arXiv subjects

Itamar Yaakov

Publications and source records attributed to Itamar Yaakov.

At least 19 recordsLinked to original sources

arXiv2026

The resurgence of errors in the localization of $\mathcal{N} = 2$ superconformal Yang-Mills

We give a physical interpretation for the analytic continuation of the partition function of superconformal SU$(2)$ $\mathcal{N}=2$ gauge theory on the four-sphere to all values of the Yang-Mills coupling. We show that a well-motivated 2d construction associates two-dimensional unstable instantons to the 4d complex saddles which appear as singularities in the integrand of the supersymmetric localization expression. The construction is based on the chiral algebra subsector, and aligns with the alternative Higgs branch localization.

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arXiv2025

Lattice defect networks in 2d Yang-Mills

We construct defect networks in pure Yang-Mills theory in two dimensions using a refinement of the lattice approach. The refinement preserves the locality properties of individual defects, and is compatible with solvability of the theory via subdivision invariance. We explicitly demonstrate closure of the building blocks under fusion.

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arXiv2024

Localization and resummation of unstable instantons in 2d Yang-Mills

We compute the exact all-orders perturbative expansion for the partition function of 2d $\mathrm{SU}(2)$ Yang-Mills theory on closed surfaces around higher critical points. We demonstrate that the expansion can be derived from the lattice partition function for all genera using a distributional generalization of the Poisson summation formula. We then recompute the expansion directly, using a stationary phase version of supersymmetric localization. The result of localization is a novel effective action which is itself a distribution rather than a function of the supersymmetric moduli. We comment on possible applications to A-twisted models and their analogs in higher dimensions.

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arXiv2022

Generating functions for Higgs/Coulomb branch operators from 1d-3d cohomological equivalence

We provide a proof for the conjectured equality of the generating function of integrated Higgs and Coulomb branch topological operators in 3d $\mathcal{N}\ge 4$ gauge theories and the three sphere partition function deformed by mass or FI parameters. The equality is the result of cohomological equivalence and applies to all theories in this class, including ABJM and other generalized Gaiotto-Witten models, and those without an explicit supersymmetric Lagrangian.

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arXiv2021

The joy of factorization at large $N$: five-dimensional indices and AdS black holes

We discuss the large $N$ factorization properties of five-dimensional supersymmetric partition functions for CFT with a holographic dual. We consider partition functions on manifolds of the form $\mathcal{M}= \mathcal{M}_3 \times S^2_ε$, where $ε$ is an equivariant parameter for rotation. We show that, when $\mathcal{M}_3$ is a squashed three-sphere, the large $N$ partition functions can be obtained by gluing elementary blocks associated with simple physical quantities. The same is true for various observables of the theories on $\mathcal{M}_3=Σ_\mathfrak{g} \times S^1$, where $Σ_\mathfrak{g}$ is a Riemann surface of genus $\mathfrak{g}$, and, with a natural assumption on the form of the saddle point, also for the partition function, corresponding to either the topologically twisted index or a mixed one. This generalizes results in three and four dimensions and correctly reproduces the entropy of known black objects in AdS$_6 \times_{w} S^4$ and AdS$_7\times S^4$. We also provide the supersymmetric background and explicitly perform localization for the mixed index on $Σ_\mathfrak{g} \times S^1 \times S^2_ε$, filling a gap in the literature.

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arXiv2021

Localization and Duality for ABJM Latitude Wilson Loops

We investigate several aspects of BPS latitude Wilson loops in gauge theories in three dimensions with $\mathcal{N}\ge 4$ supersymmetry. We derive a matrix model for the bosonic latitude Wilson loop in ABJM using supersymmetric localization, and show how to extend the computation to more general Chern-Simons-matter theories. We then define latitude type Wilson and vortex loop operators in theories without Chern-Simons terms, and explore a connection to the recently derived superalgebra defining local Higgs and Coulomb branch operators in these theories. Finally, we identify a BPS loop operator dual to the bosonic latitude Wilson loop which is a novel bound state of Wilson and vortex loops, defined using a worldvolume supersymmetric quantum mechanics.

