scholarly journals Partition Function in One, Two, and Three Spatial Dimensions from Effective Lagrangian Field Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Christoph P. Hofmann
Keyword(s):  
Partition Function ◽  
Degrees Of Freedom ◽  
Spatial Dimension ◽  
Lagrangian Method ◽  
Point Of View ◽  
Low Energy ◽  
Effective Theory ◽  
Goldstone Bosons ◽  
Effective Lagrangian ◽  
Spatial Dimensions

The systematic effective Lagrangian method was first formulated in the context of the strong interaction; chiral perturbation theory (CHPT) is the effective theory of quantum chromodynamics (QCD). It was then pointed out that the method can be transferred to the nonrelativistic domain—in particular, to describe the low-energy properties of ferromagnets. Interestingly, whereas for Lorentz-invariant systems the effective Lagrangian method fails in one spatial dimension (ds=1), it perfectly works for nonrelativistic systems in ds=1. In the present brief review, we give an outline of the method and then focus on the partition function for ferromagnetic spin chains, ferromagnetic films, and ferromagnetic crystals up to three loops in the perturbative expansion—an accuracy never achieved by conventional condensed matter methods. We then compare ferromagnets in ds=1, 2, 3 with the behavior of QCD at low temperatures by considering the pressure and the order parameter. The two apparently very different systems (ferromagnets and QCD) are related from a universal point of view based on the spontaneously broken symmetry. In either case, the low-energy dynamics is described by an effective theory containing Goldstone bosons as basic degrees of freedom.

scholarly journals MAGNETIC ZN SYMMETRY IN 2+1 DIMENSIONS

2002 ◽  
Vol 17 (16) ◽  
pp. 2113-2164 ◽  
Author(s):  
A. KOVNER
Keyword(s):  
Degrees Of Freedom ◽  
Gauge Theories ◽  
Chiral Symmetry Breaking ◽  
Low Energy ◽  
Effective Theory ◽  
Spontaneous Breaking ◽  
Range Interaction ◽  
Strongly Coupled ◽  
Effective Lagrangian ◽  
Magnetic Symmetry

This review describes the role of magnetic symmetry in (2+1)-dimensional gauge theories. In confining theories without matter fields in fundamental representation the magnetic symmetry is spontaneously broken. Under some mild assumptions, the low-energy dynamics is determined universally by this spontaneous breaking phenomenon. The degrees of freedom in the effective theory are magnetic vortices. Their role in confining dynamics is similar to that played by pions and σ in the chiral symmetry breaking dynamics. I give an explicit derivation of the effective theory in (2+1)-dimensional weakly coupled confining models and argue that it remains qualitatively the same in strongly coupled (2+1)-dimensional gluodynamics. Confinement in this effective theory is a very simple classical statement about the long range interaction between topological solitons, which follows (as a result of a simple direct classical calculation) from the structure of the effective Lagrangian. I show that if fundamentally charged dynamical fields are present the magnetic symmetry becomes local rather than global. The modifications to the effective low energy description in the case of heavy dynamical fundamental matter are discussed. This effective Lagrangian naturally yields a bag like description of baryonic excitations. I also discuss the fate of the magnetic symmetry in gauge theories with the Chern–Simons term.

scholarly journals The low-energy effective theory of axions and ALPs

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Martin Bauer ◽  
Matthias Neubert ◽  
Sophie Renner ◽  
Marvin Schnubel ◽  
Andrea Thamm
Keyword(s):  
High Energy ◽  
New Physics ◽  
Mass Scale ◽  
Low Energy ◽  
Effective Theory ◽  
Loop Order ◽  
Flavor Changing ◽  
Effective Lagrangian ◽  
Anomalous Dimensions ◽  
Pseudoscalar Mesons

Abstract Axions and axion-like particles (ALPs) are well-motivated low-energy relics of high-energy extensions of the Standard Model, which interact with the known particles through higher-dimensional operators suppressed by the mass scale Λ of the new-physics sector. Starting from the most general dimension-5 interactions, we discuss in detail the evolution of the ALP couplings from the new-physics scale to energies at and below the scale of electroweak symmetry breaking. We derive the relevant anomalous dimensions at two-loop order in gauge couplings and one-loop order in Yukawa interactions, carefully considering the treatment of a redundant operator involving an ALP coupling to the Higgs current. We account for one-loop (and partially two-loop) matching contributions at the weak scale, including in particular flavor-changing effects. The relations between different equivalent forms of the effective Lagrangian are discussed in detail. We also construct the effective chiral Lagrangian for an ALP interacting with photons and light pseudoscalar mesons, pointing out important differences with the corresponding Lagrangian for the QCD axion.

