arXiv subjects

Elli Pomoni

Publications and source records attributed to Elli Pomoni.

At least 19 recordsLinked to original sources

arXiv2026

Analytic thermal bootstrap in momentum space: From thermal OPE to QNMs

We initiate a bootstrap program that relates ultraviolet data, encoded in the thermal OPE, to infrared observables, namely, the low-frequency behavior and quasinormal modes. Starting from KMS-symmetric completions of individual thermal OPE blocks, which play the role of thermal Polyakov blocks, we construct their Fourier transform, yielding an asymptotic expansion of retarded thermal correlators valid at any spatial momentum. We use these results to derive inversion formulae and connect thermal OPE data to the analytic structure of retarded correlators in the complex frequency plane. Under the assumption of meromorphicity, the inversion formulae express OPE coefficients in terms of the quasinormal-mode frequencies, leading to nontrivial sum rules, constraints on the quasinormal spectrum, and its asymptotics at large spatial momentum. We illustrate these results in free theories, two-dimensional CFTs, the large-$N$ limit and $\varepsilon$-expansion of the $\mathrm{O}(N)$ model, and the $R$-current correlator of strongly coupled $\mathcal N = 4$ SYM at zero spatial momentum. As a byproduct, we derive universal asymptotic formulae for thermal OPE coefficients of heavy operators, resolving their dependence on spin and extending previous results at zero spatial separation. We test these formulae in the three-dimensional Ising CFT, finding good agreement between the resulting truncated correlators and Monte Carlo data.

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arXiv2026

Multiplet Recombination and the CFT Distance Conjecture

Motivated by quantum gravity and the CFT Distance Conjecture, we study infinite-distance limits in four-dimensional ${\cal N}=2$ superconformal field theories with higher-dimensional conformal manifolds and their AdS duals. We focus on partial decoupling limits where a gauge sector becomes weakly coupled while an interacting sector persists. We analyse the structure of towers of states emerging in these limits. The weakly coupled sector contributes, among others, the massless higher-spin tower predicted by the CFT Distance Conjecture exhibiting polynomial degeneracy. The key novelty is the appearance of a protected BPS tower in the interacting sector, characterised by exponential degeneracy and masses at the AdS scale. This structure follows from multiplet recombination in the ${\cal N}=2$ superconformal algebra: As unprotected long multiplets hit the unitarity bound at weak coupling, they recombine into protected short multiplets. We verify this picture through an explicit one-loop computation in the simplest two-node quiver gauge theory with a two-dimensional conformal manifold.

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arXiv2025

Analytic thermal bootstrap meets holography

We compute thermal holographic correlators by combining their analytic structure with the Kubo-Martin-Schwinger (KMS) condition and multi-stress tensor OPE coefficients determined from the dual AdS description. We focus on two-point functions of identical scalar operators with integer conformal dimensions at zero spatial separation. In the black brane background, we show explicitly that holographic two-point functions split into three contributions: a principal one, computed exactly, plus regularized and arcs contributions, both approximated through the use of OPE coefficients asymptotics. For $\Delta_\phi=3$, we show that the principal contribution agree with good approximation with the numerical solution of the bulk wave equation. Moreover, we demonstrate that the expansion in generalized free field correlators proposed in [Barrat,6/2025] admits a natural interpretation in terms of Witten diagrams. Finally, we initiate the study of thermal correlators in the spherically symmetric black hole background, computing their principal contributions.

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arXiv2025

Long-range to the Rescue of Yang-Baxter II

We study the spin chain model capturing the one-loop spectral problem of the simplest $\mathcal{N}=2$ superconformal quiver gauge theory in four dimensions, obtained from a marginal deformation of the $\mathbb{Z}_2$ orbifold of $\mathcal{N}=4$ SYM. In Part I of this work \cite{Bozkurt:2024tpz}, we solved for the three-magnon eigenvector and found that it exhibits long-range behavior, despite the Hamiltonian being of nearest-neighbor type. In this paper, we extend the analysis to the four-magnon sector and construct explicit eigenvectors. These solutions are compatible with both untwisted and twisted periodic boundary conditions, and they allow for the computation of anomalous dimensions of single-trace operators of the gauge theory. We validate our results by direct comparison with brute-force diagonalization of the spin chain Hamiltonian. Additionally, we uncover a novel structural relation between eigenstates with different numbers of excitations. In particular, we show that the four-magnon eigenstates can be written in terms of the three-magnon solution, revealing a recursive pattern and hinting at a deeper underlying structure. Lastly, the four-magnon solution obeys an infinite tower of Yang-Baxter equations, as was the case for the three-magnon solution.

