arXiv subjects

Petar Tadić

Publications and source records attributed to Petar Tadić.

14 recordsLinked to original sources

arXiv2026

Quantum dynamics of perfect fluids

We study the quantum field theory of zero temperature perfect fluids. Such systems are defined by quantizing a classical field theory of scalar fields $ϕ^I$ that act as Lagrange coordinates on an internal spatial manifold of fluid configurations. Invariance under volume preserving diffeomorphisms acting on these scalars implies that the long-wavelength spectrum contains vortex (transverse modes) with an exact $ω_T=0$ dispersion relation. As a consequence, physically interpreting the results obtained via perturbative quantization of this theory has proven to be challenging. In this paper, we show that correlators evaluated in a class of semi-classical (Gaussian) initial states prepared at $t=0$ are well-defined and accessible via perturbation theory. The width of the initial state effectively acts as an infrared regulator without explicitly breaking diffeomorphism invariance of the classical action. As an application, we compute the stress tensor two-point correlators and show that vortex modes give a non-trivial contribution to the response function, non-local in both space and time.

hep-th↗

arXiv2026

Bootstrapping Open Quantum Many-body Systems with Absorbing Phase Transitions

We demonstrate that combining the positivity of density matrices with steady-state conditions yields a systematic bootstrap method for studying open quantum many-body systems governed by Lindblad master equations on infinite lattices, which exhibit absorbing phase transitions. As a concrete example, we apply this method to the quantum contact process with an absorbing state. We obtain bootstrap bounds on steady-state expectation values, the critical coupling, certain ratios of expectation values in the nontrivial steady state in the supercritical phase, and the Liouvillian spectral gap in the subcritical phase.

quant-ph↗

arXiv2025

Coarse-grained Bootstrap of Quantum Many-body Systems

We present a new computational framework combining coarse-graining techniques with bootstrap methods to study quantum many-body systems. The method efficiently computes rigorous upper and lower bounds on both zero- and finite-temperature expectation values of any local observables of infinite quantum spin chains. This is achieved by using tensor networks to coarse-grain bootstrap constraints, including positivity, translation invariance, equations of motion, and energy-entropy balance inequalities. Coarse-graining allows access to constraints from significantly larger subsystems than previously possible, yielding tighter bounds compared to those obtained without coarse-graining.

hep-th↗

arXiv2025

Mixed five-point correlators in the 3d Ising model

We study five-point correlators of the $σ$, $ε$, and $ε'$ operators in the critical 3d Ising model. We consider the $σ\times σ$ and $σ\times ε$ operator product expansions (OPEs) and truncate them by including a finite set of exchanged operators. We approximate the truncated operators by the corresponding contributions in appropriate disconnected five-point correlators. We compute a number of OPE coefficients that were previously unknown and show that these are consistent with predictions obtained using the fuzzy sphere regularization of the critical 3d Ising model.

hep-th↗

arXiv2025

Improving the five-point bootstrap

We present a new algorithm for the numerical evaluation of five-point conformal blocks in $d$-dimensions, greatly improving the efficiency of their computation. To do this we use an appropriate ansatz for the blocks as a series expansion in radial coordinates, derive a set of recursion relations for the unknown coefficients in the ansatz, and evaluate the series using a Padé approximant to accelerate its convergence. We then study the $\langleσσεσσ\rangle$ correlator in the 3d critical Ising model by truncating the operator product expansion (OPE) and only including operators with conformal dimension below a cutoff $Δ\leqslant Δ_{\rm cutoff}$. We approximate the contributions of the operators above the cutoff by the corresponding contributions in a suitable disconnected five-point correlator. Using this approach, we compute a number of OPE coefficients with greater accuracy than previous methods.

