scholarly journals Symmetry structure of the interactions in near-BPS corners of $$ \mathcal{N} $$ = 4 super-Yang-Mills

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Stefano Baiguera ◽  
Troels Harmark ◽  
Yang Lei ◽  
Nico Wintergerst
Keyword(s):  
Irreducible Representation ◽  
Classical Limit ◽  
Positive Definiteness ◽  
Yang Mills ◽  
Three Sphere ◽  
Effective Dynamics ◽  
Coupling Dynamics ◽  
Full Interaction ◽  
Interaction Term ◽  
Symmetry Structure

Abstract We consider limits of $$ \mathcal{N} $$ N = 4 super-Yang-Mills (SYM) theory that approach BPS bounds. These limits result in non-relativistic near-BPS theories that describe the effective dynamics near the BPS bounds and upon quantization are known as Spin Matrix theories. The near-BPS theories can be obtained by reducing $$ \mathcal{N} $$ N = 4 SYM on a three-sphere and integrating out the fields that become non-dynamical in the limits. We perform the sphere reduction for the near-BPS limit with SU(1, 2|2) symmetry, which has several new features compared to the previously considered cases with SU(1) symmetry, including a dynamical gauge field. We discover a new structure in the classical limit of the interaction term. We show that the interaction term is built from certain blocks that comprise an irreducible representation of the SU(1, 2|2) algebra. Moreover, the full interaction term can be interpreted as a norm in the linear space of this representation, explaining its features including the positive definiteness. This means one can think of the interaction term as a distance squared from saturating the BPS bound. The SU(1, 1|1) near-BPS theory, and its subcases, is seen to inherit these features. These observations point to a way to solve the strong coupling dynamics of these near-BPS theories.

scholarly journals Nonrelativistic near-BPS corners of $$ \mathcal{N} $$ = 4 super-Yang-Mills with SU(1, 1) symmetry

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Stefano Baiguera ◽  
Troels Harmark ◽  
Nico Wintergerst
Keyword(s):  
Classical Limit ◽  
Particle Number ◽  
Matrix Theory ◽  
Companion Paper ◽  
Positive Definite ◽  
Normal Ordering ◽  
Yang Mills ◽  
Three Sphere ◽  
Dilatation Operator ◽  
Definite Expressions

Abstract We consider limits of $$ \mathcal{N} $$ N = 4 super Yang-Mills (SYM) theory that approach BPS bounds and for which an SU(1,1) structure is preserved. The resulting near-BPS theories become non-relativistic, with a U(1) symmetry emerging in the limit that implies the conservation of particle number. They are obtained by reducing $$ \mathcal{N} $$ N = 4 SYM on a three-sphere and subsequently integrating out fields that become non-dynamical as the bounds are approached. Upon quantization, and taking into account normal-ordering, they are consistent with taking the appropriate limits of the dilatation operator directly, thereby corresponding to Spin Matrix theories, found previously in the literature. In the particular case of the SU(1,1—1) near-BPS/Spin Matrix theory, we find a superfield formulation that applies to the full interacting theory. Moreover, for all the theories we find tantalizingly simple semi-local formulations as theories living on a circle. Finally, we find positive-definite expressions for the interactions in the classical limit for all the theories, which can be used to explore their strong coupling limits. This paper will have a companion paper in which we explore BPS bounds for which a SU(2,1) structure is preserved.

THE CONFINEMENT MECHANISM IN YANG–MILLS THEORY?

1999 ◽  
Vol 14 (06) ◽  
pp. 447-457 ◽  
Author(s):  
JOSE A. MAGPANTAY
Keyword(s):  
Gluon Propagator ◽  
Statistical Treatment ◽  
Gauge Condition ◽  
Classical Solutions ◽  
Spherically Symmetric ◽  
Yang Mills ◽  
Effective Dynamics ◽  
Gauge Fixing ◽  
Parallel Surfaces ◽  
Nonlinear Gauge

Using the recently proposed nonlinear gauge condition [Formula: see text] we show the area law behavior of the Wilson loop and the linear dependence of the instantaneous gluon propagator. The field configurations responsible for confinement are those in the nonlinear sector of the gauge-fixing condition (the linear sector being the Coulomb gauge). The nonlinear sector is actually composed of "Gribov horizons" on the parallel surfaces ∂ · Aa=fa≠0. In this sector, the gauge field [Formula: see text] can be expressed in terms of fa and a new vector field [Formula: see text]. The effective dynamics of fa suggests nonperturbative effects. This was confirmed by showing that all spherically symmetric (in 4-D Euclidean) fa(x) are classical solutions and averaging these solutions using a Gaussian distribution (thereby treating these fields as random) lead to confinement. In essence the confinement mechanism is not quantum mechanical in nature but simply a statistical treatment of classical spherically symmetric fields on the "horizons" of ∂ · Aa=fa(x) surfaces.

