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Functional Dimensional Regularization for O(N) Models

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abstract

The novel functional dimensional regularization (FDR) scheme has proven capable of yielding results that are competitive with the state-of-the-art in the computation of critical exponents in $d=3$, while also reproducing those from the $\varepsilon$-expansion for the Ising and other universality classes. In this work, we show that this is not a mere coincidence: by applying the scheme to the $O(N)$ universality class, we explicitly derive the flow equations and obtain critical exponents that are comparable to those obtained with higher-order non-perturbative approaches. In this case, FDR retains the features already highlighted in previous works -- namely, its efficiency and rapid convergence.

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hep-th 1

years

2026 1

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CONDITIONAL 1

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Towards gauge independence in asymptotically safe quantum gravity

hep-th · 2026-07-07 · conditional · novelty 6.0

In an essential proper-time scheme, gauge dependence of the flow for Newton's constant cancels order-by-order once redundant off-shell terms are absorbed by field redefinitions, leaving a gauge-independent non-Gaussian fixed point.

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  • Towards gauge independence in asymptotically safe quantum gravity hep-th · 2026-07-07 · conditional · none · ref 35 · internal anchor

    In an essential proper-time scheme, gauge dependence of the flow for Newton's constant cancels order-by-order once redundant off-shell terms are absorbed by field redefinitions, leaving a gauge-independent non-Gaussian fixed point.