hep-th↗

arXiv2024

The five-point bootstrap

We study five-point correlation functions of scalar operators in d-dimensional conformal field theories. We develop a new approach to computing the five-point conformal blocks for exchanged primary operators of arbitrary spin by introducing a generalization of radial coordinates, using an appropriate ansatz, and perturbatively solving two quadratic Casimir differential equations. We then study five-point correlators $\langle σσεσσ\rangle$ in the critical 3d Ising model. We truncate the operator product expansions (OPEs) in the correlator by including a finite number of primary operators with conformal dimension below a cutoff $Δ\leqslant Δ_{\rm cutoff}$. We then compute several OPE coefficients involving $ε$ and two spinning operators by demanding that the truncated correlator approximately satisfies the crossing relation.

hep-th↗

arXiv2023

Hydrodynamic dispersion relations at finite coupling

By using holographic methods, the radii of convergence of the hydrodynamic shear and sound dispersion relations were previously computed in the ${\cal N} = 4$ supersymmetric Yang-Mills theory at infinite 't Hooft coupling and infinite number of colours. Here, we extend this analysis to the domain of large but finite 't Hooft coupling. To leading order in the perturbative expansion, we find that the radii grow with increasing inverse coupling, contrary to naive expectations. However, when the equations of motion are solved using a qualitative non-perturbative resummation, the dependence on the coupling becomes piecewise continuous and the initial growth is followed by a decrease. The piecewise nature of the dependence is related to the dynamics of branch point singularities of the energy-momentum tensor finite-temperature two-point functions in the complex plane of spatial momentum squared. We repeat the study using the Einstein-Gauss-Bonnet gravity as a model where the equations can be solved fully non-perturbatively, and find the expected decrease of the radii of convergence with the effective inverse coupling which is also piecewise continuous. Finally, we provide arguments in favour of the non-perturbative approach and show that the presence of non-perturbative modes in the quasinormal spectrum can be indirectly inferred from the analysis of perturbative critical points.

hep-th↗

arXiv2022

CFT correlators, ${\cal W}$-algebras and Generalized Catalan Numbers

In two spacetime dimensions the Virasoro heavy-heavy-light-light (HHLL) vacuum block in a certain limit is governed by the Catalan numbers. The equation for their generating function can be generalized to a differential equation which the logarithm of the block satisfies. We show that a similar story holds for the HHLL ${\cal W}_N$ vacuum blocks, where a suitable generalization of the Catalan numbers plays the main role. Moreover, the ${\cal W}_N$ blocks have the same form as the stress tensor sector of HHLL near lightcone conformal correlators in $2(N-1)$ spacetime dimensions. In the latter case the Catalan numbers are generalized to the numbers of linear extensions of certain partially ordered sets.

hep-th↗

arXiv2021

Thermalization in Large-N CFTs

In d-dimensional CFTs with a large number of degrees of freedom an important set of operators consists of the stress tensor and its products, multi stress tensors. Thermalization of such operators, the equality between their expectation values in heavy states and at finite temperature, is equivalent to a universal behavior of their OPE coefficients with a pair of identical heavy operators. We verify this behavior in a number of examples which include holographic and free CFTs and provide a bootstrap argument for the general case. In a free CFT we check the thermalization of multi stress tensor operators directly and also confirm the equality between the contributions of multi stress tensors to heavy-heavy-light-light correlators and to the corresponding thermal light-light two-point functions by disentangling the contributions of other light operators. Unlike multi stress tensors, these light operators violate the Eigenstate Thermalization Hypothesis and do not thermalize.

hep-th↗

arXiv2020

Stress Tensor Sector of Conformal Correlators

An important part of a CFT four-point function, the stress tensor sector, comprises the exchanges of the stress tensor and its composites. The OPE coefficients of these multi-stress tensor operators and consequently, the complete stress tensor sector of four-point functions in CFTs with a large central charge, can be determined by computing a heavy-heavy-light-light correlator. We show how one can make substantial progress in this direction by bootstrapping a certain ansatz for the stress tensor sector of the correlator, iteratively computing the OPE coefficients of multi-stress tensor operators with increasing twist. Some parameters are not fixed by the bootstrap - they correspond to the OPE coefficients of multi-stress tensors with spin zero and two. We further show that in holographic CFTs one can use the phase shift computed in the dual gravitational theory to reduce the set of undetermined parameters to the OPE coefficients of multi-stress tensors with spin zero. Finally, we verify some of these results using the Lorentzian OPE inversion formula and comment on its regime of applicability.