Electroweak Bosons, Leptons and Han-Nambu Quarks in a Unified Spinor-Isospinor Preon Field Model

1986 ◽  
Vol 41 (12) ◽  
pp. 1399-1411
Author(s):  
H. Stumpf
Keyword(s):  
Shell Model ◽  
Bound States ◽  
First Generation ◽  
Composite Fermions ◽  
Energy Limit ◽  
Mapping Procedure ◽  
Effective Interactions ◽  
Yang Mills ◽  
Effective Dynamics ◽  
Left Handed

The model is defined by a selfregularizing nonlinear spinor-isospinor preon field equation and all observable (elementary and non-elementary) particles are assumed to be bound states o f the quantized preon field. In a series o f preceding papers this model was extensively studied. In particular for com posite electroweak bosons the Yang-Mills dynamics was derived as the effective dynamics o f these bosons. In this paper the first generation o f com posite leptons and com posite Han-Nam bu quarks is introduced and together with electroweak bosons, these particles are interpreted as “shell model” states o f the underlying preon field. The choice o f the shell model states is justified by deriving the effective fermion-boson coupling and demonstrating its equivalence with the phenom enological electroweak coupling terms o f the Weinberg-Salam model. The investigation is restricted to the left-handed parts o f the composite fermions. Color is revealed to be a hidden orbital angular momentum in the shell model and hypercharge follows from the effective coupling. The techniques o f deriving effective interactions is a “weak mapping” procedure and the calculations are done in the “low” energy limit.

scholarly journals Asymptotic dynamics on the worldline for spinning particles

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Domenico Bonocore
Keyword(s):  
Scattering Amplitudes ◽  
Gauge Boson ◽  
Classical Limit ◽  
Wilson Line ◽  
Background Field ◽  
Spinning Particle ◽  
Spinning Particles ◽  
Yang Mills ◽  
Asymptotic Dynamics ◽  
Gravity Theories

Abstract There has been a renewed interest in the description of dressed asymptotic states à la Faddeev-Kulish. In this regard, a worldline representation for asymptotic states dressed by radiation at subleading power in the soft expansion, known as the Generalized Wilson Line (GWL) in the literature, has been available for some time, and it recently found applications in the derivation of factorization theorems for scattering processes of phenomenological relevance. In this paper we revisit the derivation of the GWL in the light of the well-known supersymmetric wordline formalism for the relativistic spinning particle. In particular, we discuss the importance of wordline supersymmetry to understand the contribution of the soft background field to the asymptotic dynamics. We also provide a derivation of the GWL for the gluon case, which was not previously available in the literature, thus extending the exponentiation of next-to-soft gauge boson corrections to Yang-Mills theory. Finally, we comment about possible applications in the current research about asymptotic states in scattering amplitudes for gauge and gravity theories and their classical limit.

Construction of a translation-invariant U(N) damped noncommutative gauge model

2020 ◽  
Vol 35 (22) ◽  
pp. 2050118
Author(s):  
Ouahiba Toumi ◽  
Smain Kouadik
Keyword(s):  
Covariant Derivative ◽  
Torsion Tensor ◽  
Tree Level ◽  
Dirac Field ◽  
Translation Invariance ◽  
Group Model ◽  
Translation Invariant ◽  
Yang Mills ◽  
Interaction Term ◽  
Popov Ghost

We have built a noncommutative unitary gauge group model preserving translation invariance. It describes the interaction of the Dirac field with the gauge field. The interaction term is expanded as a power series resulting from the introduction of the inverse covariant derivative. The consistency of the model is sustained by the fact that the Ward identity holds at tree level. The pure Yang–Mills action, including the fixing term and the Faddeev–Popov ghost term were constructed. It is striking that the commutator of our covariant derivative contained the torsion tensor, in addition to the field strength from which the Yang–Mills action was built.

scholarly journals Glueball spectra from a matrix model of pure Yang–Mills theory

2018 ◽  
Vol 33 (13) ◽  
pp. 1850073 ◽  
Author(s):  
Nirmalendu Acharyya ◽  
A. P. Balachandran ◽  
Mahul Pandey ◽  
Sambuddha Sanyal ◽  
Sachindeo Vaidya
Keyword(s):  
Renormalization Group ◽  
Excellent Agreement ◽  
Matrix Model ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Yang Mills ◽  
Three Sphere ◽  
Simple Matrix

We present variational estimates for the low-lying energies of a simple matrix model that approximates SU(3) Yang–Mills theory on a three-sphere of radius R. By fixing the ground state energy, we obtain the (integrated) renormalization group (RG) equation for the Yang–Mills coupling g as a function of R. This RG equation allows to estimate the mass of other glueball states, which we find to be in excellent agreement with lattice simulations.

scholarly journals CHAPLINE–MANTON INTERACTION VERTICES AND HAMILTONIAN BRST COHOMOLOGY

