scholarly journals The Global Symmetry Group of Quantum Spectral Beams and Geometric Phase Factors

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Elias Zafiris
Keyword(s):  
Geometric Phase ◽  
Affine Space ◽  
Differential Invariant ◽  
Space Structure ◽  
Equivalence Classes ◽  
Global Symmetry ◽  
State Spaces ◽  
Gauge Equivalence ◽  
Global Symmetry Group ◽  
De Rham

We propose a cohomological modelling schema of quantum state spaces and their connectivity structures in relation to the formulation of global geometric phase phenomena. In the course of this schema, we introduce the notion of Hermitian differential line sheaves or unitary rays and classify their gauge equivalence classes in terms of a global differential invariant given by the de Rham cohomology class of the curvature. Furthermore, we formulate and interpret physically the curvature recognition integrality theorem for unitary rays. Using this recognition theorem, we define the notion of a quantum spectral beam and show that it has an affine space structure with structure group given by the characters of the fundamental group.

scholarly journals On the Connectedness of Moduli Spaces of Flat Connections over Compact Surfaces

2004 ◽  
Vol 56 (6) ◽  
pp. 1228-1236 ◽  
Author(s):  
Nan-Kuo Ho ◽  
Chiu-Chu Melissa Liu
Keyword(s):  
Lie Groups ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Orientable Surface ◽  
Equivalence Classes ◽  
Nonorientable Surface ◽  
Flat Connections ◽  
Gauge Equivalence ◽  
Compact Orientable Surface ◽  
Simply Connected

AbstractWe study the connectedness of the moduli space of gauge equivalence classes of flat G-connections on a compact orientable surface or a compact nonorientable surface for a class of compact connected Lie groups. This class includes all the compact, connected, simply connected Lie groups, and some non-semisimple classical groups.

scholarly journals A Bosonisation of QCD and Realisations of Chiral Symmetry

1987 ◽  
Vol 40 (4) ◽  
pp. 499 ◽  
Author(s):  
CD Roberts ◽  
RT Cahill
Keyword(s):  
Symmetry Group ◽  
Chiral Symmetry ◽  
Functional Integral ◽  
Vacuum Field ◽  
Global Symmetry ◽  
Field Representation ◽  
Generating Functional ◽  
Global Symmetry Group ◽  
Vacuum Field Equation ◽  
Alternative Solutions

We employ the functional integral formalism to study quantum chromodynamics (QCD) with Nf quarks of zero bare mass. In addition to local SU(Nc) colour symmetry, this theory possesses exact global G = UdNf)@UR(Nf) chiral symmetry. We obtain an exact bilocal Bose field representation of the generating functional which, as we prove after establishing the manner in which the bilocal fields transform under G, preserves the global chiral symmetry. We demonstrate how a local Bose field representation of the generating functional may be obtained from the bilocal bosonisation. This provides a direct link between QCD and low energy meson phenomenological models. We utilise the bilocal bosonisation in the study of the dynamical breakdown of the global chiral symmetry group G. We derive the vacuum field equation from the exact bilocal Bose field effective action and discuss two alternative solutions: one corresponding to a Wigner-Weyl realisation of the global symmetry group G in which the vacuum configuration is invariant under G; the other to a mixed realisation in which the vacuum manifold is the coset space G/H = U A(Nf ), where H = Uv(Nf ) is a subgroup of G.

scholarly journals Multi-fixed point numerical conformal bootstrap: a case study with structured global symmetry

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Matthew T. Dowens ◽  
Chris A. Hooley
Keyword(s):  
Group Symmetry ◽  
Global Symmetry ◽  
Minimal Set ◽  
Conformal Field ◽  
Conformal Bootstrap ◽  
Critical Theories ◽  
Global Symmetry Group ◽  
Starting Point ◽  
Future Utility

Abstract In large part, the future utility of modern numerical conformal bootstrap depends on its ability to accurately predict the existence of hitherto unknown non-trivial conformal field theories (CFTs). Here we investigate the extent to which this is possible in the case where the global symmetry group has a product structure. We do this by testing for signatures of fixed points using a mixed-correlator bootstrap calculation with a minimal set of input assumptions. This ‘semi-blind’ approach contrasts with other approaches for probing more complicated groups, which ‘target’ known theories with additional spectral assumptions or use the saturation of the single-correlator bootstrap bound as a starting point. As a case study, we select the space of CFTs with product-group symmetry O(15) ⊗ O(3) in d = 3 dimensions. On the assumption that there is only one relevant scalar (ℓ = 0) singlet operator in the theory, we find a single ‘allowed’ region in our chosen space of scaling dimensions. The scaling dimensions corresponding to two known large-N critical theories, the Heisenberg and the chiral ones, lie on or very near the boundary of this region. The large-N antichiral point lies well outside the ‘allowed’ region, which is consistent with the expectation that the antichiral theory is unstable, and thus has an additional relevant scalar singlet operator. We also find a sharp kink in the boundary of the ‘allowed’ region at values of the scaling dimensions that do not correspond to the (N, M ) = (3, 15) instance of any large-N -predicted O(N ) ⊗ O(M ) critical theory.

