Nontrivial Vacuum Structure Research Articles

Adler-Bell-Jackiw anomaly in the 3-brane scenario

We investigate the ABJ anomaly in the framework of an effective field theory for a 3-brane scenario and show that the contribution from induced gravity on the brane depends on both the topological structure of the bulk space-time and the embedding of the brane in the bulk. This fact implies the existence of a nontrivial vacuum structure of bulk quantum gravity. Furthermore, we argue that this axial gravitational anomaly may not necessarily be canceled by choosing the matter content on the brane since it could be considered as a possible effect from bulk quantum gravity.

SMALL x DIVERGENCES IN THE SIMILARITY RG APPROACH TO LF QCD

We study small x divergences in boost invariant similarity renormalization group approach to light-front QCD in a heavy quark–antiquark state. With the boost invariance maintained, the infrared divergences do not cancel out in the physical states, contrary to previous studies where boost invariance was violated by a choice of a renormalization scale. This may be an indication that the zero mode, or nontrivial light-cone vacuum structure, might be important for recovering full Lorentz invariance.

Domain walls in QCD

QCD was shown to have a nontrivial vacuum structure due to the topology of the theta = theta+2*pi*n parameter. As a result of this nontrivial topology, in the large N_c limit, quasi-stable QCD domain walls appear, characterized by a transition in the singlet eta' field. We discuss the physics of these QCD domain walls as well as related axion domain walls and we present a new type of axion wall which also contains an eta' transition. We argue that these domain walls are topologically stable in the limit N_c->infinity and classically stable for large but finite N_c, however, they can decay through a tunneling process. We argue that the qualitative features of these QCD domain walls -- namely their classical stability -- persist to the realistic case of N_c=3 and that it is at least possible that their lifetime could be macroscopically large. If it is, then QCD domain walls could play an important role in the evolution of early universe and may be detectable in energetic collisions such as those at the Relativistic Heavy Ion Collider (RHIC).

Multiple vacua in two-dimensional Yang-Mills theory

Two-dimensional SU( N) Yang-Mills theory is endowed with a non-trivial vacuum structure (κ-sectors). The presence of κ-sectors modifies the energy spectrum of the theory and its instanton content, the (Euclidean) spacetime being compactified on a sphere. For the exact solution, in the limit in which the sphere is decompactified, a κ-sector cane mimicked by the presence of κ-fundamental charges at ∞, according to a Witten's suggestion. However, this property neither holds before decompactification nor for the genuine perturbative solution which corresponds to the zero-instanton contribution on the sphere.

Wilson Loops in the Adjoint Representation and Multiple Vacua in Two-Dimensional Yang–Mills Theory

QCD2 with fermions in the adjoint representation is invariant under SU(N)/ZN and thereby is endowed with a nontrivial vacuum structure (k-sectors). The static potential between adjoint charges, in the limit of infinite mass, can be therefore obtained by computing Wilson loops in the pure Yang–Mills theory with the same nontrivial structure. When the (Euclidean) space-time is compacted on a sphere S2, Wilson loops can be exactly expressed in terms of an infinite series of topological excitations (instantons). The presence of k-sectors modifies the energy spectrum of the theory and its instanton content. For the exact solution, in the limit in which the sphere is decompacted, a k-sector can be mimicked by the presence of k-fundamental charges at ∞, according to Witten's suggestion. However, this property does not hold before decompaction or for the genuine perturbative solution which corresponds to the zero-instanton contribution on S2.

Much ado about nothing: Vacuum and renormalization in the light-front framework

In the light-front (LF) formulation of quantum field theory, nontrivial vacuum structure can appear only in zero-modes. Integrating out zero-mode degrees of freedom leads to an effective LF Hamiltonian, which acts only on nonzero-modes and thus has a trivial vacuum, but is nevertheless equivalent to the Hamiltonian in normal coordinates (with nontrivial vacuum) since the nontrivial vacuum structure enters through the coefficients of the eff. LF Hamiltonian.

A New Mechanism of Spontaneous SUSY Breaking

We propose a new mechanism of spontaneous supersymmetry breaking. The existence of extra dimensions with nontrivial topology plays an important role. We investigate new features resulted from the mechanism in two simple supersymmetric Z_2 and U(1) models. One of remarkable features is that there exists a phase in which the translational invariance for the compactified directions is broken spontaneously, accompanying the breakdown of the supersymmetry. The mass spectrum of the models appeared in reduced dimensions is a full of variety, reflecting the highly nontrivial vacuum structure of the models. The Nambu-Goldstone bosons (fermions) associated with breakdown of symmetries are found in the mass spectrum. Our mechanism also yields quite different vacuum structures if models have different global symmetries.

