arXiv subjects

Laurence G. Yaffe

Publications and source records attributed to Laurence G. Yaffe.

At least 19 recordsLinked to original sources

arXiv2026

Resurrecting the coherent state variational algorithm for large $N$ gauge theories

The feasibility of studying, numerically, properties of infinite volume QCD-like theories in the large $N$ limit using coherent state variational methods is reassessed. An entirely new implementation of this approach is described, applicable to SU($N$) lattice gauge theories, with or without fundamental representation fermions, on cubic lattices of up to four dimensions. In addition to various test cases, initial results are presented for Hamiltonian Yang-Mills theory on an infinite two-dimensional spatial lattice.

hep-lat↗

arXiv2024

Line operators, vortex statistics, and Higgs versus confinement dynamics

We study a $2{+}1$D lattice gauge theory with fundamental representation scalar fields which has both Higgs and confining regimes with a spontaneously-broken $U(1)$ $0$-form symmetry. We show that the Higgs and confining regimes may be distinguished by a natural gauge invariant observable: the phase $Ω$ of a correlation function of a vortex line operator linking with an electric Wilson line. We employ dualities and strong coupling expansions to analytically explore parameter regimes which were inaccessible in previous continuum calculations, and discuss possible implications for the phase diagram.

hep-th↗

arXiv2023

Colliding localized, lumpy holographic shocks with a granular nuclear structure

We apply a recent and simple technique which speeds up the calculation of localized collisions in holography to study more realistic models of heavy ion collisions via the gauge/gravity duality. The initial data takes into account the lumpy nuclear structure of real heavy ions and the projectiles' aspect ratio mimics the Lorentz contraction of nuclei during RHIC collisions. At the hydrodynamization time of the central region of the quark gluon plasma developed during the collision, we find that most of the vorticity three vector's absolute value is deposited far away from the hydrodynamized part of the plasma. Only the relativistic corrections to the thermal vorticity in the hydrodynamized region are non-negligible. We compare the transverse flow after the collision determined in this work with previous results, without granular initial conditions and determine the proper energy density and fluid velocity in a hydrodynamized subregion of the plasma.

hep-th↗

arXiv2022

Collision of localized shocks in AdS$_5$ as a series expansion in transverse gradients

We introduce a computational framework to more efficiently calculate the collision of localized shocks in five dimensional asymptotically Anti-de Sitter space. We expand the Einstein equations in transverse gradients and find that our numerical results agree well with exact solutions already at first order in the expansion. Moreover, the Einstein equations at first order in transverse gradients can be decoupled into two sets of differential equations. The bulk fields of one of these sets has only a negligible contribution to boundary observables, such that the computation on each time slice can be simplified to the solution of several planar shockwave equations plus four further differential equations for each transverse plane `pixel'. At the cost of errors of $\lesssim 10 \%$ at the hydrodynamization time and for low to mid rapidities, useful numerical solutions can be sped up by roughly one order of magnitude.

hep-th↗

arXiv2022

Vortices in spin-0 superfluids carry magnetic flux

Vortices in spin-$0$ superfluids generically carry magnetic fields inside their cores, so that even neutral superfluid vortices may be thought of as magnetic flux tubes. We give a systematic analysis of this `vortex magnetic effect' using effective field theory, clarifying earlier literature on the subject. Our analysis shows that in superfluid Helium-$4$ the vortex magnetic effect may be large enough to be experimentally detectable.

cond-mat.quant-gas↗

arXiv2020

Higgs-confinement phase transitions with fundamental representation matter

We discuss the conditions under which Higgs and confining regimes in gauge theories with fundamental representation matter fields can be sharply distinguished. It is widely believed that these regimes are smoothly connected unless they are distinguished by the realization of global symmetries. However, we show that when a $U(1)$ global symmetry is spontaneously broken in \emph{both} the confining and Higgs regimes, the two phases can be separated by a phase boundary. The phase transition between the two regimes may be detected by a novel topological vortex order parameter. We first illustrate these ideas by explicit calculations in gauge theories in three spacetime dimensions. Then we show how our analysis generalizes to four dimensions, where it implies that nuclear matter and quark matter are sharply distinct phases of QCD with an approximate $SU(3)$ flavor symmetry.

hep-th↗

arXiv2020

Phenomenological implications of asymmetric $AdS_5$ shockwave collision studies for heavy ion physics

