Partition function (quantum field theory)
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T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ -deformed 2D quantum field theories Open
It was noticed many years ago, in the framework of massless RG flows, that the irrelevant composite operator T¯T, built with the components of the energy-momentum tensor, enjoys very special properties in 2D quantum field theories, and can b…
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Tensor Network Renormalization Open
We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a quantum many-body system. The scheme is based…
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Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model Open
We study spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model, a variant of the k-body embedded random ensembles studied for several decades in the context of nuclear physics and quantum chaos. We show analytically that the…
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Average-Case Complexity Versus Approximate Simulation of Commuting Quantum Computations Open
A line of work initiated by Terhal and DiVincenzo [Terhal/DiVincenzo, arXiv, 2002] and Bremner, Jozsa, and Shepherd [Bremner/Jozsa/Sheperd, Proc. Royal Soc. A, 2010], shows that restricted classes of quantum computation can efficiently sam…
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Learning thermodynamics with Boltzmann machines Open
A Boltzmann machine is a stochastic neural network that has been extensively\nused in the layers of deep architectures for modern machine learning\napplications. In this paper, we develop a Boltzmann machine that is capable of\nmodelling t…
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The $$ T\overline{T} $$ deformation of quantum field theory as random geometry Open
A bstract We revisit the results of Zamolodchikov and others on the deformation of two-dimensional quantum field theory by the determinant det T of the stress tensor, commonly referred to as $$ T\overline{T} $$ . Infinitesimally this …
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JT gravity as a matrix integral Open
We present exact results for partition functions of Jackiw-Teitelboim (JT) gravity on two-dimensional surfaces of arbitrary genus with an arbitrary number of boundaries. The boundaries are of the type relevant in the NAdS${}_2$/NCFT${}_1$ …
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Power-law out of time order correlation functions in the SYK model Open
We evaluate the finite temperature partition sum and correlation functions of the Sachdev–Ye–Kitaev (SYK) model. Starting from a recently proposed mapping of the SYK model onto Liouville quantum mechanics, we obtain our results by exact in…
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Experimental Observation of Lee-Yang Zeros Open
Lee-Yang zeros are points on the complex plane of physical parameters where the partition function of a system vanishes and hence the free energy diverges. Lee-Yang zeros are ubiquitous in many-body systems and fully characterize their the…
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General instanton counting and 5d SCFT Open
Instanton partition functions of 5d N = 1 gauge theories are Witten indices for the ADHM gauged quantum mechanics with (0, 4) SUSY. We derive the integral contour prescriptions for these indices using the Jeffrey-Kirwan method, for gauge t…
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Random statistics of OPE coefficients and Euclidean wormholes Open
We propose an ansatz for OPE coefficients in chaotic conformal field theories which generalizes the eigenstate thermalization hypothesis and describes any OPE coefficient involving heavy operators as a random variable with a Gaussian distr…
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Lectures on non-equilibrium effective field theories and fluctuating hydrodynamics Open
We review recent progress in developing effective field theories (EFTs) for non-equilibrium processes at finite temperature, including a new formulation of fluctuating hydrodynamics, and a new proof of the second law of thermodynamics. The…
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Correlation functions of Coulomb branch operators Open
We consider the correlation functions of Coulomb branch operators in four-dimensional N=2 Superconformal Field Theories (SCFTs) involving exactly one anti-chiral operator. These extremal correlators are the "minimal" non-holomorphic local …
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Spectral Statistics and Many-Body Quantum Chaos with Conserved Charge Open
We investigate spectral statistics in spatially extended, chaotic many-body quantum systems with a conserved charge. We compute the spectral form factor K(t) analytically for a minimal Floquet circuit model that has a U(1) symmetry encoded…
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On the superconformal index of Argyres–Douglas theories Open
We conjecture a closed-form expression for the Schur limit of the\nsuperconformal index of two infinite series of Argyres-Douglas (AD)\nsuperconformal field theories (SCFTs): the (A_1,A_{2n-3}) and the (A_1,D_{2n})\ntheories. While these S…
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Superconformal partition functions and non-perturbative topological strings Open
