arXiv subjects

Rudolfs Treilis

Publications and source records attributed to Rudolfs Treilis.

5 recordsLinked to original sources

arXiv2026

New Exotic Operators in the Spectrum of Wilson Lines in General Representations

Wilson lines are fundamental probes of gauge theories. We show that, in sufficiently rich representations, they support a large new class of operator insertions. For half-BPS lines in $\mathcal{N}=4$ SYM many of these operators have the quantum numbers of the displacement supermultiplet. Their dimension-one superprimaries define natural deformations of the defect theory. By analyzing the associated beta functions, and relating them to specific OPE coefficients, we show that the deformations are marginally relevant. We support our finding with a weak-coupling computation of the four-point function of these operators for any gauge group and representation.

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arXiv2026

Dynamics of Heavy Operators in $\mathcal{N}=4$ SYM: Integrated Correlators and AdS Bubbles

We study integrated correlation functions of half-BPS operators in $SU(N)$ $\mathcal{N} = 4$ supersymmetric Yang-Mills theory (SYM) involving two superconformal primary operators in the stress-tensor multiplet and two identical maximal-trace operators of arbitrary $R$-charge $p$. Thanks to $\mathcal{N}=4$ SYM electro-magnetic duality these integrated correlators have recently been computed as exact functions of $N$, $p$, and of the Yang-Mills complexified coupling $\tau$. Using a combination of tools from ${\rm SL}(2,\mathbb{Z})$ spectral theory and resurgence analysis, we study the landscape of large-$N$ and/or large-charge expansions for these correlators. In particular, we find novel non-perturbative effects in the limit where $N\rightarrow \infty$ with $p/N^2$ fixed. From a holographic point of view this double-scaling regime is deeply connected with a second family of correlators which we analyse. Using the results for the maximal-trace operators, we derive an exact expression for a new integrated correlator involving two coherent-state operators, defined via an exponential generating function of multi-graviton states. At large-$N$ this correlator admits a holographic dual description in terms of a back-reacted geometry known as the AdS bubble. First, we show that the leading supergravity contribution to the integrated correlator agrees with a direct explicit integration of the correlator itself. Secondly, we derive predictions for the integrated version of the Virasoro-Shapiro amplitude evaluated on the AdS bubble background. Lastly, we demonstrate that the large-$N$ non-perturbative contributions to this integrated correlator emerge from giant-magnon configurations in the dual AdS bubble.

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arXiv2024

Large-$N$ integrated correlators in $\mathcal{N}=4$ SYM: when resurgence meets modularity

Exact expressions for certain integrated correlators of four half-BPS operators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory with gauge group $SU(N)$ have been recently obtained thanks to a beautiful interplay between supersymmetric localisation and modular invariance. The large-$N$ expansion at fixed Yang-Mills coupling of such integrated correlators produces an asymptotic series of perturbative terms, holographically related to higher derivative interactions in the low energy expansion of the type IIB effective action, as well as exponentially suppressed corrections at large $N$, interpreted as contributions from coincident $(p,q)$-string world-sheet instantons. In this work we define a manifestly modular invariant Borel resummation of the perturbative large-$N$ expansion of these integrated correlators, from which we extract the exact non-perturbative large-$N$ sectors via resurgence analysis. Furthermore, we show that in the 't Hooft limit such modular invariant non-perturbative completions reduce to known resurgent genus expansions. Finally, we clarify how the same non-perturbative data is encoded in the decomposition of the integrated correlators based on $\rm{SL}(2,\mathbb{Z})$ spectral theory.

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arXiv2023

Two string theory flavours of generalised Eisenstein series

Generalised Eisenstein series are non-holomorphic modular invariant functions of a complex variable, $τ$, subject to a particular inhomogeneous Laplace eigenvalue equation on the hyperbolic upper-half $τ$-plane. Two infinite classes of such functions arise quite naturally within different string theory contexts. A first class can be found by studying the coefficients of the effective action for the low-energy expansion of type IIB superstring theory, and relatedly in the analysis of certain integrated four-point functions of stress tensor multiplet operators in $\mathcal{N} = 4$ supersymmetric Yang-Mills theory. A second class of such objects is known to contain all two-loop modular graph functions, which are fundamental building blocks in the low-energy expansion of closed-string scattering amplitudes at genus one. In this work, we present a Poincaré series approach that unifies both classes of generalised Eisenstein series and manifests certain algebraic and differential relations amongst them. We then combine this technique with spectral methods for automorphic forms to find general and non-perturbative expansions at the cusp $τ\to i \infty$. Finally, we find intriguing connections between the asymptotic expansion of these modular functions as $τ\to 0$ and the non-trivial zeros of the Riemann zeta function.

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arXiv2022

To the cusp and back: Resurgent analysis for modular graph functions

Modular graph functions arise in the calculation of the low-energy expansion of closed-string scattering amplitudes. For toroidal world-sheets, they are ${\rm SL}(2,\mathbb{Z})$-invariant functions of the torus complex structure that have to be integrated over the moduli space of inequivalent tori. We use methods from resurgent analysis to construct the non-perturbative corrections arising when the argument of the modular graph function approaches the cusp on this moduli space. ${\rm SL}(2,\mathbb{Z})$-invariance will in turn strongly constrain the behaviour of the non-perturbative sector when expanded at the origin of the moduli space.

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