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arXiv2019

Supersymmetric Rényi entropy and charged hyperbolic black holes

The supersymmetric Rényi entropy across a spherical entangling surface in a $d$-dimensional SCFT with flavor defects is equivalent to a supersymmetric partition function on $\mathbb{H}^{d-1} \times \mathbb{S}^1$, which can be computed exactly using localization. We consider the holographically dual BPS solutions in $(d +1)$-dimensional matter coupled supergravity $(d = 3 , 5)$, which are charged hyperbolically sliced AdS black holes. We compute the renormalized on-shell action and the holographic supersymmetric Rényi entropy and show a perfect match with the field theory side. Our setup allows a direct map between the chemical potentials for the global symmetries of the field theories and those of the gravity solutions. We also discuss a simple case where angular momentum is added.

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arXiv2019

Roadmap on Wilson loops in 3d Chern-Simons-matter theories

This is a compact review of recent results on supersymmetric Wilson loops in ABJ(M) and related theories. It aims to be a quick introduction to the state of the art in the field and a discussion of open problems. It is divided into short chapters devoted to different questions and techniques. Some new results, perspectives and speculations are also presented. We hope this might serve as a baseline for further studies of this topic.

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arXiv2018

Topologically twisted indices in five dimensions and holography

We provide a formula for the partition function of five-dimensional $\mathcal{N}=1$ gauge theories on $\mathcal{M}_4 \times S^1$, topologically twisted along $\mathcal{M}_4$ in the presence of general background magnetic fluxes, where $\mathcal{M}_4$ is a toric Kähler manifold. The result can be expressed as a contour integral of the product of copies of the K-theoretic Nekrasov's partition function, summed over gauge magnetic fluxes. The formula generalizes to five dimensions the topologically twisted index of three- and four-dimensional field theories. We analyze the large $N$ limit of the partition function and some related quantities for two theories: $\mathcal{N}=2$ SYM and the $\mathrm{USp}(2N)$ theory with $N_f$ flavors and an antisymmetric matter field. For $\mathbb{P}^1 \times \mathbb{P}^1 \times S^1$, which can be easily generalized to $Σ_{\mathfrak{g}_2} \times Σ_{\mathfrak{g}_1} \times S^1$, we conjecture the form of the relevant saddle point at large $N$. The resulting partition function for $\mathcal{N}=2$ SYM scales as $N^3$ and is in perfect agreement with the holographic results for domain walls in AdS$_7 \times S^4$. The large $N$ partition function for the $\mathrm{USp}(2N)$ theory scales as $N^{5/2}$ and gives a prediction for the entropy of a class of magnetically charged black holes in massive type IIA supergravity.

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arXiv2017

Supersymmetric Rényi Entropy and Defect Operators

We describe the defect operator interpretation of the supersymmetric Renyi entropies of superconformal field theories in three, four and five dimensions. The operators involved are supersymmetric codimension-two defects in an auxiliary Z_n gauge theory coupled to n copies of the SCFT. We compute the exact expectation values of such operators using localization, and compare the results to the supersymmetric Renyi entropy. The agreement between the two implies a relationship between the partition function on a squashed sphere and the one on a round sphere in the presence of defects.

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arXiv2016

Monopole operators from the $4-ε$ expansion

Three-dimensional quantum electrodynamics with $N$ charged fermions contains monopole operators that have been studied perturbatively at large $N$. Here, we initiate the study of these monopole operators in the $4-ε$ expansion by generalizing them to codimension-3 defect operators in $d = 4-ε$ spacetime dimensions. Assuming the infrared dynamics is described by an interacting CFT, we define the "conformal weight" of these operators in terms of the free energy density on $S^2 \times \mathbb{H}^{2-ε}$ in the presence of magnetic flux through the $S^2$, and calculate this quantity to next-to-leading order in $ε$. Extrapolating the conformal weight to $ε= 1$ gives an estimate of the scaling dimension of the monopole operators in $d=3$ that does not rely on the $1/N$ expansion. We also perform the computation of the conformal weight in the large $N$ expansion for any $d$ and find agreement between the large $N$ and the small $ε$ expansions in their overlapping regime of validity.

