We compute the rate of growth of operator size in matrix models by probing the Lin-Maldacena class of geometries with classical probes. We consider massive point particle probes whose proper momentum equals the size of the gauge invariant operator in the matrix model. We work out the example of the BMN Plane Wave Matrix Model using the electrostatic approach and the method of background fluxes. We also work out complexities in the D2 brane as well as NS5 brane limits of the BMN matrix model along with an example of the irrelevant deformation namely the non-Abelian T-dual of $\textit{AdS}$ × $\textit{S}$ . Finally, we carry out a possible calculation of the Krylov complexity on the matrix model counterpart by using a simple reduction ansatz known as the pulsating fuzzy sphere model. We outline an algorithm to define Krylov basis elements for the matrix model and compute a few Lanczos coefficients. Our analysis reveals that both the Krylov basis states as well as Lanczos coefficients are uniquely fixed in terms of the mass parameter of the matrix model.

India

Dibakar Roychowdhury

Krylov complexity for Lin-Maldacena geometries and their holographic duals

It is well known that atoms can change their shape when subject to external electromagnetic fields. Analogous phenomena are expected for particles that are much smaller in size, with the corresponding shape change much harder to observe. We point out that the shape change of particles can be accessed by measurements of their spin alignment. Motivated by recent measurements of spin alignment in relativistic heavy ion collisions, we consider quarkonia in electromagnetic fields as an example. We show that the quarkonia spin alignment receives both spin contributions from spin state mixing and orbital contributions from shape changes. By a proper choice of quantization axis, it is possible to switch off the spin contribution, leaving only the orbital contribution. This makes the spin alignment measurement a valuable probe of quarkonium structure.

China

Guowei Yan

Shu Lin

Distorted quarkonia and spin alignment

The spin polarization for a baryon in a hydrodynamic medium has been extensively studied in the weakly coupled regime using quantum kinetic theory. As a first study of this problem in the strongly coupled regime, we investigate holographically the spectral function of a probe baryon in the fluid-gravity background. This is done by carefully performing gradient expansion of the Dirac equation in the fluid-gravity background. Different contributions in the expansion are understood in terms of density matrices of the probe baryon and the medium. The resulting spectral functions indicate that the holographic baryon is polarized as responses to fluid acceleration, shear stress, and vorticity. The structures of the responses are similar to those found in weakly coupled studies.

Si-wen Li

Spin polarization of holographic baryon in strongly coupled fluid

We classify radiative corrections to spin polarization into three types: (i) spectral function, (ii) modified distribution function, and (iii) modified Kubo-Martin-Schwinger relation. The last two contributions modify the well-known free theory results. The first contribution is present with radiative correction only. We perform a detailed analysis on the first type for an energetic quark in a medium with hydrodynamic gradients, finding the radiative correction to spectral function leads to a polarized quasiparticle. The degeneracy of spin polarization induced by different hydrodynamic sources in free theory is lifted by radiative correction. We argue that the corrections of the last two types are parametrically suppressed with respect to the first type for the energetic quark we consider.

United States

Jiayuan Tian

Spin polarized quasiparticle in an off-equilibrium medium

Recent experiments have found spin alignment of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> with respect to the event plane in heavy ion collisions, suggesting a medium effect that is spin dependent. We propose a possible mechanism with polarized dissociation from the motion of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> with respect to the medium. We calculate the polarized dissociation rate for a quarkonium spin triplet state from spin chromomagnetic coupling in the potential nonrelativistic QCD framework. This is done for the leading order gluo-dissociation process and the next to leading order inelastic Coulomb scattering process. The polarized dissociation rate is expressed as a function of relative velocity between quarkonium and quark-gluon plasma and the quantization axis. Applying the polarized dissociation rate to quarkonium evolution with a dissociation effect only in a Bjorken flow, we find the spin 0 state to dissociate less than the other spin states, leading to positive <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>ρ</mi></mrow><mrow><mn>00</mn></mrow></msub><mo>−</mo><mn>1</mn><mo>/</mo><mn>3</mn></mrow></math>. The regeneration contribution is expected to give a contribution with the opposite sign.

