arXiv subjects

Tomas Brauner

Publications and source records attributed to Tomas Brauner.

At least 19 recordsLinked to original sources

arXiv2026

Chiral soliton lattice in inhomogeneous magnetic fields

It has been known that in sufficiently strong uniform magnetic fields, the ground state of quantum chromodynamics (QCD) supports a spatially modulated condensate of neutral pions, dubbed chiral soliton lattice (CSL). In this paper, we investigate whether a similar ordered ground state might exist when the external magnetic field is nonuniform, as appropriate for potential phenomenological applications, including heavy-ion collisions and neutron stars. To that end, we use the low-energy effective field theory of QCD, restricted to the neutral pions as the sole low-energy degrees of freedom in strong magnetic fields. In the limit of vanishing pion mass, we achieve a complete characterization of magnetic fields supporting a CSL-like ground state. Moreover, for a simple but infinite family of magnetic fields, we find the corresponding CSL state analytically. Going away from the massless limit requires full numerical minimization of the energy functional. Here we provide some sample numerical results, focusing on the qualitative differences as compared to the situations with a uniform magnetic field or a vanishing pion mass. The main conclusion remains unchanged: while bending the magnetic field typically reduces the energy gain due to the neutral pion condensation, a CSL-type ground state is still possible. As a byproduct of our work, we map the location of the CSL phase in the phase diagram of QCD in a uniform magnetic field and finite volume.

hep-ph↗

arXiv2025

Geometric duality between effective field theories I: scattering amplitudes

We propose a novel type of duality that connects a sequence of well-known theories with even-multiplicity scalar amplitudes: it relates the Yang-Mills theory coupled to a specific scalar matter sector to the nonlinear sigma model on a symmetric coset space, the (multiflavor) Dirac-Born-Infeld theory, and the special Galileon theory. The duality is manifested with the help of a covariant formulation of the classical equations of motion that features a contact quartic scalar self-coupling combined with propagation on a dynamical background of elementary or composite gauge fields. This is augmented with a set of constitutive relations that reflect the intrinsic or extrinsic geometry of the target space of the theory. The universality of the underlying geometric structure allows for an unambiguous mapping between different theories.

hep-th↗

arXiv2025

Analytical Mechanics and Field Theory

Lecture notes for a one-semester master-level course on analytical mechanics and classical field theory, covering: 0 Mathematical Introduction, 1 Lagrangian Mechanics, 2 Application: Motion in Central Fields, 3 Hamiltonian Mechanics, 4 Application: Oscillations of Mechanical Systems, 5 Application: Relativistic Mechanics, 6 Geometry of Classical Mechanics, 7 Application: Dynamics of Rigid Bodies, 8 Lagrangian and Hamiltonian Mechanics of Continuous Systems, 9 Application: Elasticity of Solids, 10 Symmetries and Conservation Laws, 11 Application: Fluid Dynamics, 12 Application: Electrodynamics

physics.class-ph↗

arXiv2024

The surprising subtlety of electrostatic field lines

Electric fields are commonly visualized with field line diagrams, which only unambiguously specify the field's direction. We consider two simple questions. First, can one deduce if an electric field is conservative, as required e.g. in electrostatics, from its field lines alone? Second, are there conservative electric fields with straight field lines, besides the familiar textbook examples with spherical, cylindrical, or planar symmetry? We give a self-contained introduction to the differential geometry required to answer these questions, assuming only vector calculus background.

physics.class-ph↗

arXiv2024

Effective Field Theory for Spontaneously Broken Symmetry

This is a preprint of an open-access book published by Springer Cham. The book gives an up-to-date overview of the physics of spontaneously broken continuous symmetry from the point of view of effective field theory. Upon building up the necessary foundations, the text reviews the classification of Nambu-Goldstone bosons and then focuses on the construction of the effective-field-theoretic description of their dynamics. Both internal and spacetime broken symmetries are covered, including numerous illustrative examples and a few selected applications, worked out in greater detail.

hep-th↗

arXiv2023

Dipole symmetries from the topology of the phase space and the constraints on the low-energy spectrum

We demonstrate the general existence of a local dipole conservation law in bosonic field theory. The scalar charge density arises from the symplectic form of the system, whereas the tensor current descends from its stress tensor. The algebra of spatial translations becomes centrally extended in presence of field configurations with a finite nonzero charge. Furthermore, when the symplectic form is closed but not exact, the system may, surprisingly, lack a well-defined momentum density. This leads to a theorem for the presence of additional light modes in the system whenever the short-distance physics is governed by a translationally invariant local field theory. We also illustrate this mechanism for axion electrodynamics as an example of a system with Nambu--Goldstone modes of higher-form symmetries.