scholarly journals INFINITE STATISTICS, SYMMETRY BREAKING AND COMBINATORIAL HIERARCHY

2009 ◽  
Vol 24 (18) ◽  
pp. 1425-1435 ◽  
Author(s):  
VLADIMIR SHEVCHENKO
Keyword(s):  
Symmetry Breaking ◽  
Mechanical Model ◽  
Degrees Of Freedom ◽  
High Energy ◽  
Low Energy ◽  
Effective Theory ◽  
Quantum Mechanical ◽  
Hierarchy Problem ◽  
Induced Gravity ◽  
Large Numbers

The physics of symmetry breaking in theories with strongly interacting quanta obeying infinite (quantum Boltzmann) statistics known as quons is discussed. The picture of Bose/Fermi particles as low energy excitations over nontrivial quon condensate is advocated. Using induced gravity arguments, it is demonstrated that the Planck mass in such low energy effective theory can be factorially (in number of degrees of freedom) larger than its true ultraviolet cutoff. Thus, the assumption that statistics of relevant high energy excitations is neither Bose nor Fermi but infinite can remove the hierarchy problem without necessity to introduce any artificially large numbers. Quantum mechanical model illustrating this scenario is presented.

scholarly journals Lattice Clifford fractons and their Chern-Simons-like theory

2021 ◽  
Vol 4 (2) ◽  
Author(s):  
Weslei Fontana ◽  
Pedro Gomes ◽  
Claudio Chamon
Keyword(s):  
Clifford Algebra ◽  
Degrees Of Freedom ◽  
Quantum Hall ◽  
Effective Theory ◽  
Matrix Representations ◽  
Quantum Hall States ◽  
Dirac Matrix ◽  
Spatial Dimensions ◽  
K Matrix ◽  
Chern Simons

We use Dirac matrix representations of the Clifford algebra to build fracton models on the lattice and their effective Chern-Simons-like theory. As an example, we build lattice fractons in odd D spatial dimensions and their (D+1) spacetime dimensional effective theory. The model possesses an anti-symmetric K matrix resembling that of hierarchical quantum Hall states. The gauge charges are conserved in sub-dimensional manifolds which ensures the fractonic behavior. The construction extends to any lattice fracton model built from commuting projectors and with tensor products of spin-1/2 degrees of freedom at the sites.

scholarly journals Localization of the gauged linear sigma model for KK5-branes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Yuki Hiraga ◽  
Yuki Sato
Keyword(s):  
Partition Function ◽  
Sigma Model ◽  
Low Energy ◽  
Target Space ◽  
Linear Sigma Model ◽  
Effective Theory ◽  
Coulomb Branch ◽  
World Sheet ◽  
The World ◽  
Gauged Linear Sigma Model

Abstract We study quantum aspects of the target space of the non-linear sigma model, which is a low-energy effective theory of the gauged linear sigma model (GLSM). As such, we especially compute the exact sphere partition function of the GLSM for KK$5$-branes whose background geometry is a Taub–NUT space, using the supersymmetric localization technique on the Coulomb branch. From the sphere partition function, we distill the world-sheet instanton effects. In particular, we show that, concerning the single-centered Taub–NUT space, instanton contributions exist only if the asymptotic radius of the $S^1$ fiber in the Taub–NUT space is zero.

scholarly journals How general relativity and Lorentz covariance arise from the spatially-covariant effective field theory of the transverse, traceless graviton

2014 ◽  
Vol 23 (12) ◽  
pp. 1442012 ◽  
Author(s):  
Justin Khoury ◽  
Godfrey E. J. Miller ◽  
Andrew J. Tolley
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Effective Field Theory ◽  
Degrees Of Freedom ◽  
Effective Field ◽  
Point Of View ◽  
Low Energy ◽  
Fundamental Physics ◽  
Lorentz Covariance

Traditional derivations of general relativity (GR) from the graviton degrees of freedom assume spacetime Lorentz covariance as an axiom. In this paper, we survey recent evidence that GR is the unique spatially-covariant effective field theory of the transverse, traceless graviton degrees of freedom. The Lorentz covariance of GR, having not been assumed in our analysis, is thus plausibly interpreted as an accidental or emergent symmetry of the gravitational sector. From this point of view, Lorentz covariance is a necessary feature of low-energy graviton dynamics, not a property of spacetime. This result has revolutionary implications for fundamental physics.