FURTHER COMMENTS ON A VANISHING SINGLET AXIAL VECTOR CHARGE

The recent suggestion of a vanishing flavor-singlet axial-charge of nucleon due to a nontrivial vacuum structure is further amplified. A perturbative QCD discussion, applicable for the heavy quark contributions, relates it to the physics of the decoupling theorem. It is also shown that [Formula: see text] leads to a negative η′-meson-quark coupling, which has been found to be compatible with the chiral quark model phenomenology.

Vacuum Structure, Chiral Symmetry Breaking and Radiative Decays of Vector Mesons

The radiative decay widths of vector mesons were considered in a model involving chiral symmetry breaking through a nontrivial vacuum structure where the pion and kaon being treating consistently yield the constituent quark wave functions, approximately the same as that obtained from the gap equations and thus in a way determine the constituent quark field operators. Like its earlier success to some low energy hadronic phenomena, here also the model calculations of radiative decay widths of mesons are in reasonable agreements with other theoretical estimations as well as experimental measurements.

VACUUM STRUCTURE, CHIRAL SYMMETRY BREAKING AND STATIC PROPERTIES OF OCTET AND DECUPLET BARYONS

The static properties of the octet and decuplet baryons are considered within the framework of a quark model of hadrons where the chiral symmetry is broken dynamically through a nontrivial vacuum structure. The pion and kaon being treated consistently within the model yield to the constituent quark wave function approximately same as the wave functions from the gap equations and thus determine consequently the constituent quark field operators. The model was successfully used earlier to study some hadronic phenomena and here also it estimates the static properties of the octet and decuplet baryons in a unified manner, in reasonable agreement with the available measurements. The only parameter of the model is the harmonic oscillator radius for the baryons. The method is nonperturbative with respect to the equal time algebra for the constituent quark field operators.

VACUUM STRUCTURE, CHIRAL SYMMETRY BREAKING AND RADIATIVE DECAYS OF BARYONS

Radiative decays of baryons are considered in a model involving chiral symmetry breaking through a nontrivial vacuum structure. Pion and kaon, being treated consistently within the model, yield to the constituent quark wave functions approximately in the same way as the wave functions from the gap equations, and thus in a way determine the constituent quark field operators. The model had a reasonable success earlier in its applications to some low energy hadronic phenomena, and here also estimates radiative decay widths of baryons in reasonable agreement with other theoretical calculations as well as the available experimental measurements.

Light-front QCD 1+1 coupled to chiral adjoint fermions

We consider SU( N) gauge theory in 1+1 dimensions coupled to chiral fermions in the adjoint representation of the gauge group. With all fields in the adjoint representation the gauge group is actually SU(N) Z N , which possesses nontrivial topology. In particular, there are N distinct topological sectors and the physical vacuum state has a structure analogous to a θ vacuum. We show how this feature is realized in light-front quantization for the case N = 2, using discretization as an infrared regulator. In the discretized form of the theory the nontrivial vacuum structure is associated with the zero momentum mode of the gauge field A +. We find exact expressions for the degenerate vacuum states and the analog of the θ vacuum. The model also possesses a condensate which we calculate. We discuss the difference between this chiral light-front theory and the theories that have previously been considered in the equal-time approach.

Nontrivial vacua in higher-derivative gravitation.

A discussion of an extended class of higher-derivative classical theories of gravity is presented. A procedure is given for exhibiting the new propagating degrees of freedom, at the full non-linear level, by transforming the higher-derivative action to a canonical second-order form. For general fourth-order theories, described by actions which are general functions of the scalar curvature, the Ricci tensor and the full Riemann tensor, it is shown that the higher-derivative theories may have multiple stable vacua. The vacua are shown to be, in general, non-trivial, corresponding to deSitter or anti-deSitter solutions of the original theory. It is also shown that around any vacuum the elementary excitations remain the massless graviton, a massive scalar field and a massive ghost-like spin-two field. The analysis is extended to actions which are arbitrary functions of terms of the form $\nabla^{2k}R$, and it is shown that such theories also have a non-trivial vacuum structure.

Light-front view of the axial anomaly.