scholarly journals Models of hypercolor based on symplectic gauge group with three heavy vectorlike hyperquarks

2019 ◽  
Vol 28 (13) ◽  
pp. 1941002 ◽  
Author(s):  
Nikolay Volchanskiy ◽  
Vladimir Kuksa ◽  
Vitaly Beylin
Keyword(s):  
Higgs Boson ◽  
Standard Model ◽  
Symmetry Group ◽  
Gauge Group ◽  
Global Symmetry ◽  
Composite Higgs ◽  
Global Symmetry Group ◽  
The Standard Model ◽  
Dynamical Breaking ◽  
Partially Composite

We study possibilities to extend the Standard Model (SM) by three flavors of vectorlike heavy quarks in pseudoreal representation of symplectic hypercolor gauge group. This extension of SM predicts a rich spectra of heavy composite hypermesons and hyperbaryons (all of them carry integer spins) including 14 pseudo-Nambu–Goldstone states emerging in dynamical breaking of the global symmetry group of the H-quarks, [Formula: see text], to its Sp(6) subgroup. The properties of the lightest states depend strongly on the choice of heavy-quark hypercharges. Our focus is placed on the variants of the model with partially composite Higgs boson, i.e. the experimentally observed boson comprised the elementary SM Higgs and a mixture of H-hadrons.

Local and global color symmetries of a symmetrical pattern

2019 ◽  
Vol 75 (5) ◽  
pp. 730-745
Author(s):  
Agatha Kristel Abila ◽  
Ma. Louise Antonette De Las Peñas ◽  
Eduard Taganap
Keyword(s):  
Symmetry Group ◽  
Local Symmetry ◽  
Global Symmetry ◽  
Color Symmetry ◽  
Usual Approach ◽  
Symmetrical Pattern ◽  
Symmetry Theory ◽  
Global Symmetry Group ◽  
Local Symmetries ◽  
Global And Local

This study addresses the problem of arriving at transitive perfect colorings of a symmetrical pattern {\cal P} consisting of disjoint congruent symmetric motifs. The pattern {\cal P} has local symmetries that are not necessarily contained in its global symmetry group G. The usual approach in color symmetry theory is to arrive at perfect colorings of {\cal P} ignoring local symmetries and considering only elements of G. A framework is presented to systematically arrive at what Roth [Geom. Dedicata (1984), 17, 99–108] defined as a coordinated coloring of {\cal P}, a coloring that is perfect and transitive under G, satisfying the condition that the coloring of a given motif is also perfect and transitive under its symmetry group. Moreover, in the coloring of {\cal P}, the symmetry of {\cal P} that is both a global and local symmetry, effects the same permutation of the colors used to color {\cal P} and the corresponding motif, respectively.

Seifert-fibred homology 3-spheres,V-surfaces and the Floer index

1992 ◽  
Vol 111 (3) ◽  
pp. 461-485
Author(s):  
Emile Ben Nasatyr
Keyword(s):  
Moduli Space ◽  
Floer Homology ◽  
Direct Method ◽  
Chain Complex ◽  
Equivalence Classes ◽  
Spectral Flow ◽  
Flat Connections ◽  
Gauge Equivalence ◽  
Numerical Result ◽  
Adjoint Bundle

Let Σ be a Seifert-fibred homology 3-sphere. We are interested in the chain complex for the Floer homology of Σ. This is generated by the critical points of the ChernSimons functional acting on the moduli space of irreducibleSU(2)-connections modulo gauge-equivalence, i.e. the equivalence classes of flat connections: see [6]. Specifically, we ask the question: given the holonomy ρ of a flat connectionCρ, what is the index ofCρin the chain complex? By definition thisFloer indexis given by the spectral flow of a family of twisted signature operators with coefficients in the adjoint bundle (with fibre su(2)) corresponding to any path of connections joining the trivial connection toCρ. We will calculate this spectral flow by an almost entirely direct method, obtaining a formula in terms of the dimensions of spaces of π1(Σ)- automorphic functions. These dimensions will be evaluated to give the numerical result previously obtained using a different method by Fintushel and Stern: see [5].