Galilean covariant effective theory for bound states of heavy mesons

2018 ◽  
Vol 33 (30) ◽  
pp. 1850180
Author(s):  
L. M. Abreu ◽  
M. de Montigny ◽  
E. S. Santos ◽  
D. F. C. A. Silva
Keyword(s):  
Bound States ◽  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Heavy Meson ◽  
Effective Theory ◽  
Heavy Mesons ◽  
Interaction Terms ◽  
Effective Lagrangian ◽  
Dimensional Space Time ◽  
Covariant Version

In this work we formulate the Galilei-covariant version of an effective theory containing nonrelativistic heavy mesons and pions as degrees of freedom. This manifestly Galilean covariant framework is based on a five-dimensional space–time that has been used in the description of covariant nonrelativistic physics. In this context, effective Lagrangian is introduced without ambiguities, containing kinetic and interaction terms that are naturally Galilean invariant. The leading-order scattering amplitudes and the properties of possible heavy-meson bound states are calculated and discussed.

scholarly journals EFFECTIVE LOW-ENERGY THEORIES AND QCD DIRAC SPECTRA

2001 ◽  
Vol 15 (10n11) ◽  
pp. 1404-1415 ◽  
Author(s):  
D. TOUBLAN ◽  
J. J. M. VERBAARSCHOT
Keyword(s):  
Partition Function ◽  
Dirac Operator ◽  
Spectral Density ◽  
Random Matrix ◽  
Matrix Theory ◽  
Low Energy ◽  
Effective Theory ◽  
Kinetic Term ◽  
Dirac Spectrum ◽  
Energy Theory

We analyze the smallest Dirac eigenvalues by formulating an effective theory for the Dirac spectrum. We find that in a domain where the kinetic term of the effective theory can be ignored, the Dirac eigenvalues are distributed according to a Random Matrix Theory with the global symmetries of the QCD partition function. The kinetic term provides information on the slope of the average spectral density of the Dirac operator. In the second half of this lecture we interpret quenched QCD Dirac spectra (with eigenvalues scattered in the complex plane) in terms of an effective low energy theory.

scholarly journals MODULI SPACE OF GLOBAL SYMMETRY IN N=1 SUPERSYMMETRIC THEORIES AND THE QUASI-NAMBU–GOLDSTONE BOSONS

1999 ◽  
Vol 14 (15) ◽  
pp. 2397-2430 ◽  
Author(s):  
MUNETO NITTA
Keyword(s):  
Moduli Space ◽  
Arbitrary Function ◽  
Singular Points ◽  
Low Energy ◽  
Global Symmetry ◽  
Goldstone Bosons ◽  
Effective Lagrangian ◽  
Generic Points ◽  
Supersymmetric Theories

We derive the moduli space of the global symmetry in N=1 supersymmetric theories. We show that, at the generic points, it coincides with the space of quasi-Nambu–Goldstone (QNG) bosons, which appear besides the ordinary Nambu–Goldstone (NG) bosons when the global symmetry G breaks down spontaneously to its subgroup H with preservation of N=1 supersymmetry. At the singular points, most of the NG bosons change to QNG bosons and the unbroken global symmetry is enhanced. The G orbits parametrized by the NG bosons are the fiber at the moduli space and the singular points correspond to the point where the H orbit (in the G orbit) shrinks. We also show that the low energy effective Lagrangian is the arbitrary function of the moduli parameters.

scholarly journals Holography in a background-independent effective theory

2015 ◽  
Vol 12 (07) ◽  
pp. 1550075
Author(s):  
Giorgio Torrieri
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Partition Function ◽  
Equivalence Principle ◽  
Degrees Of Freedom ◽  
Functional Integral ◽  
Effective Theory ◽  
Quantum Field ◽  
Strong Equivalence Principle ◽  
Accelerated Frames

We discuss the meaning of the strong equivalence principle when applied to a quantum field theory. We show that, because of unitary inequivalence of accelerated frames, the only way for the strong equivalence principle to apply exactly is to add a boundary term representing the decoherence of degrees of freedom leaving the observable region of the bulk. We formulate the constraints necessary for the partition function to be covariant with respect to non-inertial transformations and argue that, when the non-unitary part is expressed as a functional integral over the horizon, holography arises naturally as a consequence of the equivalence principle.

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