39,961 research outputs found

    The full Schwinger-Dyson tower for random tensor models

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    We treat random rank-DD tensor models as DD-dimensional quantum field theories---tensor field theories (TFT)---and review some of their non-perturbative methods. We classify the correlation functions of complex tensor field theories by boundary graphs, sketch the derivation of the Ward-Takahashi identity and stress its relevance in the derivation of the tower of exact, analytic Schwinger-Dyson equations for all the correlation functions (with connected boundary) of TFTs with quartic pillow-like interactions.Comment: Proceedings: Corfu 2017 Training School "Quantum Spacetime and Physics Models

    The twisted gradient flow coupling at one loop

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    We compute the one-loop running of the SU(N)SU(N) 't Hooft coupling in a finite volume gradient flow scheme using twisted boundary conditions. The coupling is defined in terms of the energy density of the gradient flow fields at a scale l~\tilde{l} given by an adequate combination of the torus size and the rank of the gauge group, and is computed in the continuum using dimensional regularization. We present the strategy to regulate the divergences for a generic twist tensor, and determine the matching to the MS\overline{\rm MS} scheme at one-loop order. For the particular case in which the twist tensor is non-trivial in a single plane, we evaluate the matching coefficient numerically and determine the ratio of Λ\Lambda parameters between the two schemes. We analyze the NN dependence of the results and the possible implications for non-commutative gauge theories and volume independence.Comment: 52 pages, 12 figure

    An empirical calibration of nebular abundances based on the sulphur emission lines

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    We present an empirical calibration of nebular abundances based on the strong emission lines of [SII] and [SIII] in the red part of the spectrum through the definition of a sulphur abundance parameter S23. This calibration presents two important advantages against the commonly used one based on the optical oxygen lines: it remains single-valued up to abundances close to solar and is rather independent of the degree of ionization of the nebula.Comment: 10 pages, 8 figures. Accepted for publication in MNRA

    A1A_1 theory of weights for rough homogeneous singular integrals and commutators

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    Quantitative A1AA_1-A_\infty estimates for rough homogeneous singular integrals TΩT_{\Omega} and commutators of BMOBMO symbols and TΩT_{\Omega} are obtained. In particular the following estimates are proved: % TΩLp(w)cn,pΩL[w]A11p[w]A1+1pfLp(w) \|T_\Omega \|_{L^p(w)}\le c_{n,p}\|\Omega\|_{L^\infty} [w]_{A_1}^{\frac{1}{p}}\,[w]_{A_{\infty}}^{1+\frac{1}{p'}}\|f\|_{L^p(w)} % and % [b,TΩ]fLp(w)cn,pbBMOΩL[w]A11p[w]A2+1pfLp(w), \| [b,T_{\Omega}]f\|_{L^{p}(w)}\leq c_{n,p}\|b\|_{BMO}\|\Omega\|_{L^{\infty}} [w]_{A_1}^{\frac{1}{p}}[w]_{A_{\infty}}^{2+\frac{1}{p'}}\|f\|_{L^{p}\left(w\right)}, % for 1<p<1<p<\infty and 1/p+1/p=11/p+1/p'=1.Comment: 19 page