A bstract We propose a non-perturbative definition for refined topological strings. This can be used to compute the partition function of superconformal theories in 5 dimensions on squashed S 5 and the superconformal index of a large numbe…
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The statistical mechanics of near-BPS black holes Open
Due to the failure of thermodynamics for low temperature near-extremal black holes, it has long been conjectured that a ‘thermodynamic mass gap’ exists between an extremal black hole and the lightest near-extremal state. For non-supersymme…
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Poincaré series, 3D gravity and CFT spectroscopy Open
Modular invariance strongly constrains the spectrum of states of two dimensional conformal field theories. By summing over the images of the modular group, we construct candidate CFT partition functions that are modular invariant and have …
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Inapproximability of the Partition Function for the Antiferromagnetic Ising and Hard-Core Models Open
Recent inapproximability results of Sly (2010), together with an approximation algorithm presented by Weitz (2006), establish a beautiful picture of the computational complexity of approximating the partition function of the hard-core mode…
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Exact calculation of loop formation probability identifies folding motifs in RNA secondary structures Open
RNA secondary structure prediction is widely used to analyze RNA sequences. In an RNA partition function calculation, free energy nearest neighbor parameters are used in a dynamic programming algorithm to estimate statistical properties of…
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Simple universal models capture all classical spin physics Open
One model to rule them all? The idea of finding an all-encompassing model to describe the world around us has appealed to generations of scientists. Although we are very far from this ultimate goal, more modest steps can be taken if we foc…
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Jensen polynomials for the Riemann zeta function and other sequences Open
Significance The Pólya–Jensen criterion for the Riemann hypothesis asserts that is equivalent to the hyperbolicity of certain Jensen polynomials for all degrees and all shifts . For each degree we confirm this criterion for all suffici…
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Light-cone modular bootstrap and pure gravity Open
We explore the large spin spectrum in two-dimensional conformal field theories with a finite twist gap, using the modular bootstrap in the light-cone limit. By recursively solving the modular crossing equations associated with different PS…
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Duality walls and defects in 5d N = 1 $$ \mathcal{N}=1 $$ theories Open
We propose an explicit description of duality walls which encode at low energy the global symmetry enhancement expected in the UV completion of certain five-dimensional gauge theories. The proposal is supported by explicit localization com…
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Topological Defects on the Lattice: Dualities and Degeneracies Open
We construct topological defects in two-dimensional classical lattice models and quantum chains. The defects satisfy local commutation relations guaranteeing that the partition function is independent of their path. These relations and the…
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Breaking of Ensemble Equivalence in Networks Open
It is generally believed that, in the thermodynamic limit, the microcanonical description as a function of energy coincides with the canonical description as a function of temperature. However, various examples of systems for which the mic…
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Exact results for boundaries and domain walls in 2d supersymmetric theories Open
We apply supersymmetric localization to $$ \mathcal{N}=\left(2,2\right) $$ gauged linear sigma models on a hemisphere, with boundary conditions, i.e., D-branes, preserving B-type supersymmetries. We explain how to compute the hemisphere pa…
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Algorithms for tensor network renormalization Open
We discuss in detail algorithms for implementing tensor network\nrenormalization (TNR) for the study of classical statistical and quantum\nmany-body systems. Firstly, we recall established techniques for how the\npartition function of a 2D…
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Seifert fibering operators in 3d $$ \mathcal{N}=2 $$ theories Open
A bstract We study 3d $$ \mathcal{N}=2 $$ supersymmetric gauge theories on closed oriented Seifert manifolds — circle bundles over an orbifold Riemann surface —, with a gauge group G given by a product of simply-connected and/or unitar…
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A new handle on three-point coefficients: OPE asymptotics from genus two modular invariance Open
We derive an asymptotic formula for operator product expansion coefficients of heavy operators in two dimensional conformal field theory. This follows from modular invariance of the genus two partition function, and generalises the asympto…