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Paul Romatschke

Publications and source records attributed to Paul Romatschke.

At least 37 records · Page 2Linked to original sources
arXiv2022

Determining all thermodynamic transport coefficients for an interacting large N quantum field theory

Thermodynamic transport coefficients can be calculated directly from quantum field theory without requiring analytic continuation to real time. We determine all second-order thermodynamic transport coefficients for the uncharged N-component massless (critical) scalar field theory with quartic interaction in the large N limit, for any value of the coupling. We find that in the large N limit, all thermodynamic transport coefficients for the interacting theory can be expressed analytically in terms of the in-medium mass and sums over modified Bessel functions. We expect our technique to allow a similar determination of all thermodynamic transport coefficients for all theories that are solvable in the large N limit, including certain gauge theories.

hep-th↗
arXiv2022

On the Gravitational Wave to Matter Coupling of Superfluid Fermi Gases Near Unitarity

It is well known that gravitational waves distort equilibrium matter globally, making them amenable to detection with laser interferometers. Less well known is the fact that gravitational waves create local non-equilibrium stresses inside matter, which could conceivably lead to alternative detection methods. The gravitational wave to matter coupling $κ$ is a transport coefficient depending on the material, and is poorly known for most substances. In the present work, we calculate $κ$ for a superfluid Fermi gas near unitarity using large-$N$ techniques, finding $κ= \frac{n}{12m}$, with $n$ the number density and $m$ the mass of the fermion, matching the result for free Dirac fermions at zero temperature. Our prediction is amenable to non-perturbative theoretical as well as experimental tests.

cond-mat.str-el↗
arXiv2021

Shear Viscosity at Infinite Coupling: A Field Theory Calculation

I derive an exact integral expression for the ratio of shear viscosity over entropy density $\fracη{s}$ for the massless (critical) O(N) model at large N with quartic interactions. The calculation is set up and performed entirely from the field theory side using a non-perturbative resummation scheme that captures all contributions to leading order in large N. In 2+1d, $\fracη{s}$ is evaluated numerically at all values of the coupling. For infinite coupling, I find $\fracη{s}\simeq 0.42(1)\times N$. I show that this strong coupling result for the viscosity is universal for a large class of interacting bosonic O(N) models.

hep-th↗
arXiv2020

Quantum Mechanical Out-Of-Time-Ordered-Correlators for the Anharmonic (Quartic) Oscillator

Out-of-time-ordered correlators (OTOCs) have been suggested as a means to study quantum chaotic behavior in various systems. In this work, I calculate OTOCs for the quantum mechanical anharmonic oscillator with quartic potential, which is classically integrable and has a Poisson-like energy-level distribution. For low temperature, OTOCs are periodic in time, similar to results for the harmonic oscillator and the particle in a box. For high temperature, OTOCs exhibit a rapid (but power-like) rise at early times, followed by saturation consistent with $2\langle x^2\rangle_T \langle p^2\rangle_T$ at late times. At high temperature, the spectral form factor decreases at early times, bounces back and then reaches a plateau with strong fluctuations.

hep-th↗
arXiv2020

Real Time Quantum Gravity Dynamics from Classical Statistical Yang-Mills Simulations

We perform microcanonical classical statistical lattice simulations of SU(N) Yang-Mills theory with eight scalars on a circle. Measuring the eigenvalue distribution of the spatial Wilson loop we find two distinct phases depending on the total energy and circle radius, which we tentatively interpret as corresponding to black hole and black string phases in a dual gravity picture. We proceed to study quenches by first preparing the system in one phase, rapidly changing the total energy, and monitoring the real-time system response. We observe that the system relaxes to the equilibrium phase corresponding to the new energy, in the process exhibiting characteristic damped oscillations. We interpret this as the topology change from black hole to black string configurations, with damped oscillations corresponding to quasi-normal mode ringing of the black hole/black string final state. This would suggest that alpha' corrections alone can resolve the singularity associated with the topology change. We extract the real and imaginary part of the lowest-lying presumptive quasinormal mode as a function of energy and N.

hep-th↗
arXiv2019

Analytic Transport from Weak to Strong Coupling in the O(N) model

In this work, a second-order transport coefficient (the curvature-matter coupling $κ$) is calculated exactly for the 3+1d O(N) model at large N for any coupling value. Since the theory is `trivial' in the sense of possessing a Landau pole, the result for $κ$ only is free from cut-off artifacts much below the Landau pole in the effective field theory sense. Nevertheless, this leaves a large range of coupling values where this transport coefficient can be determined non-perturbatively and analytically with little ambiguity. Along with thermodyamic results also calculated in this work, I expect exact large N results to provide good quantitative predictions for N=1 scalar field theory with $ϕ^4$ interaction.

