Ward Identity for Membranes

Ward identities in the case of scattering of antisymmetric three form RR gauge fields off a D2-brane target has been studied in type-IIA theory.Comment: 10 pages, Revtex, Version to appear in Phys.Lett.

The Worldsheet Perspective of T-duality Symmetry in String Theory

The purpose of this article is to present a pedagogical review of T-dualityin in string theory. The evolution of the closed string is envisaged on the worldsheet in the presence of its massless excitations. The duality symmetry is studied when some of the spacial coordinates are compactified on d-dimensional torus, $T^d$. The known results are reviewed to elucidate that equations of motion for the compact coordinates are $O(d,d)$ covariant, $d$ being the number of compact directions. Next, the vertex operators of excited massive levels are considered in a simple compactification scheme. It is shown that the vertex operators for each massive level can be cast in a T-duality invariant form in such a case. Subsequently, the duality properties of superstring is investigated in the NSR formulation for the massless backgrounds such as graviton and antisymmetric tensor. The worldsheet superfield formulation is found to be very suitable for our purpose. The Hassan-Sen compactification is adopted and it is shown that the worldsheet equations of motion for compact superfields to be very suitable for our purpose. The Hassan-Sen compactification is adopted and it is shown that the worldsheet equations of motion for compact superfields are $O(d,d)$ covariant when the backgrounds are independent of superfields along compact directions. The vertex operators for excited levels are presented in the NS-NS sector and it is shown that they can be cast in T-duality invariant form for the case of Hassan-Sen compactification scheme. An illustrative example is presented to realize our proposal.Comment: review, 53 page

Analyticity Property of Scattering Amplitude in Theories with Compactified Space Dimensions

We consider a massive, neutral, scalar field theory of mass $m_0$ in a five dimensional flat spacetime. Subsequently, one spatial dimension is compactified on a circle, $S^1$, ofradius $R$. The resulting theory is defined in the manifold, $R^{3,1}\otimes S^1$. The mass spectrum is a state of lowest mass, $m_0$, and a tower of massive Kaluza-Klein states. The analyticity property of the elastic scattering amplitude is investigated in the Lehmann-Symanzik-Zimmermann (LSZ) formulation of this theory. In the context of nonrelativistic potential scattering, for the $R^3\otimes S^1$ spatial geometry, it was shown that the forward scattering amplitude does not satisfy analyticity properties in some cases for a class of potentials. If the same result is valid in relativistic quantum field theory then the consequences will be far reaching. We show that the forward elastic scattering amplitude of the theory, in the LSZ axiomatic approach, satisfies forward dispersion relations. The importance of the unitarity constraint on the S-matrix, is exhibited in displaying the properties of the absorptive part of the amplitude.Comment: 36 pages; no figure

M Theory and P-Branes

Ten dimensional type IIA and IIB theories with p-branes are compactified to 8-dimensions. It is shown that resulting branes can be classified according to the representations of $\bf {SL(3,Z) \times SL(2,Z)}$. These p-branes can also be obtained by compactification of M theory on three torus and various wrappings of membrane and five brane of the eleven dimensional theory. It is argued that there is evidence for bound states of the branes in eight dimensions as is the case in the interpretation of $\bf {SL(2,Z)}$ family of string solutions obtained by Schwarz.Comment: 12 pages, no figures, revte