2000 ◽  
Vol 15 (06) ◽  
pp. 893-903 ◽  
Author(s):  
C. BIZDADEA ◽  
L. SALIU ◽  
S. O. SALIU
Keyword(s):  
Gauge Fields ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Brst Charge ◽  
Brst Cohomology ◽  
Interaction Term ◽  
Chern Simons

Consistent interactions between Yang–Mills gauge fields and an Abelian two-form are investigated by using a Hamiltonian cohomological procedure. It is shown that the deformation of the BRST charge and the BRST-invariant Hamiltonian of the uncoupled model generates the Yang–Mills Chern–Simons interaction term. The resulting interactions deform both the gauge transformations and their algebra, but not the reducibility relations.

scholarly journals Invariants of four-manifolds with flows via cohomological field theory

2014 ◽  
Author(s):  
Hugo Garcia-Compeân ◽  
Roberto Santos-Silva ◽  
Alberto Verjovsky
Keyword(s):  
Field Theory ◽  
Probability Measure ◽  
Vector Fields ◽  
Invariant Probability Measure ◽  
Yang Mills ◽  
Higher Dimensional ◽  
Coupling Dynamics ◽  
Four Manifolds ◽  
Cohomological Field Theory ◽  
Asymptotic Cycles

This chapter argues that the Jones–Witten invariants can be generalized for smooth, nonsingular vector fields with invariant probability measure on three-manifolds, thus giving rise to new invariants of dynamical systems. After a short survey of cohomological field theory for Yang–Mills fields, Donaldson–Witten invariants are generalized to four-dimensional manifolds with non-singular smooth flows generated by homologically non-trivial p-vector fields. The chapter studies the case of Kähler manifolds by using the Witten's consideration of the strong coupling dynamics of N = 1 supersymmetric Yang–Mills theories. The whole construction is performed by implementing the notion of higher-dimensional asymptotic cycles. In the process Seiberg–Witten invariants are also described within this context. Finally, the chapter gives an interpretation of the asymptotic observables of four-manifolds in the context of string theory with flows.

DEFORMATIONS OF ALGEBRAS OF OBSERVABLES AND THE CLASSICAL LIMIT OF QUANTUM MECHANICS

1993 ◽  
Vol 05 (04) ◽  
pp. 775-806 ◽  
Author(s):  
N. P. LANDSMAN
Keyword(s):  
Classical Limit ◽  
Wigner Distribution ◽  
Distribution Functions ◽  
Poisson Manifolds ◽  
Ideal Space ◽  
Convergence Criterion ◽  
Yang Mills ◽  
C Algebra ◽  
Classical Counterpart ◽  
Deformations Of Algebras

The quantum algebra of observables of a particle moving on a homogeneous configuration space Q = G/H, the transformation group C*-algebra C* (G, G/H), is deformed into its classical counterpart C0 ((T*G)/H). The Poisson structure of the latter is obtained as the classical limit of the quantum commutator. The superselection sectors of both algebras describe the particle moving in an external Yang–Mills field. Analytical aspects of deformation theory, such as the nature of the limit ħ → 0, are studied in detail. A physically motivated convergence criterion in ħ is introduced. The Weyl–Moyal quantization formalism, and the associated use of Wigner distribution functions, is generalized from flat phase spaces T*ℝn to Poisson manifolds of the form (T*G)/H. The classical limit of quantum states as well as of superselection sectors is investigated. The former is handled by introducing the notion of a classical germ, generalizing coherent states. The latter is analyzed by studying the Jacobson topology on the primitive ideal space of a certain continuous field of C*-algebras, constructed from the classical and the quantum algebras of observables. The symplectic leaves of (T*G)/H are confirmed to be the correct classical analogue of the quantum superselection sectors of C*(G, G/H).

ALGEBRAIC SOLUTIONS OF YANG-MILLS-HIGGS EQUATIONS

1995 ◽  
Vol 10 (11) ◽  
pp. 925-930
Author(s):  
Y. BRIHAYE ◽  
STEFAN GILLER ◽  
PIOTR KOSINSKI
Keyword(s):  
Numerical Analysis ◽  
Irreducible Representation ◽  
Differential Equations ◽  
Gauge Group ◽  
Higgs Field ◽  
Regular Solutions ◽  
Yang Mills ◽  
Spatially Homogeneous ◽  
Classical Fields ◽  
Algebraic Solutions

We study the SU(2) Yang-Mills-Higgs equations with the Higgs field in an arbitrary irreducible representation of the gauge group. We propose an ansatz for the classical fields which, solving the classical equations, leads to systems of coupled differential equations. Several regular solutions of these systems can be constructed explicitly; they are spatially homogeneous and periodic in time. The connection between our solutions and a recent numerical analysis of sphaleron (monopole)’s evolution is discussed.

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