scholarly journals Confinement in 4D: An Attempt at Classical Understanding

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 291
Author(s):  
Ibrahim Burak Ilhan ◽  
Alex Kovner
Keyword(s):  
Degrees Of Freedom ◽  
Vector Fields ◽  
Scalar Fields ◽  
Effective Theory ◽  
Global Symmetry ◽  
Abelian Gauge ◽  
Infinite Dimensional ◽  
Diffeomorphism Invariance ◽  
Dimensional Phase Space ◽  
Global Symmetry Group

In this review, we revisit our approach to constructing an effective theory for Abelian and Non-Abelian gauge theories in 4D. Our goal is to have an effective theory that provides a simple classical picture of the main qualitatively important features of these theories. We set out to ensure the presence of the massless photons—Goldstone bosons in Abelian theory and their disappearance in the Non-Abelian case—accompanied by the formation of confining strings between charged states. Our formulation avoids using vector fields and instead operates with the basic degrees of freedom that are the scalar fields of a nonlinear σ-model. The Mark 1 model we study turns out to have a large global symmetry group-the 2D diffeomorphism invariance in the Abelian limit, which is isomorphic to the group of all canonical transformations in the classical two dimensional phase space. This symmetry is not present in QED, and we eliminate it by “gauging” this infinite dimensional global group. Introducing additional modifications to the model (Mark 2), we are able to prove that the “Abelian” version is equivalent to the theory of a free photon. Achieving the desired property in the “Non-Abelian” regime turns out to be tricky. We are able to introduce a perturbation that leads to the formation of confining strings in our Mark 1 model. These strings have somewhat unusual properties, in that their profile does not decay exponentially away from the center of the string. In addition, the perturbation explicitly breaks the diffeomorphism invariance. Preserving this invariance in the gauged model as well as achieving confining strings in Mark 2 model remains an open question.

scholarly journals The axion quality problem: global symmetry breaking and wormholes

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
James Alvey ◽  
Miguel Escudero
Keyword(s):  
String Theory ◽  
Symmetry Breaking ◽  
Global Symmetries ◽  
Open String ◽  
Einstein Gravity ◽  
Current Status ◽  
Global Symmetry ◽  
Quality Problem ◽  
Global Symmetry Group ◽  
The Impact

Abstract Continuous global symmetries are expected to be broken by gravity, which can lead to important phenomenological consequences. A prime example is the threat that this poses to the viability of the Peccei-Quinn solution to the strong CP problem. In this paper, we explore the impact of wormholes as a source of global symmetry breaking by gravity. We review the current status of wormholes and global symmetries and note that, surprisingly, the axion has a quality problem within non-perturbative Einstein gravity. Although these wormholes lead to a large breaking of global symmetries, we show that their effect is nonetheless relevant for the model building of gauge protected axions. We also find wormhole solutions within two scenarios: (i) an extended global symmetry group within Einstein gravity, and (ii) U(1) wormholes within the low-energy limit of an open String Theory. The former allows us to show that the concept of a global symmetry in General Relativity is somewhat ill-defined. The latter illustrates that for motivated values of the string coupling constant, axions appear to have a quality problem within the open String Theory we consider.

scholarly journals Pseudoscalar glueballs in the Klebanov-Strassler theory

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Dmitry Melnikov ◽  
Cornélio Rodrigues Filho
Keyword(s):  
Numerical Analysis ◽  
Symmetry Group ◽  
Global Symmetry ◽  
System Of Equations ◽  
Global Symmetry Group ◽  
Lattice Calculations ◽  
The Masses ◽  
Holographic Reconstruction

Abstract In this paper we describe a pseudoscalar subsector of the Klebanov-Strassler model. This subsector completes the holographic reconstruction of the spectrum of the lowest-lying glueball states, which are singlet under the global symmetry group SU(2) × SU(2). We derive the linearized supergravity equations for the pseudoscalar fluctuations and analyze their spectrum. The system of equations is shown to be compatible with six eigenmodes, as expected from supersymmetry. Our numerical analysis allows to reliably extract four of the corresponding towers. Their values match well the eigenvalues of the 0++ scalar states known from an earlier work. Assuming the masses of 0++ as a reference, we compare the lightest states of the holographic spectrum with lattice calculations in the quenched QCD at Nc = 3 and Nc = ∞.

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