arXiv subjects

Andreas Schmitt

Publications and source records attributed to Andreas Schmitt.

At least 19 recordsLinked to original sources

arXiv2026

Advances in the holographic description of hot and dense QCD matter

We review and extend recent progress on QCD-like phases at nonzero temperature and chemical potentials within the gauge-gravity duality. We focus on the Witten-Sakai-Sugimoto model, a top-down approach based on string theory which allows for a unified treatment of mesons, baryons and quarks. Phases such as pion condensation, baryonic and quarkyonic matter are located in the phase diagram, and we discuss predictions as well as weaknesses and limitations of this holographic approach. One of the novelties included in this review is the first holographic construction of a pionic phase between BEC and BCS regimes, which however is found to be metastable. We also discuss future directions in holographic QCD, within the model used here and in a wider context.

hep-ph↗

arXiv2026

High-Frequency Pricing at Scale for E-Commerce

This paper presents the design, development, and implementation of a specialized forecast-then-optimize algorithmic pricing tool for sales campaigns in fashion e-commerce. Sales events present unique challenges for pricing including volatile demand patterns, rapid pricing decisions, and the need to balance short-term revenue with long-term profitability. We describe our approach combining daily-resolution demand forecasting using gradient-boosted trees with a multi-objective optimization framework that maximizes both long-term profit and net merchandise value for more than 5 million articles. Our solution addresses key limitations of existing weekly-granularity systems by implementing a forecast-then-optimize architecture that reduces pricing decision time from hours to minutes. We validate our approach through 23 A/B tests across 12 markets during 2023-2024 sales campaigns at Zalando, one of Europe's leading online fashion retailers. Experimental results demonstrate that the new pricing system achieves approximately 6% higher profit while maintaining equivalent performance on sales and revenue compared to the previous manual-algorithmic hybrid approach. Based on these results, the algorithm was successfully deployed to production and now handles the majority of algorithmic pricing decisions for sales campaigns at the company.

cs.LG↗

arXiv2026

Softening holographic nuclear matter

Baryons in the holographic Witten-Sakai-Sugimoto model are described by instanton solutions on the flavor branes. A commonly used approximation for dense baryonic matter replaces the many-instanton solution by a simpler, spatially homogeneous, ansatz, which requires a discontinuity in the holographic direction of the non-abelian gauge field in order to account for topological baryon number. We point out that the simplest configuration with a single jump - often used in previous studies - results in matter at saturation density that is much stiffer than real-world nuclear matter. This is improved, although not completely remedied, by adding a second jump. We present a systematic discussion of all possible configurations up to four jumps, dynamically computing locations of and behavior at the discontinuities. We find solutions that continuously connect to those based on pointlike baryons, thus, for the first time, establishing a concrete link between the instantonic and homogeneous pictures. This is supported by translating the multi-jump profiles of the gauge field into gauge invariant multi-layer charge distributions. The most important of our novel configurations has a block-like structure in the bulk, becomes pointlike at low density and/or large coupling, and is energetically preferred over all previously studied configurations. Therefore, our work lays the ground for improved predictions from holography for dense nuclear matter in neutron stars.

hep-ph↗

arXiv2025

Phases and properties of color superconductors

Cold and dense matter is expected to be in a color-superconducting state. Here we review two calculations, relevant for fundamental properties and applications of color superconductivity, respectively: the weak-coupling QCD calculation of the fermionic energy gap together with the magnetic screening masses of the gauge bosons, and the calculation of bulk viscosity from a non-leptonic electroweak process. These calculations are supplemented by a discussion of color superconductors with mismatched Fermi momenta, and they are embedded in the context of the state of the art by giving an overview of previous and ongoing work and future directions.

hep-ph↗

arXiv2025

Nuclear chiral density wave in neutron stars?