Zhishun Chen

Polarized dissociation and spin alignment of moving quarkonia in a quark-gluon plasma

Motivated by the key role of shear induced polarization in understanding the local spin polarization puzzle of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi></math> hyperons in heavy ion collisions, we perform a complete analysis of spin polarization of massive fermion in a quantum electrodynamic plasma with shear flow. Apart from the well-known spin-shear coupling in free theory, we include two more collision dependent contributions: one is a nondynamical contribution fixed by shifted spin-averaged distribution in steady state; the other is a dynamical contribution following from spin evolution. Despite of the dependencies on collision, we find the dependencies on coupling drop out in the final results. These contributions can lead to significant enhancement of the spin-shear coupling in phenomenologically interesting regime.

Ziyue Wang

Spin polarization for massive fermion in a shear flow: Complete results at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><mo>∂</mo><mo stretchy="false">)</mo></math>

We consider spin polarization of massless fermions in a shear flow, whose complete contributions contain magnetization current and side-jump current known from collisional chiral kinetic theory. We argue that the side-jump current adopts interpretation of displacement current. We explicitly determine the displacement current contribution in the steady state reached in shear flow for a quantum electrodynamics (QED) plasma. We find the displacement contribution enhances the magnetization contribution at small and large momenta, but leads to a suppression effect at intermediate momenta. Major differences from previous studies on collisional effect are (i) the fermions are in the same steady state as the medium rather than being probes; (ii) Compton scattering and pair annihilation are also included in addition to the Coulomb scattering considered before.

Steady state, displacement current, and spin polarization for massless fermion in a shear flow

It is commonly understood that the strong magnetic field produced in heavy ion collisions is short-lived. The electric conductivity of the quark-gluon plasma is unable to significantly extend the lifetime of the magnetic field. We propose an alternative scenario to achieve this: with finite baryon density and spin polarization by the initial magnetic field, the quark-gluon plasma behaves as a paramagnet, which may continue to polarize the quark after fading of the initial magnetic field. We confirm this picture by calculations in both quantum electrodynamics and quantum chromodynamics. In the former case, we find a splitting in the damping rates of probe fermions with an opposite spin component along the magnetic field. In the latter case, we find a similar splitting in damping rate of the probe quark in quark-gluon plasma in both high and low density limits. The splitting provides a way of polarizing strange quarks by the quark-gluon plasma paramagnet consisting of light quarks, which effectively extends the lifetime of the magnetic field in heavy ion collisions.

Lihua Dong

Polarization dynamics in the paramagnet of a charged quark-gluon plasma

We present a systematic treatment of non-Gaussianity in stochastic systems using the Schwinger-Keldysh effective field theory framework, in which the non-Gaussianity is realized as nonlinear terms in the fluctuation field. We establish two stochastic formulations of the Schwinger-Keldysh effective field theory, with those nonlinear terms manifested as multiple non-Gaussian noises in the Langevin equation and as higher order diffusive terms in the Fokker-Planck equation. The equivalence of the stochastic formulations with the original Schwinger-Keldysh effective field theory is demonstrated with nontrivial examples for arbitrary non-Gaussian parameters. The stochastic formulations will be more flexible and effective in studying nonequilibrium dynamics. We also reveal an ambiguity when coarse-graining timescale and non-Gaussian parameters vanish simultaneously, which may be responsible for the unphysical divergence found in perturbative analysis.

Yanyan Bu

Chang Lei

Non-Gaussianity from Schwinger-Keldysh effective field theory

Gauge fields provide the fundamental interactions in the Standard Model of particle physics. Gauge field configurations with nontrivial topological windings are known to play crucial roles in many important phenomena, from matter-antimatter asymmetry of today’s universe to spontaneous chiral symmetry breaking in strong interaction. Their presence is, however, elusive for direct detection in experiments. Here we show that measurements of the chiral magnetic effect (CME) in heavy ion collisions can be used for accessing the topological fluctuations of the non-Abelian gauge fields in the quantum chromodynamics (QCD). To achieve this, we implemented a key ingredient, the stochastic dynamics of gauge field topological fluctuations, into a state-of-the-art framework for simulating the CME in these collisions. This new framework provides the necessary tool to quantify initial topological fluctuations from any definitive CME signal to be extracted from experimental data. It also reveals a universal scaling relation between initial topological fluctuations and particle multiplicity produced in the corresponding collision events.