hep-th↗

arXiv2019

Leading Multi-Stress Tensors and Conformal Bootstrap

Near lightcone correlators are dominated by operators with the lowest twist. We consider the contributions of such leading lowest twist multi-stress tensor operators to a heavy-heavy-light-light correlator in a CFT of any even dimensionality with a large central charge. An infinite number of such operators contribute, but their sum is described by a simple ansatz. We show that the coefficients in this ansatz can be determined recursively, thereby providing an operational procedure to compute them. This is achieved by bootstrapping the corresponding near lightcone correlator: conformal data for any minimal-twist determines that for the higher minimal-twist and so on. To illustrate this procedure in four spacetime dimensions we determine the contributions of double- and triple-stress tensors. We compute the OPE coefficients; whenever results are available in the literature, we observe complete agreement. We also compute the contributions of double-stress tensors in six spacetime dimensions and determine the corresponding OPE coefficients. In all cases the results are consistent with the exponentiation of the near lightcone correlator. This is similar to the situation in two spacetime dimensions for the Virasoro vacuum block.

hep-th↗

arXiv2019

The complex life of hydrodynamic modes

We study analytic properties of the dispersion relations in classical hydrodynamics by treating them as Puiseux series in complex momentum. The radii of convergence of the series are determined by the critical points of the associated complex spectral curves. For theories that admit a dual gravitational description through holography, the critical points correspond to level-crossings in the quasinormal spectrum of the dual black hole. We illustrate these methods in ${\cal N}=4$ supersymmetric Yang-Mills theory in 3+1 dimensions, in a holographic model with broken translation symmetry in 2+1 dimensions, and in conformal field theory in 1+1 dimensions. We comment on the pole-skipping phenomenon in thermal correlation functions, and show that it is not specific to energy density correlations.

hep-th↗

arXiv2019

Black Holes and Conformal Regge Bootstrap

Highly energetic particles traveling in the background of an asymptotically AdS black hole experience a Shapiro time delay and an angle deflection. These quantities are related to the Regge limit of a heavy-heavy-light-light four-point function of scalar operators in the dual CFT. The Schwarzschild radius of the black hole in AdS units is proportional to the ratio of the conformal dimension of the heavy operator and the central charge. This ratio serves as a useful expansion parameter; its power counts the number of stress tensors in the multi-stress tensor operators which contribute to the four-point function. In the cross-channel the four-point function is determined by the OPE coefficients and anomalous dimensions of the heavy-light double-trace operators. We explain how this data can be obtained and explicitly compute the first and second order terms in the expansion of the anomalous dimensions. We observe perfect agreement with known results in the lightcone limit, which were obtained by computing perturbative corrections to the energy eigenstates in AdS spacetimes.

hep-th↗

arXiv2019

On the convergence of the gradient expansion in hydrodynamics

Hydrodynamic excitations corresponding to sound and shear modes in fluids are characterised by gapless dispersion relations. In the hydrodynamic gradient expansion, their frequencies are represented by power series in spatial momenta. We investigate the analytic structure and convergence properties of the hydrodynamic series by studying the associated spectral curve in the space of complexified frequency and complexified spatial momentum. For the strongly coupled ${\cal N}=4$ supersymmetric Yang-Mills plasma, we use the holographic duality methods to demonstrate that the derivative expansions have finite non-zero radii of convergence. Obstruction to the convergence of hydrodynamic series arises from level-crossings in the quasinormal spectrum at complex momenta.

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