Anisotropic phases potentially play a role in the internal composition of neutron stars, the main laboratory for the phase structure of QCD at high baryon densities. We review the study of such a phase, the chiral density wave, within a phenomenological nucleon-meson model, including nucleonic vacuum fluctuations within a renormalization scheme recently developed. Neutron stars in this model and within our approximations either do not contain a chiral density wave core or they are too light to agree with observations.

nucl-th↗

arXiv2025

Tricks from the Trade for Large-Scale Markdown Pricing: Heuristic Cut Generation for Lagrangian Decomposition

In automated decision making processes in the online fashion industry, the 'predict-then-optimize' paradigm is frequently applied, particularly for markdown pricing strategies. This typically involves a mixed-integer optimization step, which is crucial for maximizing profit and merchandise volume. In practice, the size and complexity of the optimization problem is prohibitive for using off-the-shelf solvers for mixed integer programs and specifically tailored approaches are a necessity. Our paper introduces specific heuristics designed to work alongside decomposition methods, leading to almost-optimal solutions. These heuristics, which include both primal heuristic methods and a cutting plane generation technique within a Lagrangian decomposition framework, are the core focus of the present paper. We provide empirical evidence for their effectiveness, drawing on real-world applications at Zalando SE, one of Europe's leading online fashion retailers, highlighting the practical value of our work. The contributions of this paper are deeply ingrained into Zalando's production environment to its large-scale catalog ranging in the millions of products and improving weekly profits by millions of Euros.

math.OC↗

arXiv2025

How neutron star properties disfavor a nuclear chiral density wave

Cold and dense matter may break rotational symmetry spontaneously and thus form an anisotropic phase in the interior of neutron stars. We consider the concrete example of an anisotropic chiral condensate in the form of a chiral density wave. Employing a nucleon-meson model and taking into account fermionic vacuum fluctuations, we improve and extend previous results by imposing the conditions of electric charge neutrality and electroweak equilibrium, by allowing for a more general form of the vector meson self-interactions, and by including properties of pure neutron matter into the fit of the model parameters. We find that the conditions inside neutron stars postpone the onset of the chiral density wave to larger densities compared to isospin-symmetric nuclear matter. While this still allows for the construction of stars with an anisotropic core, we find that the chiral density wave is energetically preferred only in a corner of the parameter space where matter is too soft to generate stars with realistic masses. Therefore, taking into account constraints from astrophysical data, our calculation predicts an isotropic neutron star core.

nucl-th↗

arXiv2024

Thermal pion condensation: holography meets lattice QCD

The holographic Witten-Sakai-Sugimoto model is often employed to describe strongly-coupled baryonic and isospin-asymmetric matter, for example in the context of neutron stars. Here we consider the case of vanishing baryon chemical potential, where detailed comparisons to data from lattice QCD are possible. To this end, we extend previous works by including a realistic pion mass and pion condensation into the decompactified limit of the model and evaluate the system for arbitrary isospin chemical potentials and temperatures. After suitably fixing the 3 parameters of the model, we find that the overall phase structure is in excellent agreement with lattice results. This also holds for observables at low temperatures in the strongly coupled regime, while we discover and discuss some discrepancies at large temperatures. Our findings give reassurance for the validity of previous and future applications of this model and highlight the aspects where improvements are needed.

hep-ph↗

arXiv2024

Chiral crossover vs chiral density wave in dense nuclear matter

We employ a model based on nucleonic and mesonic degrees of freedom to discuss the competition between isotropic and anisotropic phases in cold and dense matter. Assuming isotropy, the model exhibits a chiral phase transition which is of second order in the chiral limit and becomes a crossover in the case of a realistic pion mass. This observation crucially depends on the presence of the nucleonic vacuum contribution. Allowing for an anisotropic phase in the form of a chiral density wave can disrupt the smooth crossover. We identify the regions in the parameter space of the model where a chiral density wave is energetically preferred. A high-density re-appearance of the chiral density wave with unphysical behavior, as seen in previous studies, is avoided by a suitable renormalization scheme. A nonzero pion mass tends to disfavor the anisotropic phase compared to the chiral limit and we find that, within our model, the chiral density wave is only realized for baryon densities of at least about 6 times nuclear saturation density.

