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Register a new userWilson Coefficients in the Operator Product Expansion of Scalar Currents at Finite Temperature
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In this paper, we investigate operator product expansion for thermal correlation function of the two scalar currents. Due to breakdown of Lorentz invariance at finite temperature, more operators of the same dimension appear in the operator product expansion than at zero temperature. We calculated Wilson coefficients in the short distance expansion and obtain operator product expansion for thermal correlation function in terms of quark condensate, gluon condensate, quark energy density and gluon energy density.
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We present first results for Wilson coefficients of operators up to first order in the covariant derivatives for the case of Wilson fermions. They are derived from the off-shell Compton scattering amplitude $mathcal{W}_{mu u}(a,p,q)$ of massless quarks with momentum $p$. The Wilson coefficients are classified according to the transformation of the corresponding operators under the hypercubic group H(4). We give selected examples for a special choice of the momentum transfer $q$. All Wilson coefficients are given in closed analytic form and in an expansion in powers of $a$ up to first corrections.
We apply the $delta$-expansion perturbation scheme to the $lambda phi^{4}$ self-interacting scalar field theory in 3+1 D at finite temperature. In the $delta$-expansion the interaction term is written as $lambda (phi^{2})^{ 1 + delta}$ and $delta$ is considered as the perturbation parameter. We compute within this perturbative approach the renormalized mass at finite temperature at a finite order in $delta$. The results are compared with the usual loop-expansion at finite temperature.
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We revisit the computation of instanton effects to various correlation functions in ${cal N}=4$ SYM and clarify a controversy existing in the literature regarding their consistency with the OPE and conformal symmetry. To check these properties, we examine the conformal partial wave decomposition of four-point correlators involving combinations of half-BPS and Konishi operators and isolate the contribution from the conformal primary scalar operators of twist four. We demonstrate that the leading instanton correction to this contribution is indeed consistent with conformal symmetry and compute the corresponding corrections to the OPE coefficients and the scaling dimensions of such twist-four operators. Our analysis justifies the regularization procedure used to compute ultraviolet divergent instanton contribution to correlation functions involving unprotected operators.
We study the entanglement entropy and the mutual information in coupled harmonic systems at finite temperature. Interestingly, we find that the mutual information does not vanish at infinite temperature, but it rather reaches a specific finite value, which can be attributed to classical correlations solely. We further obtain high and low temperature expansions for both quantities. Then, we extend the analysis performed in the seminal paper by Srednicki (Phys. Rev. Lett. 71, 666 (1993)) for free real scalar field theories in Minkowski space-time in 3+1 dimensions at a thermal state. We find that the mutual information obeys an area law, similar to that obeyed by the entanglement entropy at vanishing temperature. The coefficient of this area law does not vanish at infinite temperature. Then, we calculate this coefficient perturbatively in an $1/mu$ expansion, where $mu$ is the mass of the scalar field. Finally, we study the high and low temperature behaviour of the area law term.
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