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arXiv2025

The analytic bootstrap at finite temperature

We propose new universal formulae for thermal two-point functions of scalar operators based on their analytic structure, constructed to manifestly satisfy all the bootstrap conditions. We derive a dispersion relation in the complexified time plane, which fixes the correlator up to an additive constant and theory-dependent dynamical information. At non-zero spatial separation we introduce a formula for the thermal two-point function obtained by summing over images of the dispersion relation result obtained in the OPE regime. This construction satisfies all thermal bootstrap conditions, with the exception of clustering at infinite distance, which must be verified on a case-by-case basis. We test our results both in weakly and strongly-coupled theories. In particular, we show that the asymptotic behavior for the heavy sector proposed in~\cite{Marchetto:2023xap} and its correction can be explicitly derived from the dispersion relation. We combine analytical and numerical results to compute the thermal two-point function of the energy operator in the $3d$ Ising model and find agreement with Monte Carlo simulations.

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arXiv2024

Hidden Symmetries of 4D N=2 Gauge Theories

We study the global symmetries of the $\mathbb{Z}_2$-orbifold of N=4 Super-Yang-Mills theory and its marginal deformations. The process of orbifolding to obtain an N=2 theory would appear to break the $\mathrm{SU}(4)$ R-symmetry down to $\mathrm{SU}(2)\times \mathrm{SU}(2)\times \mathrm{U}(1)$. We show that the broken generators can be recovered by moving beyond the Lie algebraic setting to that of a Lie algebroid. This remains true when marginally deforming away from the orbifold point by allowing the couplings of the $ \mathrm{SU}(N)\times \mathrm{SU}(N)$ gauge groups to vary independently. The information about the marginal deformation is captured by a Drinfeld-type twist of this $\mathrm{SU}(4)$ Lie algebroid. The twist is read off from the F- and D- terms, and thus directly from the Lagrangian. Even though at the orbifold point the algebraic structure is associative, it becomes non-associative after the marginal deformation. We explicitly check that the planar Lagrangian of the theory is invariant under this twisted version of the $\mathrm{SU}(4)$ algebroid and we discuss implications of this hidden symmetry for the spectrum of the N=2 theory.

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arXiv2024

The thermal bootstrap for the critical O(N) model

We propose a numerical method to estimate one-point functions and the free-energy density of conformal field theories at finite temperature by solving the Kubo-Martin-Schwinger condition for the two-point functions of identical scalars. We apply the method for the critical O(N) model for N = 1,2,3 in 3 $\leq$ d $\leq$ 4. We find agreement with known results from Monte Carlo simulations and previous results for the 3d Ising model, and we provide new predictions for N = 2,3.

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arXiv2024

Constraints on RG Flows from Protected Operators

We consider protected operators with the same conformal dimensions in the ultraviolet and infrared fixed point. We derive a sum rule for the difference between the two-point function coefficient of these operators in the ultraviolet and infrared fixed point which depends on the two-point function of the scalar operator. In even dimensional conformal field theories, scalar operators with exactly integer conformal dimensions are associated with Type-B conformal anomalies. The sum rule, in these cases, computes differences between Type-B anomaly coefficients. We argue the positivity of this difference in cases in which the conformal manifold contains weakly coupled theories. The results are tested in free theories as well as in $\mathcal N = 2$ superconformal QCD, necklace quivers and holographic RG flows. We further derive sum rules for currents and stress tensor two-point functions.

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arXiv2024

Long-range to the Rescue of Yang-Baxter

We study the spin chain model which captures the one-loop spectral problem of a prototypical example of an $\mathcal{N}=2$ SCFT in four dimensions. Up to date, this spin chain model remains unfathomable; the coordinate Bethe Ansatz does not lead to a solution from three magnons on, as the Yang-Baxter equation is not satisfied by the two-magnon scattering coefficients. In this paper, we find a long-range solution to the eigenvalue problem for three magnons. Remarkably, the scattering coefficients of our solution together with the position-dependent corrections, obey an infinite tower of Yang-Baxter equations. Our method of solving the three-magnon problem is interesting in its own right and generalizes the coordinate Bethe Ansatz approach to cases where the permutation symmetry is broken.

