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- W4225581301 abstract "We focus on functional renormalization for ensembles of several (say $ngeq 1$) random matrices, whose potentials include multi-traces, to wit, the probability measure contains factors of the form $ exp[-mathrm{Tr}(V_1)timesldotstimes mathrm{Tr}(V_k)]$ for certain noncommutative polynomials $V_1,ldots,V_kin mathbb{C}_{langle n rangle}$ in the $n$ matrices. This article shows how the algebra of functional renormalization -- that is, the structure that makes the renormalization flow equation computable -- is derived from ribbon graphs, only by requiring the one-loop structure that such equation (due to Wetterich) is expected to have. Whenever it is possible to compute the renormalization flow in terms of $mathrm U(N)$-invariants, the structure gained is the matrix algebra $M_n( mathcal{A}_{n,N}, star ) $ with entries in $mathcal{A}_{n,N}=(mathbb{C}_{langle n rangle} otimes mathbb{C}_{langle n rangle} )oplus( mathbb{C}_{langle n rangle} boxtimes mathbb{C}_{langle n rangle})$, being $mathbb{C}_{langle n rangle} $ the free algebra generated by the $n$ Hermitian matrices of size $N$ (the flowing random variables) with multiplication of homogeneous elements in $mathcal{A}_{n,N}$ given, for each $P,Q,U,Winmathbb{C}_{langle n rangle}$, by begin{align*}(U otimes W) star ( Potimes Q) &= PU otimes WQ ,, & (Uboxtimes W) star ( Potimes Q) &=U boxtimes PWQ ,, (U otimes W) star ( Pboxtimes Q) &= WPU boxtimes Q ,, & (Uboxtimes W) star ( Pboxtimes Q) &= mathrm{Tr} (WP) Uboxtimes Q ,,end{align*} which, together with the condition $(lambda U) boxtimes W = Uboxtimes (lambda W) $ for each complex $lambda$, fully define the symbol $boxtimes$." @default.
- W4225581301 created "2022-05-05" @default.
- W4225581301 creator A5091165291 @default.
- W4225581301 date "2021-11-04" @default.
- W4225581301 modified "2023-10-16" @default.
- W4225581301 title "A ribbon graph derivation of the algebra of functional renormalization for random multi-matrices with multi-trace interactions" @default.
- W4225581301 doi "https://doi.org/10.1007/s11005-022-01546-x" @default.
- W4225581301 hasPublicationYear "2021" @default.
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