39,961 research outputs found

### The full Schwinger-Dyson tower for random tensor models

We treat random rank-$D$ tensor models as $D$-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

We compute the one-loop running of the $SU(N)$ '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
$\tilde{l}$ 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 $\overline{\rm MS}$
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 $\Lambda$ parameters between the two schemes. We
analyze the $N$ 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

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

### $A_1$ theory of weights for rough homogeneous singular integrals and commutators

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

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