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arXiv2024

Conformal line defects at finite temperature

We study conformal field theories at finite temperature in the presence of a temporal conformal line defect, wrapping the thermal circle, akin to a Polyakov loop in gauge theories. Although several symmetries of the conformal group are broken, the model can still be highly constrained from its features at zero-temperature. In this work we show that the defect and bulk one and two-point correlators can be written as functions of zero-temperature data and thermal one-point functions (defect and bulk). The defect one-point functions are new data and they are induced by thermal effects of the bulk. For this new set of data we derive novel sum rules and establish a bootstrap problem for the thermal defect one-point functions from the KMS condition. We also comment on the behaviour of operators with large scaling dimensions. Additionally, we relate the free energy and entropy density to the OPE data through the one-point function of the stress-energy tensor. Our formalism is validated through analytical computations in generalized free scalar field theory, and we present new predictions for the O(N) model with a magnetic impurity in the $\varepsilon$-expansion and the large N limit.

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arXiv2023

Sum rules & Tauberian theorems at finite temperature

We study CFTs at finite temperature and derive explicit sum rules for one-point functions of operators by imposing the KMS condition. In the case of a large gap between light and heavy operators, we explicitly compute one-point functions for light operators. Turning to heavy operators we employ Tauberian theorems and compute the asymptotic OPE density for heavy operators, from which we extract the leading terms of the OPE coefficients associated with heavy operators. Furthermore, we approximate and establish bounds for the two-point functions.

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arXiv2023

Broken (super) conformal Ward identities at finite temperature

When a (super) conformal field theory is placed on a non-trivial manifold, the (super) conformal symmetry is broken. However, it is still possible to derive broken Ward identities for these broken symmetries, which provide additional constraints on the theory. We derive and apply the broken Ward identities associated with the (super) conformal group on the thermal manifold $\mathcal{M}_β= S_β^1 \times \mathbb{R}^{d-1}$ and $\mathcal{M} = T^2 \times \mathbb{R}^{d-2}$. The novel constraints not only systematically reproduce known results, including an implicit formulation of the generalized Cardy formula, but also elegantly relate the thermal energy spectrum with the conformal spectrum.

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arXiv2023

Probing M-theory with tetrahedron instantons

The duality between type IIA superstring theory and M-theory enables us to lift bound states of D$0$-branes and $n$ parallel D$6$-branes to M-theory compactified on an $n$-centered multi-Taub-NUT space $\mathbb{TN}_{n}$. Accordingly, the rank $n$ K-theoretic Donaldson-Thomas invariants of $\mathbb{C}^{3}$ are connected with the index of M-theory on $\mathbb{C}^{3}\times\mathbb{TN}_{n}$. In this paper, we extend this connection by considering intersecting D$6$-branes. In the presence of a suitable Neveu-Schwarz $B$-field, the system preserves two supercharges. This system is T-dual to the configuration of tetrahedron instantons which we introduced in \cite{Pomoni:2021hkn}. We conjecture a closed-form expression for the K-theoretic tetrahedron instanton partition function, which is the generating function of the D$0$-D$6$ partition functions. We find that the tetrahedron instanton partition function coincides with the partition function of the magnificent four model for special values of the parameters, leading us to conjecture that our system of intersecting D$6$-branes can be obtained from the annihilation of D$8$-branes and anti-D$8$-branes. Remarkably, the K-theoretic tetrahedron instanton partition function allows an interpretation in terms of the index of M-theory on a noncompact Calabi-Yau fivefold which is related to a superposition of Kaluza-Klein monopoles. The dimensional reduction of the system allows us to express the cohomological tetrahedron instanton partition function in terms of the MacMahon function, generalizing the correspondence between Gromov-Witten invariants and Donaldson-Thomas invariants for Calabi-Yau threefolds.

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arXiv2022

Covariantly Constant Anomalies on Conformal Manifolds

Operators with integer scaling dimensions in even-dimensional conformal field theories exhibit well-known type-B Weyl anomalies. In general, these anomalies depend non-trivially on exactly marginal couplings. We study the corresponding fully covariantised anomaly functional on conformal manifolds in several examples. We show that a natural consequence of the Wess-Zumino consistency condition is that the anomalies are covariantly constant with respect to the exactly marginal couplings. The argument is general and applies even when the conformal symmetry is spontaneously broken on moduli spaces of vacua.