This paper discusses possible phenomenological implications for p+A and A+A collisions of the results of recent numerical AdS/CFT calculations examining asymmetric collisions of planar shocks. In view of the extreme Lorentz contraction, we model highly relativistic heavy ion collisions (HICs) as a superposition of collisions between many near-independent transverse "pixels" with differing incident longitudinal momenta. It was found that also for asymmetric collisions the hydrodynamization time is in good approximation a proper time, just like for symmetric collisions, depending on the geometric mean of the longitudinally integrated energy densities of the incident projectiles. For realistic collisions with fluctuations in the initial energy densities, these results imply a substantial increase in the hydrodynamization time for highly asymmetric pixels. However, even in this case the local hydrodynamization time still is significantly smaller than perturbative results for the thermalization time.

hep-ph↗

arXiv2019

Anyonic particle-vortex statistics and the nature of dense quark matter

We show that $\mathbb{Z}_3$-valued particle-vortex braiding phases are present in high density quark matter. Certain mesonic and baryonic excitations, in the presence of a superfluid vortex, have orbital angular momentum quantized in units of $\hbar/3$. Such non-local topological features can distinguish phases whose realizations of global symmetries, as probed by local order parameters, are identical. If $\mathbb{Z}_3$ braiding phases and angular momentum fractionalization are absent in lower density hadronic matter, as is widely expected, then the quark matter and hadronic matter regimes of dense QCD must be separated by at least one phase transition.

hep-th↗

arXiv2019

Asymmetric shockwave collisions in $\text{AdS}_{5}$

Collisions of asymmetric planar shocks in maximally supersymmetric Yang-Mills theory are studied via their dual gravitational formulation in asymptotically anti-de Sitter spacetime. The post-collision hydrodynamic flow is found to be very well described by appropriate means of the results of symmetric shock collisions. This study extends, to asymmetric collisions, previous work of Chesler, Kilbertus, and van der Schee examining the special case of symmetric collisions. Given the universal description of hydrodynamic flow produced by asymmetric planar collisions one can model, quantitatively, non-planar, non-central collisions of highly Lorentz contracted projectiles without the need for computing, holographically, collisions of finite size projectiles with very large aspect ratios. This paper also contains a pedagogical description of the computational methods and software used to compute shockwave collisions using pseudo-spectral methods, supplementing the earlier overview of Chesler and Yaffe.

hep-th↗

arXiv2017

Large $N$ phase transitions and the fate of small Schwarzschild-AdS black holes

Sufficiently small Schwarzschild-AdS black holes in asymptotically global AdS$_5 \times S^5$ spacetime are known to become dynamically unstable toward deformation of the internal $S^5$ geometry. The resulting evolution of such an unstable black hole is related, via holography, to the dynamics of supercooled plasma which has reached the limit of metastability in maximally supersymmetric large-$N$ Yang-Mills theory on $R \times S^3$. Puzzles related to the resulting dynamical evolution are discussed, with a key issue involving differences between the large $N$ limit in the dual field theory and typical large volume thermodynamic limits.

hep-th↗

arXiv2017

QCD on a small circle

QCD-like theories can be engineered to remain in a confined phase when compactified on an arbitrarily small circle, where their features may be studied quantitatively in a controlled fashion. Previous work has elucidated the generation of a non-perturbative mass gap and the spontaneous breaking of chiral symmetry in this regime. Here, we study the rich spectrum of hadronic states, including glueball, meson, and baryon resonances. We find an exponentially growing Hagedorn density of states, as well as the emergence of non-perturbative energy scales given by iterated exponentials of the inverse Yang-Mills coupling $g^2$.

hep-th↗

arXiv2017

Order parameters and color-flavor center symmetry in QCD

Common lore suggests that $N$-color QCD with massive quarks has no useful order parameters which can be non-trivial at zero baryon density. However, such order parameters do exist when there are $n_f$ quark flavors with a common mass and $d\equiv\gcd(n_f,N) > 1$. These theories have a $\mathbb Z_d$ color-flavor center symmetry arising from intertwined color center transformations and cyclic flavor permutations. The symmetry realization depends on the temperature, baryon chemical potential and value of $n_f/N$, with implications for conformal window studies and dense quark matter.