nucl-th↗

arXiv2024

Chiral Soliton Lattice turns into 3D crystal

Chiral perturbation theory predicts the chiral anomaly to induce a so-called Chiral Soliton Lattice at sufficiently large magnetic fields and baryon chemical potentials. This state breaks translational invariance in the direction of the magnetic field and was shown to be unstable with respect to charged pion condensation. Improving on previous work by considering a realistic pion mass, we employ methods from type-II superconductivity and construct a three-dimensional pion (and baryon) crystal perturbatively, close to the instability curve of the Chiral Soliton Lattice. We find an analogue of the usual type-I/type-II transition in superconductivity: Along the instability curve for magnetic fields $eB > 0.12\, {\rm GeV}^2$ and chemical potentials $μ< 910\, {\rm MeV}$, this crystal can continuously supersede the Chiral Soliton Lattice. For smaller magnetic fields the instability curve must be preceded by a discontinuous transition.

hep-th↗

arXiv2023

Phases of cold holographic QCD: baryons, pions and rho mesons

We improve the holographic description of isospin-asymmetric baryonic matter within the Witten-Sakai-Sugimoto model by accounting for a realistic pion mass, computing the pion condensate dynamically, and including rho meson condensation by allowing the gauge field in the bulk to be anisotropic. This description takes into account the coexistence of baryonic matter with pion and rho meson condensates. Our main result is the zero-temperature phase diagram in the plane of baryon and isospin chemical potentials. We find that the effective pion mass in the baryonic medium increases with baryon density and that, as a consequence, there is no pion condensation in neutron-star matter. Our improved description also predicts that baryons are disfavored at low baryon chemical potentials even for arbitrarily large isospin chemical potential. Instead, rho meson condensation sets in on top of the pion condensate at an isospin chemical potential of about $9.4\, m_π$. We further observe a highly non-monotonic phase boundary regarding the disappearance of pion condensation.

hep-ph↗

arXiv2022

Strange quark matter from a baryonic approach

We construct a model for dense matter based on low-density nuclear matter properties that exhibits a chiral phase transition and that includes strangeness through hyperonic degrees of freedom. Empirical constraints from nuclear matter alone allow for various scenarios, from a strong first-order chiral transition at relatively low densities through a weaker transition at higher densities, even up to a smooth crossover not far beyond the edge of the allowed range. The model parameters can be chosen such that at asymptotically large densities the chirally restored phase contains strangeness and the speed of sound approaches the conformal limit, resulting in a high-density phase that resembles deconfined quark matter. Additionally, if the model is required to reproduce sufficiently massive compact stars, the allowed parameter range is significantly narrowed down, resulting for instance in a very narrow range for the poorly known slope parameter of the symmetry energy, $L\simeq (88-92)\, {\rm MeV}$. We also find that for the allowed parameter range strangeness does not appear in the form of hyperons in the chirally broken phase and the chiral transition is of first order. Due to its unified approach and relative simplicity - here we restrict ourselves to zero temperature and the mean-field approximation - the model can be used in the future to study dense matter under compact star conditions in the vicinity of the chiral phase transition, for instance to compute the surface tension or to investigate spatially inhomogeneous phases.

nucl-th↗

arXiv2022

Chiral restoration of strange baryons

We review the results of a phenomenological model for cold and dense nuclear matter exhibiting a chiral phase transition. The idea is to model the quark-hadron phase transition under neutron star conditions within a single model, but without adding quark degrees of freedom by hand. To this end, strangeness is included in the form of hyperonic degrees of freedom, whose light counterparts provide the strangeness in the chirally restored phase. In the future, the model can be used for instance to compute the surface tension at the (first-order) chiral phase transition and to study the possible existence of inhomogeneous phases.