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arXiv2022

Tetrahedron instantons

We introduce and study tetrahedron instantons, which can be realized in string theory by D$1$-branes probing a configuration of intersecting D$7$-branes in flat spacetime with a proper constant $B$-field. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting real codimension-two supersymmetric defects. Moreover, we construct the tetrahedron instantons as particular solutions of general instanton equations in noncommutative field theory. We analyze the moduli space of tetrahedron instantons and discuss the geometric interpretations. We compute the instanton partition function both via the equivariant localization on the moduli space of tetrahedron instantons and via the elliptic genus of the worldvolume theory on the D$1$-branes probing the intersecting D$7$-branes, obtaining the same result. The instanton partition function of the tetrahedron instantons lies between the higher-rank Donaldson-Thomas invariants on $\mathbb{C}^{3}$ and the partition function of the magnificent four model, which is conjectured to be the mother of all instanton partition functions. Finally, we show that the instanton partition function admits a free field representation, suggesting the existence of a novel kind of symmetry which acts on the cohomology of the moduli spaces of tetrahedron instantons.

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arXiv2021

$\mathcal{N}=1$ Curves on Generalized Coulomb Branches

We study the low energy effective dynamics of four-dimensional $\mathcal{N}=1$ supersymmetric gauge theories of class $\mathcal{S}_k$ on the generalized Coulomb branch. The low energy effective gauge couplings are naturally encoded in algebraic curves $\mathcal{X}$, which we derive for general values of the couplings and mass deformations. We then recast these IR curves $\mathcal{X}$ to the UV or M-theory form $\mathcal{C}$: the punctured Riemann surfaces on which the six-dimensional $\mathcal{N}=(1,0)$ ${A_{k-1}}$ SCFTs are compactified giving the class $\mathcal{S}_k$ theories. We find that the UV curves $\mathcal{C}$ and their corresponding meromorphic differentials take the same form as those for their mother four-dimensional $\mathcal{N}=2$ theories of class $\mathcal{S}$. They have the same poles, and their residues are functions of all the exactly marginal couplings and the bare mass parameters which we can compute exactly.

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arXiv2021

Dynamical Spin Chains in 4D $\mathcal{N}=2$ SCFTs

This is the first in a series of papers devoted to the study of spin chains capturing the spectral problem of 4d $\mathcal{N}=2$ SCFTs in the planar limit. At one loop and in the quantum plane limit, we discover a quasi-Hopf symmetry algebra, defined by the $R$-matrix read off from the superpotential. This implies that when orbifolding the $\mathcal{N}=4$ symmetry algebra down to the $\mathcal{N}=2$ one and then marginaly deforming, the broken generators are not lost, but get upgraded to quantum generators. Importantly, we demonstrate that these chains are dynamical, in the sense that their Hamiltonian depends on a parameter which is dynamically determined along the chain. At one loop we map the holomorphic SU(3) scalar sector to a dynamical 15-vertex model, which corresponds to an RSOS model, whose adjacency graph can be read off from the gauge theory quiver/brane tiling. One scalar SU(2) sub-sector is described by an alternating nearest-neighbour Hamiltonian, while another choice of SU(2) sub-sector leads to a dynamical dilute Temperley-Lieb model. These sectors have a common vacuum state, around which the magnon dispersion relations are naturally uniformised by elliptic functions. Concretely, for the $\mathbb{Z}_2$ quiver theory we study these dynamical chains by solving the one- and two-magnon problems with the coordinate Bethe ansatz approach. We confirm our analytic results by numerical comparison with the explicit diagonalisation of the Hamiltonian for short closed chains.

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arXiv2021

The Coulomb and Higgs Branches of $\mathcal{N}=1$ Theories of Class $\mathcal{S}_k$

Even though for generic $\mathcal{N}=1$ theories it is not possible to separate distinct branches of supersymmetric vacua, in this paper we study a special class of $\mathcal{N}=1$ SCFTs, these of Class $\mathcal{S}_k$ for which it is possible to define Coulomb and Higgs branches precisely as for the $\mathcal{N}=2$ theories of Class $\mathcal{S}$ from which they descend. We study the BPS operators that parameterise these branches of vacua using the different limits of the superconformal index as well as the Coulomb and Higgs branch Hilbert Series. Finally, with the tools we have developed, we provide a check that six dimensional $(1,1)$ Little String theory can be deconstructed from a toroidal quiver in class $\mathcal{S}_k$

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