An admissible level $$\widehat{\mathfrak {osp}} \left( 1 \big \vert 2 \right) $$-model: modular transformations and the Verlinde formula

The modular properties of the simple vertex operator superalgebra associated with the affine Kac–Moody superalgebra \(\widehat{{\mathfrak {osp}}} (1|2)\) at level \(-\frac{5}{4}\) are investigated. After classifying the relaxed highest-weight modules over this vertex operator superalgebra, the characters and supercharacters of the simple weight modules are computed and their modular transforms are determined. This leads to a complete list of the Grothendieck fusion rules by way of a continuous superalgebraic analog of the Verlinde formula. All Grothendieck fusion coefficients are observed to be non-negative integers. These results indicate that the extension to general admissible levels will follow using the same methodology once the classification of relaxed highest-weight modules is completed.     

Lagrangians for conformal gauge gravity and conformal simple supergravity

The connection, curvature, and Lagrangian for a conformal gauge gravity are obtained. A set of generators of the conformal simple supergroup is given, the commutation and anticommutation relations for the superalgebra are calculated, and a Lagrangian of the simple supergravity is established.     

\hat sl(2) \oplus \hat sl(2)/\hat sl(2) coset theory is a Hamiltonian reduction of the \hat D(2|1;\alpha ) superalgebra

It is shown that $\hat sl(2)_{k_1 } \oplus \hat sl(2)_{k_2 } /\hat sl(2)_{k_1 + k_2 } $ coset theory is a quantum Hamiltonian reduction of the exceptional affine Lie superalgebra $\hat D(2|1;\alpha )$ . In addition, the W algebra of this theory is the commutant of the U _q D(2|1;a) quantum group.     

Second order Hamiltonian formalism and constraints algebra for non-polynomial supergravities

The second order Hamiltonian formalism for a non-polynomial N = 1D = 10 supergravity coupled to super Yang-Mills theory is developed. This is done by starting from the first order canoncial covariant formalism on group manifold. The Hamiltonian, generator of time evolution, is found as a functional of the first class constraints of this coupled system. These contraints close the constraint algebra and they are the generators of all the Hamiltonian gauge symmetries.     

Infinite symmetry algebras of extended supergravity theories

When extended supergravity theories with noncompact symmetry groups are written in a physical gauge, the noncompact symmetries join with the supersymmetries to generate an infinite-dimensional algebra. The details are worked out explicitly for a two-dimensional theory with an SU(1, 1) internal symmetry. Our analysis confirms the observation of Ellis et al. that the infinite rigid superalgebra should be obtained from the finite-dimensional local superalgebra by replacing scalar fields with their asymptotic values at infinity. The infinite algebra is described by extending the super-Poincaré generators to functions on the coset space defined by the scalar fields at infinity. While mathematically nontrivial, this result is, in a certain sense, trivial from a physical point of view.     

Comments on Yang-Mills thermodynamics: The Hagedorn spectrum and the gluon gas pictures for a generic gauge algebra

We discuss the dependence of pure Yang-Mills equation of state on the choice of gauge algebra. In the confined phase, we generalize to an arbitrary simple gauge algebra Meyer?s proposal of modeling the Yang-Mills matter by an ideal glueball gas in which the high-lying glueball spectrum is approximated by a Hagedorn spectrum of closed-bosonic-string type. Such a formalism is undefined above the Hagedorn temperature, corresponding to the phase transition toward a deconfined state of matter in which gluons are the relevant degrees of freedom. Under the assumption that the renormalization scale of the running coupling is gauge-algebra independent, we discuss about how the behavior of thermodynamical quantities such as the trace anomaly should depend on the gauge algebra in both the confined and deconfined phase. The obtained results compare favorably with recent and accurate lattice data in the su(3) case and support the idea that the more the gauge algebra has generators, the more the phase transition is of first-order type.     

Inönü–Wigner contraction and $$$$ supergravity

We present a generalization of the standard Inönü–Wigner contraction by rescaling not only the generators of a Lie superalgebra but also the arbitrary constants appearing in the components of the invariant tensor. The procedure presented here allows one to obtain explicitly the Chern–Simons supergravity action of a contracted superalgebra. In particular we show that the Poincaré limit can be performed to a \(D=2+1\) \(\left( p,q\right) \) AdS Chern–Simons supergravity in presence of the exotic form. We also construct a new three-dimensional \(\left( 2,0\right) \) Maxwell Chern–Simons supergravity theory as a particular limit of \(\left( 2,0\right) \) AdS–Lorentz supergravity theory. The generalization for \(\mathcal {N}=p+q\) gravitinos is also considered.     