nucl-th↗

arXiv2022

Chiral anomaly induces superconducting baryon crystal

It was previously shown within chiral perturbation theory that the ground state of QCD in a sufficiently large magnetic field and at nonvanishing, but not too large, baryon chemical potential is a so-called chiral soliton lattice. The crucial ingredient of this observation was the chiral anomaly in the form of a Wess-Zumino-Witten term, which couples the baryon chemical potential to the magnetic field and the gradient of the neutral pion field. It was also shown that the chiral soliton lattice becomes unstable towards charged pion condensation at larger magnetic fields. We point out that this instability bears a striking resemblance to the second critical magnetic field of a type-II superconductor, however with the superconducting phase appearing upon increasing the magnetic field. The resulting phase has a periodically varying charged pion condensate that coexists with a neutral pion supercurrent. We construct this phase analytically in the chiral limit and show that it is energetically preferred. Just like an ordinary type-II superconductor, it exhibits a hexagonal array of magnetic flux tubes, and, due to the chiral anomaly, a spatially oscillating baryon number of the same crystalline structure.

hep-th↗

arXiv2022

Building a realistic neutron star from holography

We employ the recently improved description of dense baryonic matter within the Witten-Sakai-Sugimoto model to construct neutron stars. In contrast to previous holographic approaches, the presence of an isospin asymmetry allows us to implement beta equilibrium and electric charge neutrality. As a consequence, we are able to model the crust of the star within the same formalism and compute the location of the crust-core transition dynamically. After showing that a simple pointlike approximation for the baryons fails to satisfy astrophysical constraints, we demonstrate that our improved description does account for neutron stars that meet the current experimental constraints for mass, radius, and tidal deformability. However, we also point out tensions in the parameter fit and large-$N_c$ artifacts and discuss how to potentially resolve them in the future.

hep-ph↗

arXiv2022

Isospin asymmetry in holographic baryonic matter

We study baryonic matter with isospin asymmetry, including fully dynamically its interplay with pion condensation. To this end, we employ the holographic Witten-Sakai-Sugimoto model and the so-called homogeneous ansatz for the gauge fields in the bulk to describe baryonic matter. Within the confined geometry and restricting ourselves to the chiral limit, we map out the phase structure in the presence of baryon and isospin chemical potentials, showing that for sufficiently large chemical potentials condensed pions and isospin-asymmetric baryonic matter coexist. We also present first results of the same approach in the deconfined geometry and demonstrate that this case, albeit technically more involved, is better suited for comparisons with and predictions for real-world QCD. Our study lays the ground for future improved holographic studies aiming towards a realistic description of charge neutral, beta-equilibrated matter in compact stars, and also for more refined comparisons with lattice studies at nonzero isospin chemical potential.

hep-ph↗

arXiv2021

Predictions for neutron stars from holographic nuclear matter

We discuss masses, radii, and tidal deformabilities of neutron stars constructed from the holographic Witten-Sakai-Sugimoto model. Using the same model for crust and core of the star, we combine our theoretical results with the latest astrophysical data, thus deriving more stringent constraints than given by the data alone. For instance, our calculation predicts -- independent of the model parameters -- an upper limit for the maximal mass of the star of about 2.46 solar masses and a lower limit of the (dimensionless) tidal deformability of a 1.4-solar-mass star of about 277.

astro-ph.HE↗

arXiv2020

Strange quark mass turns magnetic domain walls into multi-winding flux tubes

Dense quark matter is expected to behave as a type-II superconductor at strong coupling. It was previously shown that if the strange quark mass $m_s$ is neglected, magnetic domain walls in the so-called 2SC phase are the energetically preferred magnetic defects in a certain parameter region. Computing the flux tube profiles and associated free energies within a Ginzburg-Landau approach, we find a cascade of multi-winding flux tubes as "remnants" of the domain wall when $m_s$ is increased. These flux tubes exhibit an unconventional ring-like structure of the magnetic field. We show that flux tubes with winding numbers larger than one survive for values of $m_s$ up to about 20% of the quark chemical potential. This makes them unlikely to play a significant role in compact stars, but they may appear in the QCD phase diagram in the presence of an external magnetic field.

hep-ph↗