hep-th↗
arXiv2019

Fractionalized Degrees of Freedom at Infinite Coupling in large Nf QED in 2+1 dimensions

I consider quantum electrodynamics with many electrons in 2+1 space-time dimensions at finite temperature. The relevant dimensionless interaction parameter for this theory is the fine structure constant divided by the temperature. The theory is solvable at any value of the coupling, in particular for very weak (high temperature) and infinitely strong coupling (corresponding to the zero temperature limit). Concentrating on the photon, each of its physical degrees of freedom at infinite coupling only contributes half of the free-theory value to the entropy. These fractional degrees of freedom are reminiscent of what has been observed in other strongly coupled systems (such as N=4 SYM), and bear similarity to the fractional Quantum Hall effect, potentially suggesting connections between these phenomena. The results found for QED3 are fully consistent with the expectations from particle-vortex duality.

hep-th↗
arXiv2019

Exact $β$-function of Yang-Mills theory in 2+1 dimensions

To set the stage, I discuss the $β$-function of the massless O(N) model in three dimensions, which can be calculated exactly in the large N limit. Then, I consider SU(N) Yang-Mills theory in 2+1 space-time dimensions. Relating the $β$-function to the expectation value of the action in lattice gauge theory, and the latter to the trace of the energy-momentum tensor, I show that $\frac{d \ln g^2/μ}{d\ln μ}=-1$ for all $g$ and all N in one particular renormalization scheme. As a consequence, I find that the Yang-Mills $β$-function in three dimensions must have the same sign for all finite and positive bare coupling parameters in any renormalization scheme, and all non-trivial infrared fixed points are unreachable in practice.

hep-lat↗
arXiv2019

Finite temperature CFT results for all couplings: O(N) model in 2+1 dimensions

A famous example of gauge/gravity duality is the result that the entropy density of strongly coupled ${\cal N}=4$ SYM in four dimensions for large N is exactly 3/4 of the Stefan-Boltzmann limit. In this work, I revisit the massless O(N) model in 2+1 dimensions, which is analytically solvable at finite temperature $T$ for all couplings $λ$ in the large N limit. I find that the entropy density monotonically decreases from the Stefan-Boltzmann limit at $λ=0$ to exactly 4/5 of the Stefan-Boltzmann limit at $λ=\infty$. Calculating the retarded energy-momentum tensor correlator in the scalar channel at $λ=\infty$, I find that it has two logarithmic branch cuts originating at $ω=\pm 4 T \ln \frac{1+\sqrt{5}}{2}$, but no singularities in the whole complex frequency plane. I show that the ratio 4/5 and the location of the branch points both are universal within a large class of bosonic CFTs in 2+1 dimensions.

hep-th↗
arXiv2019

Thermal free energy of large Nf QED in 2+1 dimensions from weak to strong coupling

In 2+1 dimensions, QED becomes exactly solvable for all values of the fermion charge $e$ in the limit of many fermions $N_f\gg 1$. We present results for the free energy density at finite temperature $T$ to next-to-leading-order in large $N_f$. In the naive large $N_f$ limit, we uncover an apparently UV-divergent contribution to the vacuum energy at order ${\cal O}(e^6 N_f^3)$, which we argue to become a finite contribution of order ${\cal O}(N_f^4 e^6)$ when resumming formally higher-order $1/N_f$ contributions. We find the finite-temperature free energy to be well-behaved for all values of the dimensionless coupling $e^2N_f/T$, and to be bounded by the free energy of $N_f$ free fermions and non-interacting QED3, respectively. We invite follow-up studies from finite-temperature lattice gauge theory at large but fixed $N_f$ to test our results in the regime $e^2N_f/T\gg 1$.

hep-th↗
arXiv2019

Ricci cosmology

We revisit spatially flat FLRW cosmology in light of recent advances in standard model relativistic fluid dynamics. Modern fluid dynamics requires the presence of curvature-matter terms in the energy-momentum tensor for consistency. These terms are linear in the Ricci scalar and tensor, such that the corresponding cosmological model is referred to as ``Ricci cosmology''. No cosmological constant is included, there are no inflaton fields, bulk viscosity is assumed to be zero and we only employ standard Einstein gravity. Analytic solutions to Ricci cosmology are discussed, and we find that it is possible to support an early-time inflationary universe using only well-known ingredients from the Standard Model of physics and geometric properties of space-time.

