External leg amputation in conformal invariant three-point function

Amputation of external legs is carried out explicitly for the conformal invariant three-point function involving two spinors and one vector field. Our results are consistent with the general result that amputing an external leg in a conformal invariant Green function replaces a field by its conformal partner in the Green function. A new star-triangle relation, involving two spinors and one vector field, is derived and used for the calculation.Comment: 16 pages; last paragraph added in Sec. 10, presentation improved, to appear in Eur. Phys. J.

Higher spins dynamics in the closed string theory

The general $\sigma$-model-type string action including both massless and massive higher spins background fields is suggested. Field equations for background fields are followed from the requirement of quantum Weyl invariance. It is shown that renormalization of the theory can be produced level by level. The detailed consideration of background fields structure and corresponding fields equations is given for the first massive level of the closed bosonic string.Comment: 11 pages, report TSU/QFTD-36/9

Generalized Conformal Symmetry in D-Brane Matrix Models

We study in detail the extension of the generalized conformal symmetry proposed previously for D-particles to the case of supersymmetric Yang-Mills matrix models of Dp-branes for arbitrary p. It is demonstrated that such a symmetry indeed exists both in the Yang-Mills theory and in the corresponding supergravity backgrounds produced by Dp-branes. On the Yang-Mills side, we derive the field-dependent special conformal transformations for the collective coordinates of Dp-branes in the one-loop approximation, and show that they coincide with the transformations on the supergravity side. These transformations are powerful in restricting the forms of the effective actions of probe D-branes in the fixed backgrounds of source D-branes. Furthermore, our formalism enables us to extend the concept of (generalized) conformal symmetry to arbitrary configurations of D-branes, which can still be used to restrict the dynamics of D-branes. For such general configurations, however, it cannot be endowed a simple classical space-time interpretation at least in the static gauge adopted in the present formulation of D-branes.Comment: 26 pages, no figure

On "Schwinger Mechanism for Gluon Pair Production in the Presence of Arbitrary Time Dependent Chromo-Electric Field"

Recently the paper "Schwinger Mechanism for Gluon Pair Production in the Presence of Arbitrary Time Dependent Chromo-Electric Field" by G. C. Nayak was published [Eur. Phys. J. C 59, 715 (2009); arXiv:0708.2430]. Its aim is to obtain an exact expression for the probability of non-perturbative gluon pair production per unit time per unit volume and per unit transverse momentum in an arbitrary time-dependent chromo-electric background field. We believe that the obtained expression is open to question. We demonstrate its inconsistency on some well-known examples. We think that this is a consequence of using the so-called "shift theorem" [arXiv:hep-th/0609192] in deriving the expression for the probability. We make some critical comments on the theorem and its applicability to the problem in question.Comment: 4 page

Equivalence of partition functions for noncommutative U(1) gauge theory and its dual in phase space

Equivalence of partition functions for U(1) gauge theory and its dual in appropriate phase spaces is established in terms of constrained hamiltonian formalism of their parent action. Relations between the electric--magnetic duality transformation and the (S) duality transformation which inverts the strong coupling domains to the weak coupling domains of noncommutative U(1) gauge theory are discussed in terms of the lagrangian and the hamiltonian densities. The approach presented for the commutative case is utilized to demonstrate that noncommutative U(1) gauge theory and its dual possess the same partition function in their phase spaces at the first order in the noncommutativity parameter \theta .Comment: 15 pages. Version to appear in JHE

Geometric Second Order Field Equations for General Tensor Gauge Fields

Higher spin tensor gauge fields have natural gauge-invariant field equations written in terms of generalised curvatures, but these are typically of higher than second order in derivatives. We construct geometric second order field equations and actions for general higher spin boson fields, and first order ones for fermions, which are non-local but which become local on gauge-fixing, or on introducing auxiliary fields. This generalises the results of Francia and Sagnotti to all representations of the Lorentz group.Comment: 34 pages, LaTeX. Reference adde

Volkov-Akulov theory and D-branes

The action of supersymmetric Born-Infeld theory (D-9-brane in a Lorentz covariant static gauge) has a geometric form of the Volkov-Akulov-type. The first non-linearly realized supersymmetry can be made manifest, the second world-volume supersymmetry is not manifest. We also study the analogous 2 supersymmetries of the quadratic action of the covariantly quantized D-0-brane. We show that the Hamiltonian and the BRST operator are build from these two supersymmetry generators.Comment: 10 pages, Latex, Contribution to Supersymmetry and Quantum Field Theory, International Seminar dedicated to the memory of D. V. Volkov (Kharkov, 1997

The Topological Unitarity Identities in Chern-Simons Theories

Starting from the generating functional of the theory of relativistic spinors in 2+1 dimensions interacting through the pure Chern-Simons gauge field, the S-matrix is constructed and seen to be formally the same as that of spinor quantum electrodynamics in 2+1 dimensions with Feynman diagrams having external photon lines excluded, and with the propagator of the topological Chern-Simons photon substituted for the Maxwell photon propagator. It is shown that the absence of real topological photons in the complete set of vector states of the total Hilbert space leads in a given order of perturbation theory to topological unitarity identities that demand the vanishing of the gauge-invariant sum of the imaginary parts of Feynman diagrams with a given number of internal on-shell free topological photon lines. It is also shown, that these identities can be derived outside the framework of perturbation theory. The identities are verified explicitly for the scattering of a fermion-antifermion pair in one-loop order.Comment: 13 pages, LaTex file, one figure (not included

Ramond sector of superconformal algebras via quantum reduction

Quantum hamiltonian reduction of affine superalgebras is studied in the twisted case. The Ramond sector of "minimal" superconformal W-algebras is described in detail, the determinant formula is obtained. Extensive list of examples includes all the simple Lie superalgebras of rank up to 2. The paper generalizes the results of Kac and Wakimoto (math-ph/0304011) to the twisted case.Comment: 50 pages, 8 figures; v2: examples added, determinant formula derivation modified, section order change

The geometrical form for the string space-time action

In the present article, we derive the space-time action of the bosonic string in terms of geometrical quantities. First, we study the space-time geometry felt by probe bosonic string moving in antisymmetric and dilaton background fields. We show that the presence of the antisymmetric field leads to the space-time torsion, and the presence of the dilaton field leads to the space-time nonmetricity. Using these results we obtain the integration measure for space-time with stringy nonmetricity, requiring its preservation under parallel transport. We derive the Lagrangian depending on stringy curvature, torsion and nonmetricity.Comment: 13 page