Fuzzy Kaluza-Klein induced M2?s from a single M5

We propose an algorithmic procedure of obtaining multiple M2 brane dynamics starting with an action of a single M5 brane. The procedure involves a novel Kaluza-Klein reduction. First, the M5 brane action is truncated to keep a few leading terms in the derivative expansion. Then 3+3 splitting of dimensions is carried out. With expansion in terms of the S² spherical harmonics, the fields are associated with SU(N) (or its infinite extension) gauge algebra. We present an elaborate reduction procedure that leads to ABJM theory when the fuzzy spherical harmonics are replaced by SU(N) gauge generators.     

Gauge theories on the $\kappa$-Minkowski spacetime

This study of gauge field theories on -deformed Minkowski spacetime extends previous work on field theories on this example of a non-commutative spacetime. We construct deformed gauge theories for arbitrary compact Lie groups using the concept of enveloping algebra-valued gauge transformations and the Seiberg-Witten formalism. Derivative-valued gauge fields lead to field strength tensors as the sum of curvature- and torsion-like terms. We construct the Lagrangians explicitly to first order in the deformation parameter. This is the first example of a gauge theory that possesses a deformed Lorentz covariance.Received: 17 December 2003, Revised: 6 May 2004, Published online: 23 June 2004     

Coupled Channel Approach to S-Wave Hyperonic Interactions from Lattice QCD

We studied hyperonic interactions by lattice QCD simulation throuth coupled channel formalism. Our approach to baryon-baryon interactions is deriving a potential from inverting Schrödinger equation using Nambu-Bethe-Salpeter (NBS) wave function simulated on the lattice. The quark mass dependences and flavor SU(3) breaking effects of the potential matrix are also discussed by comparing with results of gauge configurations with different quark masses. Our numerical results are obtained from three ensembles of 2+1 flavor QCD gauge configurations, which corresponds to m _π ~ 700, 570 and 410 MeV, provided by the PACS-CS Collaboration.     

On free 4D Abelian 2-form and anomalous 2D Abelian 1-form gauge theories

We demonstrate a few striking similarities and some glaring differences between (i) the free four- (3+1)-dimensional (4D) Abelian 2-form gauge theory, and (ii) the anomalous two- (1+1)-dimensional (2D) Abelian 1-form gauge theory, within the framework of Becchi–Rouet–Stora–Tyutin (BRST) formalism. We demonstrate that the Lagrangian densities of the above two theories transform in a similar fashion under a set of symmetry transformations even though they are endowed with a drastically different variety of constraint structures. With the help of our understanding of the 4D Abelian 2-form gauge theory, we prove that the gauge-invariant version of the anomalous 2D Abelian 1-form gauge theory is a new field-theoretic model for the Hodge theory where all the de Rham cohomological operators of differential geometry find their physical realizations in the language of proper symmetry transformations. The corresponding conserved charges obey an algebra that is reminiscent of the algebra of the cohomological operators. We briefly comment on the consistency of the 2D anomalous 1-form gauge theory in the language of restrictions on the harmonic state of the (anti-) BRST and (anti-) co-BRST invariant version of the above 2D theory.     

Chiral anomaly in a spherical spacetime

We evaluate the chiral anomaly for a gauge theory on Sⁿ in the hyperspherical O(n + 1) covariant formalism using the method of Fujikawa and comment on related aspects.     

Dimensional regularisation and instantons

Dimensional regularisation is applied to the calculation of the quantum corrections to the instanton tunnelling amplitude in an SU(2) gauge theory. The principal feature is the introduction of an n-dimensional field configuration (a “quasi-instanton”), which generalises the O(5) invariance of the instanton and allows a coordinatisation of the function space of fields in its neighbourhood. This enables the functional integral measure to be factorised, with integrations over the translation and dilatation degrees of freedom being extracted. It is shown that a conformally invariant definition of orthogonality must be used in relation to the zero-mode eigenfunctions of the small oscillations expansion, irrespective of regularisation. An O(n + 1) covariant formalism is employed. An unconventional choice of gauge fixing term, which is not a perfect square, is made and is shown to allow the important freedom of calculating in a gauge specified by an arbitrary parameter α.     