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arXiv2014

Generalized Indices for $\mathcal{N}=1$ Theories in Four-Dimensions

We use localization techniques to calculate the Euclidean partition functions for $\mathcal{N}=1$ theories on four-dimensional manifolds $M$ of the form $S^1 \times M_3$, where $M_3$ is a circle bundle over a Riemann surface. These are generalizations of the $\mathcal{N}=1$ indices in four-dimensions including the lens space index. We show that these generalized indices are holomorphic functions of the complex structure moduli on $M$. We exhibit the deformation by background flat connections.

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arXiv2013

Supersymmetric Renyi Entropy

We consider 3d N>= 2 superconformal field theories on a branched covering of a three-sphere. The Renyi entropy of a CFT is given by the partition function on this space, but conical singularities break the supersymmetry preserved in the bulk. We turn on a compensating R-symmetry gauge field and compute the partition function using localization. We define a supersymmetric observable, called the super Renyi entropy, parametrized by a real number q. We show that the super Renyi entropy is duality invariant and reduces to entanglement entropy in the q -> 1 limit. We provide some examples.

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arXiv2013

Exact results for supersymmetric abelian vortex loops in 2+1 dimensions

We define a class of supersymmetric defect loop operators in N = 2 gauge theories in 2+1 dimensions. We give a prescription for computing the expectation value of such operators in a generic N = 2 theory on the three-sphere using localization. We elucidate the role of defect loop operators in IR dualities of supersymmetric gauge theories, and write down their transformation properties under the SL(2, Z) action on conformal theories with abelian global symmetries.

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arXiv2013

Redeeming Bad Theories

We give a Seiberg-like dual description of the interacting superconformal infrared fixed point of $\mathcal{N}=4$ gauge theory in three dimensions with vanishing Chern Simons level and $N_c\le N_f<2N_c$ fundamental flavors. These theories are known as "bad" theories due to the existence of unitarity violating monopole operators. We show that, in a dual description, all such operators are realized by free fields and the remainder theory is the Seiberg-like dual previously identified using the type IIB brane construction.

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arXiv2011

N=2 Dualities and Z Extremization in Three Dimensions

We use localization techniques to study duality in N = 2 supersymmetric gauge theories in three dimensions. Specifically, we consider a duality due to Aharony involving unitary and symplectic gauge groups, which is similar to Seiberg duality in four dimensions, as well as related dualities involving Chern-Simons terms. These theories have the possibility of non-trivial anomalous dimensions for the chiral multiplets and were previously difficult to examine. We use a matrix model to compute the partition functions on both sides of the duality, deformed by real mass and FI terms, and find that they agree. The results provide strong evidence for the validity of the proposed dualities. We also comment on a recent proposal for recovering the exact IR conformal dimensions in such theories using localization.

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arXiv2010

Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter

We use localization techniques to compute the expectation values of supersymmetric Wilson loops in Chern-Simons theories with matter. We find the path-integral reduces to a non-Gaussian matrix model. The Wilson loops we consider preserve a single complex supersymmetry, and exist in any N=2 theory, though the localization requires superconformal symmetry. We present explicit results for the cases of pure Chern-Simons theory with gauge group U(N), showing agreement with the known results, and ABJM, showing agreement with perturbative calculations. Our method applies to other theories, such as Gaiotto-Witten theories, BLG, and their variants.

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arXiv2010

Tests of Seiberg-like Duality in Three Dimensions

We use localization techniques to study several duality proposals for supersymmetric gauge theories in three dimensions reminiscent of Seiberg duality. We compare the partition functions of dual theories deformed by real mass terms and FI parameters. We find that Seiberg-like duality for N=3 Chern-Simons gauge theories proposed by Giveon and Kutasov holds on the level of partition functions and is closely related to level-rank duality in pure Chern-Simons theory. We also clarify the relationship between the Giveon-Kutasov duality and a duality in theories of fractional M2 branes and propose a generalization of the latter. Our analysis also confirms previously known results concerning decoupled free sectors in N=4 gauge theories realized by monopole operators.

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