gr-qc↗
arXiv2019

Simple non-perturbative resummation schemes beyond mean-field: case study for scalar $ϕ^4$ theory in 1+1 dimensions

I present a sequence of non-perturbative approximate solutions for scalar $ϕ^4$ theory for arbitrary interaction strength, which contains, but allows to systematically improve on, the familiar mean-field approximation. This sequence of approximate solutions is apparently well-behaved and numerically simple to calculate since it only requires the evaluation of (nested) one-loop integrals. To test this resummation scheme, the case of $ϕ^4$ theory in 1+1 dimensions is considered, finding approximate agreement with known results for the vacuum energy and mass gap up to the critical point. Because it can be generalized to other dimensions, fermionic fields and finite temperature, the resummation scheme could potentially become a useful tool for calculating non-perturbative properties approximately in certain quantum field theories.

hep-th↗
arXiv2019

Strong Coupling Universality at Large N for Pure CFT Thermodynamics in 2+1 dimensions

Pure CFTs have vanishing $β$-function at any value of the coupling. One example of a pure CFT is the O(N) Wess-Zumino model in 2+1 dimensions in the large N limit. This model can be analytically solved at finite temperature for any value of the coupling, and we find that its entropy density at strong coupling is exactly equal to 31/35 of the non-interacting Stefan-Boltzmann result. We show that a large class of theories with equal numbers of N-component fermions and bosons, supersymmetric or not, for a large class of interactions, exhibit the same universal ratio. For unequal numbers of fermions and bosons we find that the strong-weak thermodynamic ratio is bounded to lie in between 4/5 and 1.

hep-th↗
arXiv2019

Relativistic Fluid Dynamics In and Out of Equilibrium -- Ten Years of Progress in Theory and Numerical Simulations of Nuclear Collisions

Ten years ago, relativistic viscous fluid dynamics was formulated from first principles in an effective field theory framework, based entirely on the knowledge of symmetries and long-lived degrees of freedom. In the same year, numerical simulations for the matter created in relativistic heavy-ion collision experiments became first available, providing constraints on the shear viscosity in QCD. The field has come a long way since then. We present the current status of the theory of non-equilibrium fluid dynamics in 2017, including the divergence of the fluid dynamic gradient expansion, resurgence, non-equilibrium attractor solutions, the inclusion of thermal fluctuations as well as their relation to microscopic theories. Furthermore, we review the theory basis for numerical fluid dynamics simulations of relativistic nuclear collisions, and comparison of modern simulations to experimental data for nucleus-nucleus, nucleus-proton and proton-proton collisions.

nucl-th↗
arXiv2019

Simple non-perturbative resummation schemes beyond mean-field II: thermodynamics of scalar $ϕ^4$ theory in 1+1 dimensions at arbitrary coupling

Recently, non-perturbative approximate solutions were presented that go beyond the well-known mean-field resummation. In this work, these non-perturbative approximations are used to calculate finite temperature equilibrium properties for scalar $ϕ^4$ theory in two dimensions such as the pressure, entropy density and speed of sound. Unlike traditional approaches, it is found that results are well-behaved for arbitrary temperature/coupling strength, are independent of the choice of the renormalization scale $\barμ^2$, and are apparently converging as the resummation level is increased. Results also suggest the presence of a possible analytic cross-over from the high-temperature to the low-temperature regime based on the change in the thermal entropy density.

hep-th↗
arXiv2018

Holographic Heavy-Ion Collisions: Analytic Solutions with Longitudinal Flow, Elliptic Flow and Vorticity

We consider phenomenological consequences arising from simple analytic solutions for holographic heavy-ion collisions. For these solutions, early-time longitudinal flow is initially negative (inward), sizable direct, elliptic, and quadrangular flow is generated, and the average vorticity of the system is tunable by a single parameter. Despite large vorticity and angular momentum, we show that the system does not complete a single rotation.

nucl-th↗
arXiv2018

Azimuthal Anisotropies at High Momentum from Purely Non-Hydrodynamic Transport

In the limit of short mean free path, relativistic kinetic theory gives rise to hydrodynamics through a systematically improvable gradient expansion. In the present work, a systematically improvable expansion in the opposite limit of large mean free path is considered, describing the dynamics of particles which are almost, but not quite, non-interacting. This non-hydrodynamic "eremitic" expansion does not break down for large gradients, and may be useful in situations where a hydrodynamic treatment is not applicable. As applications, azimuthal anisotropies at high transverse momentum in Pb+Pb and p+Pb collisions at $\sqrt{s}=5.02$ TeV are calculated from the first order eremitic expansion of kinetic theory in the relaxation time approximation.

nucl-th↗