Angular asymmetries in the reactions \vec pp \to d\pi ^ + \eta and \vec pn \to d\pi ^0 \eta and a 0-f 0 mixing

The reactions pp → dπ ⁺ η and pn → dπ ⁰ η are of special interest for investigating the a ₀(980) (J ^P=0⁺) resonance in the process NN → da ₀ → dπη. We study some aspects of those reactions within a general formalism and also in a concrete phenomenological model. In particular, it is shown that the presence of nonresonant (i.e., without excitation of the a ₀ resonance) contributions to these reactions yields nonvanishing values for specific polarization observables, i.e., to effects like those generated by a ₀ ⁰ -f ₀ mixing. An experimental determination of these observables for the reaction $\vec pp \to d\pi ^ + \eta $ would provide concrete information on the magnitude of those nonresonant contributions to πη production. We also discuss the possibility of extracting information about a ₀ ⁰ -f ₀ mixing from the reaction $\vec pn \to d\pi ^0 \eta $ with a polarized proton beam.     

Differential geometry of the quantum supergroupGL q (1/1)

We construct a right-invariant differential calculus on the quantum supergroupGL _q (1/1) and we show that the quantum Lie algebra generators satisfy the undeformed Lie superalgebra. The deformation becomes apparent when one studies the comultiplication for these generators. We bring the algebra into the standard Drinfeld-Jimbo form by performing a suitable change of variables, and we check the consistency of the map with the induced comultiplication.     

Abelian 3-form gauge theory: Superfield approach

We discuss a D-dimensional Abelian 3-form gauge theory within the framework of Bonora-Tonin’s superfield formalism and derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for this theory. To pay our homage to Victor I. Ogievetsky (1928–1996), who was one of the inventors of Abelian 2-form (antisymmetric tensor) gauge field, we go a step further and discuss the above D-dimensional Abelian 3-form gauge theory within the framework of BRST formalism and establish that the existence of the (anti-)BRST invariant Curci-Ferrari (CF) type of restrictions is the hallmark of any arbitrary p-form gauge theory (discussed within the framework of BRST formalism).     

Uncertainties from fermion masses ine^ + e^ - \to v\bar v\gamma

In the reaction \(e^ + e^ - \to v\bar v\gamma \) , the influence of the unknown masses of heavy fermions for three and four fermion generations is studied, which arises via virtual 1-loop corrections in the framework of the standard model. These masses are the top quark massm _t and in the case of 4 generations the lepton massm t, wherel ^? is theSU(2) partner of the fourth generation neutrino. Increasing the fermion masses from 50 GeV to 250 GeV, the maximum of the total cross section is found to decrease by a few percent.     

Equations of motion of interacting massless fields of all spins as a free differential algebra

It is argued that the equations of motion of interacting massless fields of all spins s=0,1,…,∞ can naturally be formulated in terms of a free differential algebra (FDA) constructed from one-forms and zero-forms that belong both to the adjoint representation of the infinite-dimensional superalgebra of higher spins and auxiliary fields proposed previously. This FDA is found explicitly in the first non-trivial order in the zero-forms. Various properties of the proposed FDA are discussed including the ways for incorporating internal (Yang-Mills) gauge symmetries via associative algebras.     

From the Hamiltonian to the Lagrangean formalism for 1-reducible theories. The Freedman-Townsend model

The paper presents a possible path to the sp(3) BRST Lagrangean formalism for a 1-reducible gauge field theory starting from the Hamiltonian one. This appears to be not at all a trivial attempt and will allow explanation of the structure of generators and the form of the master equations in the Lagrangean sp(3) theories. The Freedman-Townsend model, for which a Lagrangean (covariant) sp(3) theory is important, is presented.     

Gauge independence of the effective potential revisited

We apply the formalism of extended BRS symmetry to the investigation of the gauge dependence of the effective potential in a spontaneously symmetry broken gauge theory. This formalism, which includes a set of Grassmann parameters defined as the BRS variations of the gauge-fixing parameters, allows us to derive in a quick and unambiguous way the related Nielsen identities, which express the physical gauge independence, in a class of generalized 't Hooft gauges, of the effective potential. We show in particular that the validity of the Nielsen identities does not require any constraint on the gauge-fixing parameters, contrary to some claims found in the literature. We use the method of algebraic renormalization, which leads to results independent of the particular renormalization scheme used.