Motivated by an apparent puzzle of the light-front vacua incompatible with the axial anomaly, we have considered the two-dimensional massless Schwinger model for an arbitrary interpolating angle of the quantization surface. By examining spectral deformation of the Dirac sea under an external electric field semiclassically, we have found that the axial anomaly is quantization angle independent. This indicates an intricate nontrivial vacuum structure present even in the light-front limit.

Vacuum structure, chiral symmetry breaking and electric dipole moment of neutron

Considering a CP-violating QCD interaction, the electric dipole moment of neutron (EDMN) is estimated in a quark model of light mesons with a dynamical breaking of chiral symmetry through a non-trivial vacuum structure. Pion and kaon, being treated consistently within the model, yield to the constituent quark wave functions as well as the dynamical quark masses and thus determine the constituent quark field operators with respect to light quark flavors. Using the translationally invariant hadronic states and these constituent quark field operators, the EDMN estimated here remains well within the recent experimental bound ofD n<11 × 10−26 e-cm with the CP-violation parameter |ϑ|=10−8, which in fact accounts for a strong CP-violation.

Angular distributions of Drell-Yan lepton pairs at the Fermilab Tevatron: Order alpha s2 corrections and Monte Carlo studies.

We investigate the angular distribution of the lepton pair in the process $p \bar{p} \rightarrow \gamma^{\ast} + X \rightarrow \ell^+\ell^- + X$, where the virtual photon is produced at high transverse momentum. The angular distribution of the leptons is very sensitive to possible nonperturbative effects, such as a nontrivial vacuum structure of QCD, and offers a good chance to test such effects. We present complete ${\cal O}(\alpha_s^2)$ calculations of the decay lepton distributions in the lepton pair rest frame. An order ${\cal O}(\alpha_s)$ Monte Carlo study of the lepton angular distributions, with acceptance cuts and energy resolution smearing applied to the leptons, is also presented.

Gluon condensates, quark matter equation of state and quark stars

We consider here quark matter equation of state including strange quarks and taking into account a nontrivial vacuum structure for QCD with gluon condensates. The parameters of condendsate function are determined from minimisation of the thermodynamic potential. The scale parameter of the gluon condensates is fixed from the SVZ parameter in the context of QCD sum rules at zero temperature and zero baryon density. The equation of state for strange matter at zero temperature as derived is used to study quark star structure using Tolman Oppenheimer Volkoff equations. Stable solutions for quark stars are obtained with a large Chandrasekhar limit as 3.2 $M_\odot$ and radii around 17 kms.

Chiral symmetry breaking and the pion wave function.

We consider here chiral symmetry breaking through nontrivial vacuum structure with quark antiquark condensates. We then relate the condensate function to the wave function of pion as a Goldstone mode. This simultaneously yields the pion also as a quark antiquark bound state as a localised zero mode in vacuum. We illustrate the above with Nambu Jona-Lasinio model to calculate different pionic properties in terms of the vacuum structure for breaking of exact or approximate chiral symmetry, as well as the condensate fluctuations giving rise to $\sigma$ mesons.

Spin effects and factorization in the Drell-Yan process

We discuss the idea that the nontrivial vacuum structure in QCD may induce transverse momentum and spin correlations of the initial state partons in Drell-Yan type reactions, i.e. in hadron-hadron collisions with production of a vector bosonV=γ*,Z,W±. Transverse momentum correlations are found to have practically no effect on observable quantities, but spin correlations have drastic consequences for the polarization density matrices of theV-bosons. We therefore propose measurements of theV polarization as a good test for the basic factorization hypothesis which, so far, has been assumed to be valid in numerous applications of the naive and QCD-improved parton model. We compare our ansatz for a spin correlation violating factorization with data from the NA 10 collaboration onγ* production inπ−N scattering. We find that the data give an indication of spin correlations of the partons in the initial state to be present.

Vacuum structures in Hamiltonian light-front dynamics

Hamiltonian light-front dynamics of quantum fields may provide a useful approach to systematic nonperturbative approximations to quantum field theories. We investigate inequivalent Hilbert-space representations of the light-front field algebra in which the stability group of the light front is implemented by unitary transformations. The Hilbert space representation of states is generated by the operator algebra from the vacuum state. There is a large class of vacuum states besides the Fock vacuum which meet all the invariance requirements. The light-front Hamiltonian must annihilate the vacuum and have a positive spectrum. We exhibit relations of the Hamiltonian to the nontrivial vacuum structure.