hep-th↗

arXiv2022

Snowmass Theory Frontier: Effective Field Theory

We summarize recent progress in the development, application, and understanding of effective field theories and highlight promising directions for future research. This Report is prepared as the TF02 "Effective Field Theory" topical group summary for the Theory Frontier as part of the Snowmass 2021 process.

hep-ph↗

arXiv2022

Snowmass White Paper: Effective Field Theories for Condensed Matter Systems

We review recent progress and a number of future directions for applications of effective field theory methods to condensed matter systems broadly defined. Our emphasis is on areas that have allowed a fertile exchange of ideas between high energy physics and many-body theory. We discuss developments in the effective field theory of spontaneous symmetry breaking, of hydrodynamics and non-equilibrium dynamics more generally, fracton phases of matter, and dualities between 2+1 dimensional field theories. We furthermore discuss the application of effective field theory to non-Fermi liquids, the dynamics of entanglement entropy and to condensed matter aspects of cosmology.

hep-th↗

arXiv2021

On-Shell Recursion Relations for Nonrelativistic Effective Field Theories

We derive on-shell recursion relations for nonrelativistic effective field theories (EFTs) with enhanced soft limits. The recursion relations are illustrated through analytic calculation of tree-level scattering amplitudes in theories with a complex Schr\"odinger-type field, real scalar with linear dispersion relation, and real scalar with Lifshitz-type dispersion relation. Our results show that the landscape of gapless nonrelativistic EFTs with local $S$-matrix can be constrained by soft theorems and the consistency of the low-energy $S$-matrix similarly to massless relativistic EFTs.

hep-th↗

arXiv2020

Field theories with higher-group symmetry from composite currents

Higher-form symmetries are associated with transformations that only act on extended objects, not on point particles. Typically, higher-form symmetries live alongside ordinary, point-particle (0-form), symmetries and they can be jointly described in terms of a direct product symmetry group. However, when the actions of 0-form and higher-form symmetries become entangled, a more general mathematical structure is required, related to higher categorical groups. Systems with continuous higher-group symmetry were previously constructed in a top-down manner, descending from quantum field theories with a specific mixed 't Hooft anomaly. I show that higher-group symmetry also naturally emerges from a bottom-up, low-energy perspective, when the physical system at hand contains at least two different given, spontaneously broken symmetries. This leads generically to a hierarchy of emergent higher-form symmetries, corresponding to the Grassmann algebra of topological currents of the theory, with an underlying higher-group structure. Examples of physical systems featuring such higher-group symmetry include superfluid mixtures and variants of axion electrodynamics.

hep-th↗

arXiv2020

Remarks on relativistic scalar models with chemical potential

We discuss selected aspects of classical relativistic scalar field theories with nonzero chemical potential. First, we offer a review of classical field theory at nonzero density within the Lagrangian formalism. The aspects covered include the question of equivalence of descriptions of finite-density states using a chemical potential or time-dependent field configurations, the choice of Hamiltonian whose minimization yields the finite-density equilibrium state, and the issue of breaking of Lorentz invariance. Second, we demonstrate how the low-energy effective field theory for Nambu-Goldstone (NG) modes arising from the spontaneous breakdown of global internal symmetries can be worked out explicitly by integrating out the heavy (Higgs) fields. This makes it possible to analyze the spectrum of NG modes and their interactions without having to deal with mixing of NG and Higgs fields, ubiquitous in the linear-sigma-model description of spontaneous symmetry breaking.

hep-th↗

arXiv2020

Exceptional nonrelativistic effective field theories with enhanced symmetries

We initiate the classification of nonrelativistic effective field theories (EFTs) for Nambu-Goldstone (NG) bosons, possessing a set of redundant, coordinate-dependent symmetries. Similarly to the relativistic case, such EFTs are natural candidates for "exceptional" theories, whose scattering amplitudes feature an enhanced soft limit, that is, scale with a higher power of momentum at long wavelengths than expected based on the mere presence of Adler's zero. The starting point of our framework is the assumption of invariance under spacetime translations and spatial rotations. The setup is nevertheless general enough to accommodate a variety of nontrivial kinematical algebras, including the Poincare, Galilei (or Bargmann) and Carroll algebras. Our main result is an explicit construction of the nonrelativistic versions of two infinite classes of exceptional theories: the multi-Galileon and the multi-flavor Dirac-Born-Infeld (DBI) theories. In both cases, we uncover novel Wess-Zumino terms, not present in their relativistic counterparts, realizing nontrivially the shift symmetries acting on the NG fields. We demonstrate how the symmetries of the Galileon and DBI theories can be made compatible with a nonrelativistic, quadratic dispersion relation of (some of) the NG modes.

