered fermion. Analytical expression of meson masses is derived at finite temperature and chemical potential. We find that meson masses are approximately proportional to the equilibrium value of the chiral condensate, which evolves as a function of temperature and chemical potential.
We construct an exact analytical solution to the integral equation which is believed to describe logarithmic growth of the anomalous dimensions of high spin operators in planar N=4 super Yang-Mills theory and use it to determine the strong coupling expansion of the cusp anomalous dimension.
We study the excited states of the pairing Hamiltonian providing an expansion for their energy in the strong coupling limit. To assess the role of the pairing interaction we apply the formalism to the case of a heavy atomic nucleus. We show that only a few statistical moments of the level distribution are sufficient to yield an accurate estimate of the energy for not too small values of the coupling $G$ and we give the analytic expressions of the first four terms of the series. Further, we discuss the convergence radius $G_{rm sing}$ of the expansion showing that it strongly depends upon the details of the level distribution. Furthermore $G_{rm sing}$ is not related to the critical values of the coupling $G_{rm crit}$, which characterize the physics of the pairing Hamiltonian, since it can exist even in the absence of these critical points.
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