hep-th↗

arXiv2016

Exponential reduction of finite volume effects with twisted boundary conditions

Flavor-twisted boundary conditions can be used for exponential reduction of finite volume artifacts in flavor-averaged observables in lattice QCD calculations with $SU(N_f)$ light quark flavor symmetry. Finite volume artifact reduction arises from destructive interference effects in a manner closely related to the phase averaging which leads to large $N_c$ volume independence. With a particular choice of flavor-twisted boundary conditions, finite volume artifacts for flavor-singlet observables in a hypercubic spacetime volume are reduced to the size of finite volume artifacts in a spacetime volume with periodic boundary conditions that is four times larger.

hep-lat↗

arXiv2016

Damping of hard excitations in strongly coupled $\mathcal N\,{=}\,4$ plasma

The damping of high momentum excitations in strongly coupled maximally supersymmetric Yang-Mills plasma is studied. Previous calculations of the asymptotic behavior of the quasinormal mode spectrum are extended and clarified. We confirm that subleading corrections to the lightlike dispersion relation $ω({\bf q}) = |{\bf q}|$ have a universal $|{\bf q}|^{-1/3}$ form. Sufficiently narrow, weak planar shocks may be viewed as coherent superpositions of short wavelength quasinormal modes. The attenuation and evolution in profile of narrow planar shocks are examined as an application of our results.

hep-th↗

arXiv2016

Numerical solution of gravitational dynamics in asymptotically anti-de Sitter spacetimes

A variety of gravitational dynamics problems in asymptotically anti-de Sitter (AdS) spacetime are amenable to efficient numerical solution using a common approach involving a null slicing of spacetime based on infalling geodesics, convenient exploitation of the residual diffeomorphism freedom, and use of spectral methods for discretizing and solving the resulting differential equations. Relevant issues and choices leading to this approach are discussed in detail. Three examples, motivated by applications to non-equilibrium dynamics in strongly coupled gauge theories, are discussed as instructive test cases. These are gravitational descriptions of homogeneous isotropization, collisions of planar shocks, and turbulent fluid flows in two spatial dimensions.

hep-th↗

arXiv2015

Finite coupling corrections to holographic predictions for hot QCD

Finite 't Hooft coupling corrections to multiple physical observables in strongly coupled $N=4$ supersymmetric Yang-Mills plasma are examined, in an attempt to assess the stability of the expansion in inverse powers of the 't Hooft coupling $λ$. Observables considered include thermodynamic quantities, transport coefficients, and quasinormal mode frequencies. Although large $λ$ expansions for quasinormal mode frequencies are notably less well behaved than the expansions of other quantities, we find that a partial resummation of higher order corrections can significantly reduce the sensitivity of the results to the value of $λ$.

hep-th↗

arXiv2015

Far-from-equilibrium dynamics of a strongly coupled non-Abelian plasma with non-zero charge density or external magnetic field

Using holography, we study the evolution of a spatially homogeneous, far from equilibrium, strongly coupled N=4 supersymmetric Yang-Mills plasma with a non-zero charge density or a background magnetic field. This gauge theory problem corresponds, in the dual gravity description, to an initial value problem in Einstein-Maxwell theory with homogeneous but anisotropic initial conditions. We explore the dependence of the equilibration process on different aspects of the initial departure from equilibrium and, while controlling for these dependencies, examine how the equilibration dynamics are affected by the presence of a non-vanishing charge density or an external magnetic field. The equilibration dynamics are remarkably insensitive to the addition of even large chemical potentials or magnetic fields; the equilibration time is set primarily by the form of the initial departure from equilibrium. For initial deviations from equilibrium which are well localized in scale, we formulate a simple model for equilibration times which agrees quite well with our results.

hep-th↗

arXiv2015

Holography and off-center collisions of localized shock waves

Using numerical holography, we study the collision, at non-zero impact parameter, of bounded, localized distributions of energy density chosen to mimic relativistic heavy ion collisions, in strongly coupled N = 4 supersymmetric Yang-Mills theory. Both longitudinal and transverse dynamics in the dual field theory are properly described. Using the gravitational description we solve 5D Einstein equations, without dimensionality reducing symmetry restrictions, to find the asymptotically anti-de Sitter spacetime geometry. Implications of our results on the understanding of early stages of heavy ion collisions, including the development of transverse radial flow, are discussed.

hep-th↗