hep-th↗

arXiv2019

Noether currents of locally equivalent symmetries

Local symmetry transformations play an important role for establishing the existence and form of a conserved (Noether) current in systems with a global continuous symmetry. We explain how this fact leads to the existence of linear relations between Noether currents of distinct global symmetries that coincide on the local level, thus generalizing the well-known relationship $\vec L=\vec r\times\vec p$ between momentum $\vec p$ and angular momentum $\vec L$. As a byproduct, we find a natural interpretation for the discrepancy between the canonical and metric energy-momentum tensors in theories of particles with spin. A symmetric energy-momentum tensor can thus be obtained from the Noether procedure without adding any ad hoc corrections or imposing additional constraints such as gauge invariance in Maxwell's electrodynamics.

hep-th↗

arXiv2018

Gauged Wess-Zumino terms for a general coset space

The low-energy physics of systems with spontaneously broken continuous symmetry is dominated by the ensuing Nambu-Goldstone bosons. It has been known for half a century how to construct invariant Lagrangian densities for the low-energy effective theory of Nambu-Goldstone bosons. Contributions, invariant only up to a surface term -- also known as the Wess-Zumino (WZ) terms -- are more subtle, and as a rule are topological in nature. Although WZ terms have been studied intensively in theoretically oriented literature, explicit expressions do not seem to be available in sufficient generality in a form suitable for practical applications. Here we construct the WZ terms in $d=1,2,3,4$ spacetime dimensions for an arbitrary compact, semisimple and simply connected symmetry group $G$ and its arbitrary connected unbroken subgroup $H$, provided that the $d$-th homotopy group of the coset space $G/H$ is trivial. Coupling to gauge fields for the whole group $G$ is included throughout the construction. We list a number of explicit matrix expressions for the WZ terms in four spacetime dimensions, including those for QCD-like theories, that is vector-like gauge theories with fermions in a complex, real or pseudoreal representation of the gauge group.

hep-th↗

arXiv2018

Helical spin texture in a thin film of superfluid ${}^3$He

We consider a thin film of superfluid ${}^3$He under conditions that stabilize the A-phase. We show that in the presence of a uniform superflow and an external magnetic field perpendicular to the film, the spin degrees of freedom develop a nonuniform, helical texture. Our prediction is robust and relies solely on Galilei invariance and other symmetries of ${}^3$He, which induce a coupling of the orbital and spin degrees of freedom. The length scale of the helical order can be tuned by varying the velocity of the superflow and the magnetic field, and may be in reach of near-future experiments.

cond-mat.supr-con↗

arXiv2018

Geometry of Multi-Flavor Galileon-Like Theories

We use Lie-algebraic arguments to classify Lorentz-invariant theories of massless interacting scalars that feature coordinate-dependent redundant symmetries of the Galileon type. We show that such theories are determined, up to a set of low-energy effective couplings, by specifying an affine representation of the Lie algebra of physical, non-redundant internal symmetries and an invariant metric on its target space. This creates an infinite catalog of theories relevant for both cosmology and high-energy physics thanks to their special properties such as enhanced scaling of scattering amplitudes in the soft limit.

hep-th↗

arXiv2017

Scattering amplitudes of massive Nambu-Goldstone bosons

Massive Nambu-Goldstone (mNG) bosons are quasiparticles whose gap is determined exactly by symmetry. They appear whenever a symmetry is broken spontaneously in the ground state of a quantum many-body system, and at the same time explicitly by the system's chemical potential. In this paper, we revisit mNG bosons and show that apart from their gap, symmetry also protects their scattering amplitudes. Just like for ordinary gapless NG bosons, the scattering amplitudes of mNG bosons vanish in the long-wavelength limit. Unlike for gapless NG bosons, this statement holds for any scattering process involving one or more external mNG states; there are no kinematic singularities associated with the radiation of a soft mNG boson from an on-shell initial or final state.

hep-th↗

arXiv2017

Anomalous low-temperature thermodynamics of QCD in strong magnetic fields

The thermodynamics of quantum chromodynamics at low temperatures and in sufficiently strong magnetic fields is governed by neutral pions. We analyze the interacting system of neutral pions and photons at zero baryon chemical potential using effective field theory. As a consequence of the axial anomaly and the external magnetic field, the pions and photons mix with one another. The resulting spectrum contains one usual, relativistic photon state, and two nonrelativistic modes, one of which is gapless and the other gapped. Furthermore, we calculate the leading, one-loop contribution to the pressure of the system. In the chiral limit, a closed analytic expression for the pressure exists, which features an unusual scaling with temperature and magnetic field, $T^3B/f_\pi$, at low temperatures, $T\ll B/f_\pi$. Finally, we determine the pion decay rate as a function of the magnetic field at the tree level. The result is affected by a competition of the anisotropic kinematics and the enlarged phase space due to the anomalous mass of the neutral pion. In the chiral limit, the decay rate scales as $B^3/f_\pi^5$.

hep-ph↗